%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW478+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:01:46 AM UTC 2026
% Result : Theorem 80.52s 13.63s
% Output : CNFRefutation 80.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 73
% Syntax : Number of formulae : 875 ( 614 unt; 0 typ; 0 def)
% Number of atoms : 4150 (2238 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 128381 (1643 ~; 986 |; 18 &;125623 @)
% ( 36 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 106 usr; 29 con; 0-8 aty)
% Number of variables : 5000 ( 0 ^;4991 !; 9 ?;5000 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_assigned,type,
assigned: $i ).
thf(tp_block,type,
block: $i > $i ).
thf(tp_bool,type,
bool: $i ).
thf(tp_char,type,
char: $i ).
thf(tp_combb,type,
combb: $i > $i > $i > $i ).
thf(tp_combc,type,
combc: $i > $i > $i > $i ).
thf(tp_combk,type,
combk: $i > $i > $i ).
thf(tp_combs,type,
combs: $i > $i > $i > $i ).
thf(tp_e,type,
e: $i ).
thf(tp_e_a,type,
e_a: $i ).
thf(tp_ea,type,
ea: $i ).
thf(tp_exp,type,
exp: $i > $i ).
thf(tp_fconj,type,
fconj: $i ).
thf(tp_fun,type,
fun: $i > $i > $i ).
thf(tp_fun_upd,type,
fun_upd: $i > $i > $i ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_h_a,type,
h_a: $i ).
thf(tp_ha,type,
ha: $i ).
thf(tp_hconf,type,
hconf: $i > $i ).
thf(tp_hp,type,
hp: $i ).
thf(tp_lAss,type,
lAss: $i > $i ).
thf(tp_l_a,type,
l_a: $i ).
thf(tp_la,type,
la: $i ).
thf(tp_lconf,type,
lconf: $i > $i ).
thf(tp_list,type,
list: $i > $i ).
thf(tp_member,type,
member: $i > $i ).
thf(tp_nat,type,
nat: $i ).
thf(tp_none,type,
none: $i > $i ).
thf(tp_option,type,
option: $i > $i ).
thf(tp_p,type,
p: $i ).
thf(tp_produc1605651328_split,type,
produc1605651328_split: $i > $i > $i > $i ).
thf(tp_product_Pair,type,
product_Pair: $i > $i > $i ).
thf(tp_product_prod,type,
product_prod: $i > $i > $i ).
thf(tp_product_prod_case,type,
product_prod_case: $i > $i > $i > $i ).
thf(tp_product_prod_rec,type,
product_prod_rec: $i > $i > $i > $i ).
thf(tp_red,type,
red: $i ).
thf(tp_redp,type,
redp: $i ).
thf(tp_sK10_SY1243,type,
sK10_SY1243: $i > $i > $i > $i > $i > $i ).
thf(tp_sK11_SY1246,type,
sK11_SY1246: $i > $i > $i > $i > $i ).
thf(tp_sK12_SY1215,type,
sK12_SY1215: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK13_SY1173,type,
sK13_SY1173: $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_SY1206,type,
sK14_SY1206: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK15_SY1265,type,
sK15_SY1265: $i > $i > $i > $i > $i > $i ).
thf(tp_sK16_SY1267,type,
sK16_SY1267: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK17_SY1271,type,
sK17_SY1271: $i > $i > $i > $i > $i > $i ).
thf(tp_sK18_SY1259,type,
sK18_SY1259: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_SY1010,type,
sK19_SY1010: $i > $i > $i > $i ).
thf(tp_sK1_SY903,type,
sK1_SY903: $i > $i > $i > $i ).
thf(tp_sK20_SY1013,type,
sK20_SY1013: $i > $i > $i > $i ).
thf(tp_sK21_SY1279,type,
sK21_SY1279: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK22_SY1282,type,
sK22_SY1282: $i > $i > $i > $i > $i > $i ).
thf(tp_sK23_SY1283,type,
sK23_SY1283: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK24_SY1286,type,
sK24_SY1286: $i > $i > $i > $i > $i > $i ).
thf(tp_sK25_SY1247,type,
sK25_SY1247: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK26_SY1287,type,
sK26_SY1287: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK27_SY1123,type,
sK27_SY1123: $i > $i > $i > $i > $i ).
thf(tp_sK28_SY1292,type,
sK28_SY1292: $i > $i > $i > $i ).
thf(tp_sK29_SY1293,type,
sK29_SY1293: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK2_SY925,type,
sK2_SY925: $i > $i > $i > $i ).
thf(tp_sK30_SY1295,type,
sK30_SY1295: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK31_SY1297,type,
sK31_SY1297: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK32_SY1273,type,
sK32_SY1273: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK33_SY1301,type,
sK33_SY1301: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK34_SY1305,type,
sK34_SY1305: $i > $i > $i > $i > $i ).
thf(tp_sK35_SY1309,type,
sK35_SY1309: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK36_SY1310,type,
sK36_SY1310: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK37_SY1311,type,
sK37_SY1311: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK38_SY1314,type,
sK38_SY1314: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK39_SY1319,type,
sK39_SY1319: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK3_SY1156,type,
sK3_SY1156: $i > $i > $i > $i ).
thf(tp_sK40_SY1322,type,
sK40_SY1322: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK41_SY1324,type,
sK41_SY1324: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK42_SY1328,type,
sK42_SY1328: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK43_SY998,type,
sK43_SY998: $i > $i > $i > $i > $i ).
thf(tp_sK44_SY1330,type,
sK44_SY1330: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK45_SY1331,type,
sK45_SY1331: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK46_SY1334,type,
sK46_SY1334: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK47_SY1336,type,
sK47_SY1336: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK48_SY1338,type,
sK48_SY1338: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK49_SY1335,type,
sK49_SY1335: $i > $i > $i > $i > $i ).
thf(tp_sK4_SY1165,type,
sK4_SY1165: $i > $i > $i > $i ).
thf(tp_sK50_SY1002,type,
sK50_SY1002: $i > $i > $i > $i > $i > $i ).
thf(tp_sK5_SY1072,type,
sK5_SY1072: $i > $i > $i > $i > $i ).
thf(tp_sK6_SY1141,type,
sK6_SY1141: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_SY1161,type,
sK7_SY1161: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_SY1213,type,
sK8_SY1213: $i > $i > $i > $i > $i ).
thf(tp_sK9_SY1127,type,
sK9_SY1127: $i > $i > $i > $i > $i ).
thf(tp_seq,type,
seq: $i > $i ).
thf(tp_some,type,
some: $i > $i ).
thf(tp_t,type,
t: $i ).
thf(tp_t_1,type,
t_1: $i ).
thf(tp_ti,type,
ti: $i > $i > $i ).
thf(tp_ty,type,
ty: $i ).
thf(tp_typeSa885026672_sconf,type,
typeSa885026672_sconf: $i ).
thf(tp_undefined,type,
undefined: $i > $i ).
thf(tp_unit,type,
unit: $i ).
thf(tp_v,type,
v: $i ).
thf(tp_v_1,type,
v_1: $i ).
thf(tp_v_2,type,
v_2: $i ).
thf(tp_val,type,
val: $i ).
thf(tp_val_1,type,
val_1: $i > $i ).
thf(tp_wTrt,type,
wTrt: $i ).
thf(tp_wf_J_mdecl,type,
wf_J_mdecl: $i ).
thf(tp_wf_prog,type,
wf_prog: $i > $i ).
thf(tp_widen,type,
widen: $i > $i ).
thf(1,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(2,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(3,axiom,
! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(4,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_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(7,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,
! [Pa: $i,X: $i,Xa: $i,Xb: $i,Xc: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ Pa ) @ X ) @ Xa ) @ Xb ) @ Xc ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ X ) @ Xa ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Xb ) @ Xc ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_redp__red__eq) ).
thf(14,axiom,
! [X_a: $i,X_b: $i,T_1: $i,K: $i,X_1: $i] :
~ ! [X: $i] :
( ( hAPP @ X_a @ ( option @ X_b ) @ ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ T_1 ) @ K ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ X_1 ) ) @ X )
= ( none @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_map__upd__nonempty) ).
thf(32,axiom,
! [X_a: $i,X_1: $i,A_5: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_5 ) )
<=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_5 @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(33,axiom,
! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ! [X: $i] :
( ( hAPP @ X_a @ X_b @ F @ X )
= ( hAPP @ X_a @ X_b @ G @ X ) )
=> ( ( 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(35,axiom,
! [X_a: $i,Exp1_2: $i,Exp2_2: $i,Exp1_1: $i,Exp2_1: $i] :
( ( ( hAPP @ ( exp @ X_a ) @ ( exp @ X_a ) @ ( hAPP @ ( exp @ X_a ) @ ( fun @ ( exp @ X_a ) @ ( exp @ X_a ) ) @ ( seq @ X_a ) @ Exp1_2 ) @ Exp2_2 )
= ( hAPP @ ( exp @ X_a ) @ ( exp @ X_a ) @ ( hAPP @ ( exp @ X_a ) @ ( fun @ ( exp @ X_a ) @ ( exp @ X_a ) ) @ ( seq @ X_a ) @ Exp1_1 ) @ Exp2_1 ) )
<=> ( ( Exp1_2 = Exp1_1 )
& ( Exp2_2 = Exp2_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_exp_Osimps_I11_J) ).
thf(36,axiom,
! [X_a: $i,Val_2: $i,Val_1: $i] :
( ( ( hAPP @ val @ ( exp @ X_a ) @ ( val_1 @ X_a ) @ Val_2 )
= ( hAPP @ val @ ( exp @ X_a ) @ ( val_1 @ X_a ) @ Val_1 ) )
<=> ( Val_2 = Val_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_exp_Osimps_I3_J) ).
thf(48,axiom,
! [Va_1: $i,Eb: $i,S: $i,E_b: $i,S_1: $i,Pa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Eb ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ E_b ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ Va_1 ) @ Eb ) ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ Va_1 ) @ E_b ) ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_red__reds_OLAssRed) ).
thf(49,axiom,
! [E_2: $i,Eb: $i,S: $i,E_b: $i,S_1: $i,Pa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Eb ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ E_b ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ Eb ) @ E_2 ) ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ E_b ) @ E_2 ) ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_red__reds_OSeqRed) ).
thf(50,axiom,
! [X_c: $i,X_a: $i,X_b: $i,R_1: $i,A_4: $i,B_1: $i,C: $i] :
( ( hBOOL @ ( hAPP @ X_c @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ X_c @ bool ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_c @ bool ) ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ ( fun @ X_c @ bool ) ) @ ( product_prod_case @ X_a @ X_b @ ( fun @ X_c @ bool ) ) @ R_1 ) @ ( 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_1 ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ X_c @ bool @ ( hAPP @ X_b @ ( fun @ X_c @ bool ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_c @ bool ) ) @ R_1 @ A_4 ) @ B_1 ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_splitD_H) ).
thf(52,axiom,
! [X_a: $i,X_c: $i,X_b: $i,Z: $i,C: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Z ) @ ( hAPP @ X_c @ ( fun @ X_a @ bool ) @ ( hAPP @ X_b @ ( fun @ X_c @ ( fun @ X_a @ bool ) ) @ C @ A_4 ) @ B_1 ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Z ) @ ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( fun @ X_a @ bool ) @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ ( fun @ X_a @ bool ) ) ) @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( fun @ X_a @ bool ) ) @ ( product_prod_case @ X_b @ X_c @ ( fun @ X_a @ bool ) ) @ C ) @ ( 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 ) @ A_4 ) @ B_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_mem__splitI) ).
thf(59,axiom,
! [X_b: $i,X_c: $i,X_a: $i,F: $i,A_4: $i,B_1: $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_case @ X_b @ X_c @ X_a ) @ F ) @ ( 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F @ A_4 ) @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_split__conv) ).
thf(60,axiom,
! [X_b: $i,X_c: $i,X_a: $i,F1: $i,A_4: $i,B_1: $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_case @ 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ A_4 ) @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_prod_Osimps_I2_J) ).
thf(65,axiom,
! [X_a: $i,X_b: $i,F: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F ) @ ( 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_1 ) ) )
=> ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F @ A_4 ) @ B_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_splitD) ).
thf(66,axiom,
! [X_b: $i,X_a: $i,F: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F @ A_4 ) @ B_1 ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F ) @ ( 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_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_splitI) ).
thf(67,axiom,
! [X_b: $i,X_a: $i,F1: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F1 @ A_4 ) @ B_1 ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F1 ) @ ( 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_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_prod__caseI) ).
thf(69,axiom,
! [X_b: $i,X_c: $i,X_a: $i,C: $i,A_4: $i,B_1: $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 ) @ ( produc1605651328_split @ X_b @ X_c @ X_a ) @ C ) @ ( 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ C @ A_4 ) @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_internal__split__conv) ).
thf(70,axiom,
! [X_a: $i,X_b: $i,P_2: $i] :
~ ! [X: $i,Y: $i] :
( ( ti @ ( product_prod @ X_a @ X_b ) @ P_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 ) @ X ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_PairE) ).
thf(71,axiom,
! [X_a: $i,X_b: $i,Pa: $i] :
( ? [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) )
<=> ? [A_6: $i,B: $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_6 ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_split__paired__Ex) ).
thf(73,axiom,
! [X_a: $i,T_3: $i,P: $i,S_2: $i,U_1: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ S_2 ) @ U_1 ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ U_1 ) @ T_3 ) )
=> ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ S_2 ) @ T_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_widen__trans) ).
thf(74,axiom,
! [X_a: $i,X_b: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i] :
( ( ti @ ( product_prod @ X_a @ X_b ) @ Y_1 )
!= ( 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_6 ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_prod_Oexhaust) ).
thf(75,axiom,
! [X_a: $i,X_b: $i,S_3: $i,R_1: $i] :
( ! [X: $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 ) @ 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 ) @ Xa ) ) @ S_3 ) ) )
<=> ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_pred__equals__eq2) ).
thf(76,axiom,
! [X_b: $i,X_c: $i,X_a: $i,F1: $i,A_4: $i,B_1: $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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ A_4 ) @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_prod_Orecs) ).
thf(78,axiom,
! [X_a: $i,X_b: $i,X_c: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ X_c ) ) @ A_6 ) @ ( 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 ) @ B ) @ C_1 ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ bool @ Pa @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_prod__induct3) ).
thf(79,axiom,
! [X_a: $i,X_b: $i,X_c: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ X_c ) ) @ A_6 ) @ ( 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 ) @ B ) @ C_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_prod__cases3) ).
thf(82,axiom,
! [X_m: $i,P: $i,T_3: $i] : ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_m ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_m ) @ P ) @ T_3 ) @ T_3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_widen__refl) ).
thf(83,axiom,
! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 )
= ( ti @ ( fun @ X_a @ X_b ) @ F ) )
<=> ( ( hAPP @ X_a @ X_b @ F @ X_1 )
= ( ti @ X_b @ Y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_fun__upd__idem__iff) ).
thf(84,axiom,
! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i,Z: $i] :
( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) ) @ X_1 ) @ Z )
= ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_fun__upd__upd) ).
thf(85,axiom,
! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( hAPP @ X_b @ X_a @ ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( hAPP @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) ) @ ( fun_upd @ X_b @ X_a ) @ F ) @ X_1 ) @ Y_2 ) @ X_1 )
= ( ti @ X_a @ Y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_fun__upd__same) ).
thf(86,axiom,
! [X_b: $i,X_a: $i,F: $i,Y_2: $i,Z: $i,X_1: $i] :
( ( ( ( ti @ X_a @ Z )
= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( ti @ X_b @ Y_2 ) ) )
& ( ( ( ti @ X_a @ Z )
!= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( hAPP @ X_a @ X_b @ F @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_fun__upd__apply) ).
thf(87,axiom,
! [X_b: $i,X_a: $i,M: $i,B_1: $i,D: $i,A_4: $i,C: $i] :
( ( ( ti @ X_a @ A_4 )
!= ( ti @ X_a @ C ) )
=> ( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ M ) @ A_4 ) @ B_1 ) ) @ C ) @ D )
= ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ M ) @ C ) @ D ) ) @ A_4 ) @ B_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_fun__upd__twist) ).
thf(88,axiom,
! [X_b: $i,X_a: $i,F: $i,Y_2: $i,Z: $i,X_1: $i] :
( ( ( ti @ X_a @ Z )
!= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( hAPP @ X_a @ X_b @ F @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_fun__upd__other) ).
thf(89,axiom,
! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ X_a @ F @ X_1 )
= ( ti @ X_a @ Y_2 ) )
=> ( ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( hAPP @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) ) @ ( fun_upd @ X_b @ X_a ) @ F ) @ X_1 ) @ Y_2 )
= ( ti @ ( fun @ X_b @ X_a ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_fun__upd__idem) ).
thf(90,axiom,
! [X_b: $i,X_a: $i,F: $i,B_1: $i,A_4: $i,X: $i] :
( ( ( ( ti @ X_a @ X )
= ( ti @ X_a @ A_4 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ A_4 ) @ B_1 ) @ X )
= ( ti @ X_b @ B_1 ) ) )
& ( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ A_4 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ A_4 ) @ B_1 ) @ X )
= ( hAPP @ X_a @ X_b @ F @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_fun__upd__def) ).
thf(91,axiom,
! [X_a: $i,X_b: $i,Pa: $i] :
( ! [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) )
<=> ! [A_6: $i,B: $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_6 ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_split__paired__All) ).
thf(92,axiom,
! [X_b: $i,X_a: $i,A_4: $i,B_1: $i,A_3: $i,B_2: $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_4 ) @ B_1 )
= ( 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 ) )
<=> ( ( ( ti @ X_a @ A_4 )
= ( ti @ X_a @ A_3 ) )
& ( ( ti @ X_b @ B_1 )
= ( ti @ X_b @ B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Pair__eq) ).
thf(93,axiom,
! [X_b: $i,X_a: $i,A_2: $i,B_4: $i,A_1: $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 ) @ A_2 ) @ B_4 )
= ( 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_1 ) @ B_3 ) )
=> ~ ( ( ( ti @ X_a @ A_2 )
= ( ti @ X_a @ A_1 ) )
=> ( ( ti @ X_b @ B_4 )
!= ( ti @ X_b @ B_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Pair__inject) ).
thf(95,axiom,
! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ X_d ) ) @ B ) @ ( hAPP @ X_d @ ( product_prod @ X_c @ X_d ) @ ( hAPP @ X_c @ ( fun @ X_d @ ( product_prod @ X_c @ X_d ) ) @ ( product_Pair @ X_c @ X_d ) @ C_1 ) @ D_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_prod__cases4) ).
thf(96,axiom,
! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ X_d ) ) @ B ) @ ( hAPP @ X_d @ ( product_prod @ X_c @ X_d ) @ ( hAPP @ X_c @ ( fun @ X_d @ ( product_prod @ X_c @ X_d ) ) @ ( product_Pair @ X_c @ X_d ) @ C_1 ) @ D_1 ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ bool @ Pa @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_prod__induct4) ).
thf(97,axiom,
! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ X_e ) ) @ C_1 ) @ ( hAPP @ X_e @ ( product_prod @ X_d @ X_e ) @ ( hAPP @ X_d @ ( fun @ X_e @ ( product_prod @ X_d @ X_e ) ) @ ( product_Pair @ X_d @ X_e ) @ D_1 ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_prod__cases5) ).
thf(98,axiom,
! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ X_e ) ) @ C_1 ) @ ( hAPP @ X_e @ ( product_prod @ X_d @ X_e ) @ ( hAPP @ X_d @ ( fun @ X_e @ ( product_prod @ X_d @ X_e ) ) @ ( product_Pair @ X_d @ X_e ) @ D_1 ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ bool @ Pa @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_prod__induct5) ).
thf(99,axiom,
! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_f: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i,F_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ C_1 ) @ ( hAPP @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( hAPP @ X_d @ ( fun @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_d @ ( product_prod @ X_e @ X_f ) ) @ D_1 ) @ ( hAPP @ X_f @ ( product_prod @ X_e @ X_f ) @ ( hAPP @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) @ ( product_Pair @ X_e @ X_f ) @ E ) @ F_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_prod__cases6) ).
thf(100,axiom,
! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_f: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i,F_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ C_1 ) @ ( hAPP @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( hAPP @ X_d @ ( fun @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_d @ ( product_prod @ X_e @ X_f ) ) @ D_1 ) @ ( hAPP @ X_f @ ( product_prod @ X_e @ X_f ) @ ( hAPP @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) @ ( product_Pair @ X_e @ X_f ) @ E ) @ F_1 ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ bool @ Pa @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_prod__induct6) ).
thf(102,axiom,
! [X_b: $i,X_a: $i,M: $i,A_4: $i,X_1: $i,N: $i,Y_2: $i] :
( ( ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ M ) @ A_4 ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ X_1 ) )
= ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ N ) @ A_4 ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ Y_2 ) ) )
=> ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ Y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_map__upd__eqD1) ).
thf(103,axiom,
! [X_b: $i,X_a: $i,T_1: $i,K: $i,X_1: $i] :
( ( ( hAPP @ X_b @ ( option @ X_a ) @ T_1 @ K )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ X_1 ) )
=> ( ( hAPP @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) @ ( hAPP @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) @ ( hAPP @ ( fun @ X_b @ ( option @ X_a ) ) @ ( fun @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) ) @ ( fun_upd @ X_b @ ( option @ X_a ) ) @ T_1 ) @ K ) @ ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ X_1 ) )
= ( ti @ ( fun @ X_b @ ( option @ X_a ) ) @ T_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_map__upd__triv) ).
thf(104,axiom,
! [X_b: $i,X_a: $i,M: $i,A_4: $i,B_1: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ ( option @ X_a ) @ ( hAPP @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) @ ( hAPP @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) @ ( hAPP @ ( fun @ X_b @ ( option @ X_a ) ) @ ( fun @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) ) @ ( fun_upd @ X_b @ ( option @ X_a ) ) @ M ) @ A_4 ) @ ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ B_1 ) ) @ X_1 )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ Y_2 ) )
<=> ( ( ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ A_4 ) )
& ( ( ti @ X_a @ B_1 )
= ( ti @ X_a @ Y_2 ) ) )
| ( ( ( ti @ X_b @ X_1 )
!= ( ti @ X_b @ A_4 ) )
& ( ( hAPP @ X_b @ ( option @ X_a ) @ M @ X_1 )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ Y_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_map__upd__Some__unfold) ).
thf(106,axiom,
! [X_b: $i,X_a: $i,F: $i,X_1: $i] :
( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ ( hAPP @ X_a @ X_b @ F @ X_1 ) )
= ( ti @ ( fun @ X_a @ X_b ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).
thf(107,axiom,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).
thf(108,axiom,
( ( hAPP @ ( list @ char ) @ ( option @ val ) @ l_a @ v_1 )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).
thf(113,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(114,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(115,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(116,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(129,axiom,
! [X_e: $i,X_f: $i] :
( ( ti @ ( fun @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_e @ X_f ) )
= ( product_Pair @ X_e @ X_f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_res) ).
thf(130,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( option @ X_a ) ) @ ( some @ X_a ) )
= ( some @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Option_Ooption_OSome_res) ).
thf(134,axiom,
! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) ) @ ( fun_upd @ X_a @ X_b ) )
= ( fun_upd @ X_a @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Fun_Ofun__upd_res) ).
thf(145,axiom,
( ( ti @ val @ v )
= v ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_v_____res) ).
thf(146,axiom,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ la )
= la ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_la_____res) ).
thf(147,axiom,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ l_a )
= l_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_l_Ha_____res) ).
thf(148,axiom,
( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ha )
= ha ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_ha_____res) ).
thf(149,axiom,
( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ h_a )
= h_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_h_Ha_____res) ).
thf(150,axiom,
( ( ti @ ( exp @ ( list @ char ) ) @ ea )
= ea ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_ea_____res) ).
thf(151,axiom,
( ( ti @ ( exp @ ( list @ char ) ) @ e_a )
= e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_e_Ha_____res) ).
thf(152,axiom,
( ( ti @ ( list @ char ) @ v_1 )
= v_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_V_____res) ).
thf(153,axiom,
( ( ti @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ p )
= p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_P_res) ).
thf(154,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(155,axiom,
( ( ti @ ( fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) ) @ red )
= red ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_SmallStep_Ored_res) ).
thf(156,conjecture,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(157,negated_conjecture,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[156]) ).
thf(158,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ) )
= $false ),
inference(unfold_def,[status(thm)],[157]) ).
thf(159,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(160,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(161,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(162,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(unfold_def,[status(thm)],[4]) ).
thf(163,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(unfold_def,[status(thm)],[6]) ).
thf(164,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(unfold_def,[status(thm)],[7]) ).
thf(165,plain,
( ( ! [Pa: $i,X: $i,Xa: $i,Xb: $i,Xc: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ Pa ) @ X ) @ Xa ) @ Xb ) @ Xc ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ X ) @ Xa ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Xb ) @ Xc ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(166,plain,
( ( ! [X_a: $i,X_b: $i,T_1: $i,K: $i,X_1: $i] :
~ ! [X: $i] :
( ( hAPP @ X_a @ ( option @ X_b ) @ ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ T_1 ) @ K ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ X_1 ) ) @ X )
= ( none @ X_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(167,plain,
( ( ! [X_a: $i,X_1: $i,A_5: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_5 ) )
<=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_5 @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(168,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ! [X: $i] :
( ( hAPP @ X_a @ X_b @ F @ X )
= ( hAPP @ X_a @ X_b @ G @ X ) )
=> ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(169,plain,
( ( ! [X_a: $i,Exp1_2: $i,Exp2_2: $i,Exp1_1: $i,Exp2_1: $i] :
( ( ( hAPP @ ( exp @ X_a ) @ ( exp @ X_a ) @ ( hAPP @ ( exp @ X_a ) @ ( fun @ ( exp @ X_a ) @ ( exp @ X_a ) ) @ ( seq @ X_a ) @ Exp1_2 ) @ Exp2_2 )
= ( hAPP @ ( exp @ X_a ) @ ( exp @ X_a ) @ ( hAPP @ ( exp @ X_a ) @ ( fun @ ( exp @ X_a ) @ ( exp @ X_a ) ) @ ( seq @ X_a ) @ Exp1_1 ) @ Exp2_1 ) )
<=> ( ( Exp1_2 = Exp1_1 )
& ( Exp2_2 = Exp2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(170,plain,
( ( ! [X_a: $i,Val_2: $i,Val_1: $i] :
( ( ( hAPP @ val @ ( exp @ X_a ) @ ( val_1 @ X_a ) @ Val_2 )
= ( hAPP @ val @ ( exp @ X_a ) @ ( val_1 @ X_a ) @ Val_1 ) )
<=> ( Val_2 = Val_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(171,plain,
( ( ! [Va_1: $i,Eb: $i,S: $i,E_b: $i,S_1: $i,Pa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Eb ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ E_b ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ Va_1 ) @ Eb ) ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ Va_1 ) @ E_b ) ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(172,plain,
( ( ! [E_2: $i,Eb: $i,S: $i,E_b: $i,S_1: $i,Pa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Eb ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ E_b ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ Eb ) @ E_2 ) ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ E_b ) @ E_2 ) ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(173,plain,
( ( ! [X_c: $i,X_a: $i,X_b: $i,R_1: $i,A_4: $i,B_1: $i,C: $i] :
( ( hBOOL @ ( hAPP @ X_c @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ X_c @ bool ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_c @ bool ) ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ ( fun @ X_c @ bool ) ) @ ( product_prod_case @ X_a @ X_b @ ( fun @ X_c @ bool ) ) @ R_1 ) @ ( 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_1 ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ X_c @ bool @ ( hAPP @ X_b @ ( fun @ X_c @ bool ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_c @ bool ) ) @ R_1 @ A_4 ) @ B_1 ) @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(174,plain,
( ( ! [X_a: $i,X_c: $i,X_b: $i,Z: $i,C: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Z ) @ ( hAPP @ X_c @ ( fun @ X_a @ bool ) @ ( hAPP @ X_b @ ( fun @ X_c @ ( fun @ X_a @ bool ) ) @ C @ A_4 ) @ B_1 ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Z ) @ ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( fun @ X_a @ bool ) @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ ( fun @ X_a @ bool ) ) ) @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( fun @ X_a @ bool ) ) @ ( product_prod_case @ X_b @ X_c @ ( fun @ X_a @ bool ) ) @ C ) @ ( 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 ) @ A_4 ) @ B_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(175,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,F: $i,A_4: $i,B_1: $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_case @ X_b @ X_c @ X_a ) @ F ) @ ( 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F @ A_4 ) @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(176,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,F1: $i,A_4: $i,B_1: $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_case @ 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ A_4 ) @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(177,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F ) @ ( 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_1 ) ) )
=> ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F @ A_4 ) @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(178,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F @ A_4 ) @ B_1 ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F ) @ ( 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_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(179,plain,
( ( ! [X_b: $i,X_a: $i,F1: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F1 @ A_4 ) @ B_1 ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F1 ) @ ( 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_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(180,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,C: $i,A_4: $i,B_1: $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 ) @ ( produc1605651328_split @ X_b @ X_c @ X_a ) @ C ) @ ( 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ C @ A_4 ) @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(181,plain,
( ( ! [X_a: $i,X_b: $i,P_2: $i] :
~ ! [X: $i,Y: $i] :
( ( ti @ ( product_prod @ X_a @ X_b ) @ P_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 ) @ X ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(182,plain,
( ( ! [X_a: $i,X_b: $i,Pa: $i] :
( ? [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) )
<=> ? [A_6: $i,B: $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_6 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(183,plain,
( ( ! [X_a: $i,T_3: $i,P: $i,S_2: $i,U_1: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ S_2 ) @ U_1 ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ U_1 ) @ T_3 ) )
=> ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ S_2 ) @ T_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(184,plain,
( ( ! [X_a: $i,X_b: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i] :
( ( ti @ ( product_prod @ X_a @ X_b ) @ Y_1 )
!= ( 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_6 ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(185,plain,
( ( ! [X_a: $i,X_b: $i,S_3: $i,R_1: $i] :
( ! [X: $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 ) @ 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 ) @ Xa ) ) @ S_3 ) ) )
<=> ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(186,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,F1: $i,A_4: $i,B_1: $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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ A_4 ) @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(187,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ X_c ) ) @ A_6 ) @ ( 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 ) @ B ) @ C_1 ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(188,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ X_c ) ) @ A_6 ) @ ( 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 ) @ B ) @ C_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(189,plain,
( ( ! [X_m: $i,P: $i,T_3: $i] : ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_m ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_m ) @ P ) @ T_3 ) @ T_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(190,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 )
= ( ti @ ( fun @ X_a @ X_b ) @ F ) )
<=> ( ( hAPP @ X_a @ X_b @ F @ X_1 )
= ( ti @ X_b @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(191,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i,Z: $i] :
( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) ) @ X_1 ) @ Z )
= ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(192,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( hAPP @ X_b @ X_a @ ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( hAPP @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) ) @ ( fun_upd @ X_b @ X_a ) @ F ) @ X_1 ) @ Y_2 ) @ X_1 )
= ( ti @ X_a @ Y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(193,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,Y_2: $i,Z: $i,X_1: $i] :
( ( ( ( ti @ X_a @ Z )
= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( ti @ X_b @ Y_2 ) ) )
& ( ( ( ti @ X_a @ Z )
!= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( hAPP @ X_a @ X_b @ F @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(194,plain,
( ( ! [X_b: $i,X_a: $i,M: $i,B_1: $i,D: $i,A_4: $i,C: $i] :
( ( ( ti @ X_a @ A_4 )
!= ( ti @ X_a @ C ) )
=> ( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ M ) @ A_4 ) @ B_1 ) ) @ C ) @ D )
= ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ M ) @ C ) @ D ) ) @ A_4 ) @ B_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(195,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,Y_2: $i,Z: $i,X_1: $i] :
( ( ( ti @ X_a @ Z )
!= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( hAPP @ X_a @ X_b @ F @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(196,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ X_a @ F @ X_1 )
= ( ti @ X_a @ Y_2 ) )
=> ( ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( hAPP @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) ) @ ( fun_upd @ X_b @ X_a ) @ F ) @ X_1 ) @ Y_2 )
= ( ti @ ( fun @ X_b @ X_a ) @ F ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(197,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,B_1: $i,A_4: $i,X: $i] :
( ( ( ( ti @ X_a @ X )
= ( ti @ X_a @ A_4 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ A_4 ) @ B_1 ) @ X )
= ( ti @ X_b @ B_1 ) ) )
& ( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ A_4 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ A_4 ) @ B_1 ) @ X )
= ( hAPP @ X_a @ X_b @ F @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(198,plain,
( ( ! [X_a: $i,X_b: $i,Pa: $i] :
( ! [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) )
<=> ! [A_6: $i,B: $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_6 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(199,plain,
( ( ! [X_b: $i,X_a: $i,A_4: $i,B_1: $i,A_3: $i,B_2: $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_4 ) @ B_1 )
= ( 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 ) )
<=> ( ( ( ti @ X_a @ A_4 )
= ( ti @ X_a @ A_3 ) )
& ( ( ti @ X_b @ B_1 )
= ( ti @ X_b @ B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(200,plain,
( ( ! [X_b: $i,X_a: $i,A_2: $i,B_4: $i,A_1: $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 ) @ A_2 ) @ B_4 )
= ( 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_1 ) @ B_3 ) )
=> ~ ( ( ( ti @ X_a @ A_2 )
= ( ti @ X_a @ A_1 ) )
=> ( ( ti @ X_b @ B_4 )
!= ( ti @ X_b @ B_3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(201,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ X_d ) ) @ B ) @ ( hAPP @ X_d @ ( product_prod @ X_c @ X_d ) @ ( hAPP @ X_c @ ( fun @ X_d @ ( product_prod @ X_c @ X_d ) ) @ ( product_Pair @ X_c @ X_d ) @ C_1 ) @ D_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(202,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ X_d ) ) @ B ) @ ( hAPP @ X_d @ ( product_prod @ X_c @ X_d ) @ ( hAPP @ X_c @ ( fun @ X_d @ ( product_prod @ X_c @ X_d ) ) @ ( product_Pair @ X_c @ X_d ) @ C_1 ) @ D_1 ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(203,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ X_e ) ) @ C_1 ) @ ( hAPP @ X_e @ ( product_prod @ X_d @ X_e ) @ ( hAPP @ X_d @ ( fun @ X_e @ ( product_prod @ X_d @ X_e ) ) @ ( product_Pair @ X_d @ X_e ) @ D_1 ) @ E ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(204,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ X_e ) ) @ C_1 ) @ ( hAPP @ X_e @ ( product_prod @ X_d @ X_e ) @ ( hAPP @ X_d @ ( fun @ X_e @ ( product_prod @ X_d @ X_e ) ) @ ( product_Pair @ X_d @ X_e ) @ D_1 ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(205,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_f: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i,F_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ C_1 ) @ ( hAPP @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( hAPP @ X_d @ ( fun @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_d @ ( product_prod @ X_e @ X_f ) ) @ D_1 ) @ ( hAPP @ X_f @ ( product_prod @ X_e @ X_f ) @ ( hAPP @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) @ ( product_Pair @ X_e @ X_f ) @ E ) @ F_1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(206,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_f: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i,F_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ C_1 ) @ ( hAPP @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( hAPP @ X_d @ ( fun @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_d @ ( product_prod @ X_e @ X_f ) ) @ D_1 ) @ ( hAPP @ X_f @ ( product_prod @ X_e @ X_f ) @ ( hAPP @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) @ ( product_Pair @ X_e @ X_f ) @ E ) @ F_1 ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(207,plain,
( ( ! [X_b: $i,X_a: $i,M: $i,A_4: $i,X_1: $i,N: $i,Y_2: $i] :
( ( ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ M ) @ A_4 ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ X_1 ) )
= ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ N ) @ A_4 ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ Y_2 ) ) )
=> ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(208,plain,
( ( ! [X_b: $i,X_a: $i,T_1: $i,K: $i,X_1: $i] :
( ( ( hAPP @ X_b @ ( option @ X_a ) @ T_1 @ K )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ X_1 ) )
=> ( ( hAPP @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) @ ( hAPP @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) @ ( hAPP @ ( fun @ X_b @ ( option @ X_a ) ) @ ( fun @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) ) @ ( fun_upd @ X_b @ ( option @ X_a ) ) @ T_1 ) @ K ) @ ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ X_1 ) )
= ( ti @ ( fun @ X_b @ ( option @ X_a ) ) @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(209,plain,
( ( ! [X_b: $i,X_a: $i,M: $i,A_4: $i,B_1: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ ( option @ X_a ) @ ( hAPP @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) @ ( hAPP @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) @ ( hAPP @ ( fun @ X_b @ ( option @ X_a ) ) @ ( fun @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) ) @ ( fun_upd @ X_b @ ( option @ X_a ) ) @ M ) @ A_4 ) @ ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ B_1 ) ) @ X_1 )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ Y_2 ) )
<=> ( ( ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ A_4 ) )
& ( ( ti @ X_a @ B_1 )
= ( ti @ X_a @ Y_2 ) ) )
| ( ( ( ti @ X_b @ X_1 )
!= ( ti @ X_b @ A_4 ) )
& ( ( hAPP @ X_b @ ( option @ X_a ) @ M @ X_1 )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ Y_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(210,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i] :
( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ ( hAPP @ X_a @ X_b @ F @ X_1 ) )
= ( ti @ ( fun @ X_a @ X_b ) @ F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(211,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(212,plain,
( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ l_a @ v_1 )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(213,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) ) @ ( member @ X_a ) )
= ( member @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(214,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(unfold_def,[status(thm)],[114]) ).
thf(215,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(unfold_def,[status(thm)],[115]) ).
thf(216,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(unfold_def,[status(thm)],[116]) ).
thf(217,plain,
( ( ! [X_e: $i,X_f: $i] :
( ( ti @ ( fun @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_e @ X_f ) )
= ( product_Pair @ X_e @ X_f ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(218,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( option @ X_a ) ) @ ( some @ X_a ) )
= ( some @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(219,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) ) @ ( fun_upd @ X_a @ X_b ) )
= ( fun_upd @ X_a @ X_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(220,plain,
( ( ( ti @ val @ v )
= v )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(221,plain,
( ( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ la )
= la )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(222,plain,
( ( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ l_a )
= l_a )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(223,plain,
( ( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ha )
= ha )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(224,plain,
( ( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ h_a )
= h_a )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(225,plain,
( ( ( ti @ ( exp @ ( list @ char ) ) @ ea )
= ea )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(226,plain,
( ( ( ti @ ( exp @ ( list @ char ) ) @ e_a )
= e_a )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(227,plain,
( ( ( ti @ ( list @ char ) @ v_1 )
= v_1 )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(228,plain,
( ( ( ti @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ p )
= p )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(229,plain,
( ( ! [B_1_1: $i] :
( ( hBOOL @ ( ti @ bool @ B_1_1 ) )
<=> ( hBOOL @ B_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(230,plain,
( ( ( ti @ ( fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) ) @ red )
= red )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(231,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[158]) ).
thf(232,plain,
( ( ( ti @ ( fun @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) ) @ red )
= red )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(233,plain,
( ( ! [B_1_1: $i] :
( ( hBOOL @ ( ti @ bool @ B_1_1 ) )
<=> ( hBOOL @ B_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(234,plain,
( ( ( ti @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ p )
= p )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(235,plain,
( ( ( ti @ ( list @ char ) @ v_1 )
= v_1 )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(236,plain,
( ( ( ti @ ( exp @ ( list @ char ) ) @ e_a )
= e_a )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(237,plain,
( ( ( ti @ ( exp @ ( list @ char ) ) @ ea )
= ea )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(238,plain,
( ( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ h_a )
= h_a )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(239,plain,
( ( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ha )
= ha )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(240,plain,
( ( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ l_a )
= l_a )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(241,plain,
( ( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ la )
= la )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(242,plain,
( ( ( ti @ val @ v )
= v )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(243,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) ) @ ( fun_upd @ X_a @ X_b ) )
= ( fun_upd @ X_a @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(244,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( option @ X_a ) ) @ ( some @ X_a ) )
= ( some @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(245,plain,
( ( ! [X_e: $i,X_f: $i] :
( ( ti @ ( fun @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_e @ X_f ) )
= ( product_Pair @ X_e @ X_f ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(246,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)],[216]) ).
thf(247,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)],[215]) ).
thf(248,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)],[214]) ).
thf(249,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)],[213]) ).
thf(250,plain,
( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ l_a @ v_1 )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v_2 ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(251,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(252,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i] :
( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ ( hAPP @ X_a @ X_b @ F @ X_1 ) )
= ( ti @ ( fun @ X_a @ X_b ) @ F ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(253,plain,
( ( ! [X_b: $i,X_a: $i,M: $i,A_4: $i,B_1: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ ( option @ X_a ) @ ( hAPP @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) @ ( hAPP @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) @ ( hAPP @ ( fun @ X_b @ ( option @ X_a ) ) @ ( fun @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) ) @ ( fun_upd @ X_b @ ( option @ X_a ) ) @ M ) @ A_4 ) @ ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ B_1 ) ) @ X_1 )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ Y_2 ) )
<=> ( ( ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ A_4 ) )
& ( ( ti @ X_a @ B_1 )
= ( ti @ X_a @ Y_2 ) ) )
| ( ( ( ti @ X_b @ X_1 )
!= ( ti @ X_b @ A_4 ) )
& ( ( hAPP @ X_b @ ( option @ X_a ) @ M @ X_1 )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ Y_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(254,plain,
( ( ! [X_b: $i,X_a: $i,T_1: $i,K: $i,X_1: $i] :
( ( ( hAPP @ X_b @ ( option @ X_a ) @ T_1 @ K )
= ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ X_1 ) )
=> ( ( hAPP @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) @ ( hAPP @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) @ ( hAPP @ ( fun @ X_b @ ( option @ X_a ) ) @ ( fun @ X_b @ ( fun @ ( option @ X_a ) @ ( fun @ X_b @ ( option @ X_a ) ) ) ) @ ( fun_upd @ X_b @ ( option @ X_a ) ) @ T_1 ) @ K ) @ ( hAPP @ X_a @ ( option @ X_a ) @ ( some @ X_a ) @ X_1 ) )
= ( ti @ ( fun @ X_b @ ( option @ X_a ) ) @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(255,plain,
( ( ! [X_b: $i,X_a: $i,M: $i,A_4: $i,X_1: $i,N: $i,Y_2: $i] :
( ( ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ M ) @ A_4 ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ X_1 ) )
= ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ N ) @ A_4 ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ Y_2 ) ) )
=> ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(256,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_f: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i,F_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ C_1 ) @ ( hAPP @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( hAPP @ X_d @ ( fun @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_d @ ( product_prod @ X_e @ X_f ) ) @ D_1 ) @ ( hAPP @ X_f @ ( product_prod @ X_e @ X_f ) @ ( hAPP @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) @ ( product_Pair @ X_e @ X_f ) @ E ) @ F_1 ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(257,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_f: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i,F_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ C_1 ) @ ( hAPP @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) @ ( hAPP @ X_d @ ( fun @ ( product_prod @ X_e @ X_f ) @ ( product_prod @ X_d @ ( product_prod @ X_e @ X_f ) ) ) @ ( product_Pair @ X_d @ ( product_prod @ X_e @ X_f ) ) @ D_1 ) @ ( hAPP @ X_f @ ( product_prod @ X_e @ X_f ) @ ( hAPP @ X_e @ ( fun @ X_f @ ( product_prod @ X_e @ X_f ) ) @ ( product_Pair @ X_e @ X_f ) @ E ) @ F_1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(258,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ X_e ) ) @ C_1 ) @ ( hAPP @ X_e @ ( product_prod @ X_d @ X_e ) @ ( hAPP @ X_d @ ( fun @ X_e @ ( product_prod @ X_d @ X_e ) ) @ ( product_Pair @ X_d @ X_e ) @ D_1 ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(259,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_e: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i,E: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ B ) @ ( hAPP @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) @ ( hAPP @ X_c @ ( fun @ ( product_prod @ X_d @ X_e ) @ ( product_prod @ X_c @ ( product_prod @ X_d @ X_e ) ) ) @ ( product_Pair @ X_c @ ( product_prod @ X_d @ X_e ) ) @ C_1 ) @ ( hAPP @ X_e @ ( product_prod @ X_d @ X_e ) @ ( hAPP @ X_d @ ( fun @ X_e @ ( product_prod @ X_d @ X_e ) ) @ ( product_Pair @ X_d @ X_e ) @ D_1 ) @ E ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(260,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i,D_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ X_d ) ) @ B ) @ ( hAPP @ X_d @ ( product_prod @ X_c @ X_d ) @ ( hAPP @ X_c @ ( fun @ X_d @ ( product_prod @ X_c @ X_d ) ) @ ( product_Pair @ X_c @ X_d ) @ C_1 ) @ D_1 ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(261,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_d: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i,D_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ A_6 ) @ ( hAPP @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) @ ( hAPP @ X_b @ ( fun @ ( product_prod @ X_c @ X_d ) @ ( product_prod @ X_b @ ( product_prod @ X_c @ X_d ) ) ) @ ( product_Pair @ X_b @ ( product_prod @ X_c @ X_d ) ) @ B ) @ ( hAPP @ X_d @ ( product_prod @ X_c @ X_d ) @ ( hAPP @ X_c @ ( fun @ X_d @ ( product_prod @ X_c @ X_d ) ) @ ( product_Pair @ X_c @ X_d ) @ C_1 ) @ D_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(262,plain,
( ( ! [X_b: $i,X_a: $i,A_2: $i,B_4: $i,A_1: $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 ) @ A_2 ) @ B_4 )
= ( 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_1 ) @ B_3 ) )
=> ~ ( ( ( ti @ X_a @ A_2 )
= ( ti @ X_a @ A_1 ) )
=> ( ( ti @ X_b @ B_4 )
!= ( ti @ X_b @ B_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(263,plain,
( ( ! [X_b: $i,X_a: $i,A_4: $i,B_1: $i,A_3: $i,B_2: $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_4 ) @ B_1 )
= ( 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 ) )
<=> ( ( ( ti @ X_a @ A_4 )
= ( ti @ X_a @ A_3 ) )
& ( ( ti @ X_b @ B_1 )
= ( ti @ X_b @ B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(264,plain,
( ( ! [X_a: $i,X_b: $i,Pa: $i] :
( ! [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) )
<=> ! [A_6: $i,B: $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_6 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(265,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,B_1: $i,A_4: $i,X: $i] :
( ( ( ( ti @ X_a @ X )
= ( ti @ X_a @ A_4 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ A_4 ) @ B_1 ) @ X )
= ( ti @ X_b @ B_1 ) ) )
& ( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ A_4 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ A_4 ) @ B_1 ) @ X )
= ( hAPP @ X_a @ X_b @ F @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(266,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ X_a @ F @ X_1 )
= ( ti @ X_a @ Y_2 ) )
=> ( ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( hAPP @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) ) @ ( fun_upd @ X_b @ X_a ) @ F ) @ X_1 ) @ Y_2 )
= ( ti @ ( fun @ X_b @ X_a ) @ F ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(267,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,Y_2: $i,Z: $i,X_1: $i] :
( ( ( ti @ X_a @ Z )
!= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( hAPP @ X_a @ X_b @ F @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(268,plain,
( ( ! [X_b: $i,X_a: $i,M: $i,B_1: $i,D: $i,A_4: $i,C: $i] :
( ( ( ti @ X_a @ A_4 )
!= ( ti @ X_a @ C ) )
=> ( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ M ) @ A_4 ) @ B_1 ) ) @ C ) @ D )
= ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ M ) @ C ) @ D ) ) @ A_4 ) @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(269,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,Y_2: $i,Z: $i,X_1: $i] :
( ( ( ( ti @ X_a @ Z )
= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( ti @ X_b @ Y_2 ) ) )
& ( ( ( ti @ X_a @ Z )
!= ( ti @ X_a @ X_1 ) )
=> ( ( hAPP @ X_a @ X_b @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) @ Z )
= ( hAPP @ X_a @ X_b @ F @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(270,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( hAPP @ X_b @ X_a @ ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( hAPP @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ X_b @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) ) @ ( fun_upd @ X_b @ X_a ) @ F ) @ X_1 ) @ Y_2 ) @ X_1 )
= ( ti @ X_a @ Y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(271,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i,Z: $i] :
( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 ) ) @ X_1 ) @ Z )
= ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(272,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_b @ ( fun @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_a @ X_b ) ) ) @ ( fun_upd @ X_a @ X_b ) @ F ) @ X_1 ) @ Y_2 )
= ( ti @ ( fun @ X_a @ X_b ) @ F ) )
<=> ( ( hAPP @ X_a @ X_b @ F @ X_1 )
= ( ti @ X_b @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(273,plain,
( ( ! [X_m: $i,P: $i,T_3: $i] : ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_m ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_m ) @ P ) @ T_3 ) @ T_3 ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(274,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i,C_1: $i] :
( ( ti @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ Y_1 )
!= ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ X_c ) ) @ A_6 ) @ ( 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 ) @ B ) @ C_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(275,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i,X_1: $i,Pa: $i] :
( ! [A_6: $i,B: $i,C_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ bool @ Pa @ ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ ( hAPP @ X_a @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) ) @ ( product_Pair @ X_a @ ( product_prod @ X_b @ X_c ) ) @ A_6 ) @ ( 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 ) @ B ) @ C_1 ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ ( product_prod @ X_b @ X_c ) ) @ bool @ Pa @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(276,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,F1: $i,A_4: $i,B_1: $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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ A_4 ) @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(277,plain,
( ( ! [X_a: $i,X_b: $i,S_3: $i,R_1: $i] :
( ! [X: $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 ) @ 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 ) @ Xa ) ) @ S_3 ) ) )
<=> ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(278,plain,
( ( ! [X_a: $i,X_b: $i,Y_1: $i] :
~ ! [A_6: $i,B: $i] :
( ( ti @ ( product_prod @ X_a @ X_b ) @ Y_1 )
!= ( 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_6 ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(279,plain,
( ( ! [X_a: $i,T_3: $i,P: $i,S_2: $i,U_1: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ S_2 ) @ U_1 ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ U_1 ) @ T_3 ) )
=> ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ X_a ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ X_a ) @ P ) @ S_2 ) @ T_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(280,plain,
( ( ! [X_a: $i,X_b: $i,Pa: $i] :
( ? [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) )
<=> ? [A_6: $i,B: $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_6 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(281,plain,
( ( ! [X_a: $i,X_b: $i,P_2: $i] :
~ ! [X: $i,Y: $i] :
( ( ti @ ( product_prod @ X_a @ X_b ) @ P_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 ) @ X ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(282,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,C: $i,A_4: $i,B_1: $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 ) @ ( produc1605651328_split @ X_b @ X_c @ X_a ) @ C ) @ ( 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ C @ A_4 ) @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(283,plain,
( ( ! [X_b: $i,X_a: $i,F1: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F1 @ A_4 ) @ B_1 ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F1 ) @ ( 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_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(284,plain,
( ( ! [X_b: $i,X_a: $i,F: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F @ A_4 ) @ B_1 ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F ) @ ( 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_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(285,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ ( product_prod_case @ X_a @ X_b @ bool ) @ F ) @ ( 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_1 ) ) )
=> ( hBOOL @ ( hAPP @ X_b @ bool @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ F @ A_4 ) @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(286,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,F1: $i,A_4: $i,B_1: $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_case @ 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ A_4 ) @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(287,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,F: $i,A_4: $i,B_1: $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_case @ X_b @ X_c @ X_a ) @ F ) @ ( 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 ) @ A_4 ) @ B_1 ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F @ A_4 ) @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(288,plain,
( ( ! [X_a: $i,X_c: $i,X_b: $i,Z: $i,C: $i,A_4: $i,B_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Z ) @ ( hAPP @ X_c @ ( fun @ X_a @ bool ) @ ( hAPP @ X_b @ ( fun @ X_c @ ( fun @ X_a @ bool ) ) @ C @ A_4 ) @ B_1 ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Z ) @ ( hAPP @ ( product_prod @ X_b @ X_c ) @ ( fun @ X_a @ bool ) @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ ( fun @ X_a @ bool ) ) ) @ ( fun @ ( product_prod @ X_b @ X_c ) @ ( fun @ X_a @ bool ) ) @ ( product_prod_case @ X_b @ X_c @ ( fun @ X_a @ bool ) ) @ C ) @ ( 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 ) @ A_4 ) @ B_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(289,plain,
( ( ! [X_c: $i,X_a: $i,X_b: $i,R_1: $i,A_4: $i,B_1: $i,C: $i] :
( ( hBOOL @ ( hAPP @ X_c @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ X_c @ bool ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ ( fun @ X_c @ bool ) ) ) @ ( fun @ ( product_prod @ X_a @ X_b ) @ ( fun @ X_c @ bool ) ) @ ( product_prod_case @ X_a @ X_b @ ( fun @ X_c @ bool ) ) @ R_1 ) @ ( 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_1 ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ X_c @ bool @ ( hAPP @ X_b @ ( fun @ X_c @ bool ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( fun @ X_c @ bool ) ) @ R_1 @ A_4 ) @ B_1 ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(290,plain,
( ( ! [E_2: $i,Eb: $i,S: $i,E_b: $i,S_1: $i,Pa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Eb ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ E_b ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ Eb ) @ E_2 ) ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ E_b ) @ E_2 ) ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(291,plain,
( ( ! [Va_1: $i,Eb: $i,S: $i,E_b: $i,S_1: $i,Pa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Eb ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ E_b ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ Va_1 ) @ Eb ) ) @ S ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ Va_1 ) @ E_b ) ) @ S_1 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(292,plain,
( ( ! [X_a: $i,Val_2: $i,Val_1: $i] :
( ( ( hAPP @ val @ ( exp @ X_a ) @ ( val_1 @ X_a ) @ Val_2 )
= ( hAPP @ val @ ( exp @ X_a ) @ ( val_1 @ X_a ) @ Val_1 ) )
<=> ( Val_2 = Val_1 ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(293,plain,
( ( ! [X_a: $i,Exp1_2: $i,Exp2_2: $i,Exp1_1: $i,Exp2_1: $i] :
( ( ( hAPP @ ( exp @ X_a ) @ ( exp @ X_a ) @ ( hAPP @ ( exp @ X_a ) @ ( fun @ ( exp @ X_a ) @ ( exp @ X_a ) ) @ ( seq @ X_a ) @ Exp1_2 ) @ Exp2_2 )
= ( hAPP @ ( exp @ X_a ) @ ( exp @ X_a ) @ ( hAPP @ ( exp @ X_a ) @ ( fun @ ( exp @ X_a ) @ ( exp @ X_a ) ) @ ( seq @ X_a ) @ Exp1_1 ) @ Exp2_1 ) )
<=> ( ( Exp1_2 = Exp1_1 )
& ( Exp2_2 = Exp2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(294,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ! [X: $i] :
( ( hAPP @ X_a @ X_b @ F @ X )
= ( hAPP @ X_a @ X_b @ G @ X ) )
=> ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(295,plain,
( ( ! [X_a: $i,X_1: $i,A_5: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_5 ) )
<=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_5 @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(296,plain,
( ( ! [X_a: $i,X_b: $i,T_1: $i,K: $i,X_1: $i] :
~ ! [X: $i] :
( ( hAPP @ X_a @ ( option @ X_b ) @ ( hAPP @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) @ ( hAPP @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) @ ( hAPP @ ( fun @ X_a @ ( option @ X_b ) ) @ ( fun @ X_a @ ( fun @ ( option @ X_b ) @ ( fun @ X_a @ ( option @ X_b ) ) ) ) @ ( fun_upd @ X_a @ ( option @ X_b ) ) @ T_1 ) @ K ) @ ( hAPP @ X_b @ ( option @ X_b ) @ ( some @ X_b ) @ X_1 ) ) @ X )
= ( none @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(297,plain,
( ( ! [Pa: $i,X: $i,Xa: $i,Xb: $i,Xc: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ Pa ) @ X ) @ Xa ) @ Xb ) @ Xc ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ X ) @ Xa ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ Xb ) @ Xc ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ Pa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(298,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)],[164]) ).
thf(299,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)],[163]) ).
thf(300,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)],[162]) ).
thf(301,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(302,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(303,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(304,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(305,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 ) )
| ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX5 ) ) ) )
| ~ ( ~ ~ ( ( ( 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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(306,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX1 ) @ SX2 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX3 ) @ SX4 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SX5 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SX1 ) @ SX0 ) ) @ SX2 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SX3 ) @ SX0 ) ) @ SX4 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(307,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( ( ti @ SX1 @ SX5 )
!= ( ti @ SX1 @ SX4 ) )
| ( ( hAPP @ SX1 @ SX0 @ ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX4 ) @ SX3 ) @ SX5 )
= ( ti @ SX0 @ SX3 ) ) )
| ~ ( ~ ( ( ( ti @ SX1 @ SX5 )
!= ( ti @ SX1 @ SX4 ) ) )
| ( ( hAPP @ SX1 @ SX0 @ ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX4 ) @ SX3 ) @ SX5 )
= ( hAPP @ SX1 @ SX0 @ SX2 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ! [SX6: $i,SX7: $i,SX8: $i,SX9: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ bool @ SX5 @ ( hAPP @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ SX6 ) @ ( hAPP @ ( product_prod @ SX2 @ SX3 ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ ( hAPP @ SX1 @ ( fun @ ( product_prod @ SX2 @ SX3 ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ ( product_Pair @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ SX7 ) @ ( hAPP @ SX3 @ ( product_prod @ SX2 @ SX3 ) @ ( hAPP @ SX2 @ ( fun @ SX3 @ ( product_prod @ SX2 @ SX3 ) ) @ ( product_Pair @ SX2 @ SX3 ) @ SX8 ) @ SX9 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ bool @ SX5 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(309,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ( ( ti @ SX1 @ SX4 )
!= ( ti @ SX1 @ SX5 ) ) )
| ( ( hAPP @ SX1 @ SX0 @ ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX5 ) @ SX3 ) @ SX4 )
= ( hAPP @ SX1 @ SX0 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(310,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( hAPP @ ( option @ SX0 ) @ ( fun @ SX1 @ ( option @ SX0 ) ) @ ( hAPP @ SX1 @ ( fun @ ( option @ SX0 ) @ ( fun @ SX1 @ ( option @ SX0 ) ) ) @ ( hAPP @ ( fun @ SX1 @ ( option @ SX0 ) ) @ ( fun @ SX1 @ ( fun @ ( option @ SX0 ) @ ( fun @ SX1 @ ( option @ SX0 ) ) ) ) @ ( fun_upd @ SX1 @ ( option @ SX0 ) ) @ SX2 ) @ SX3 ) @ ( hAPP @ SX0 @ ( option @ SX0 ) @ ( some @ SX0 ) @ SX4 ) )
!= ( hAPP @ ( option @ SX0 ) @ ( fun @ SX1 @ ( option @ SX0 ) ) @ ( hAPP @ SX1 @ ( fun @ ( option @ SX0 ) @ ( fun @ SX1 @ ( option @ SX0 ) ) ) @ ( hAPP @ ( fun @ SX1 @ ( option @ SX0 ) ) @ ( fun @ SX1 @ ( fun @ ( option @ SX0 ) @ ( fun @ SX1 @ ( option @ SX0 ) ) ) ) @ ( fun_upd @ SX1 @ ( option @ SX0 ) ) @ SX5 ) @ SX3 ) @ ( hAPP @ SX0 @ ( option @ SX0 ) @ ( some @ SX0 ) @ SX6 ) ) )
| ( ( ti @ SX0 @ SX4 )
= ( ti @ SX0 @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ! [SX3: $i,SX4: $i] :
( ( ti @ ( product_prod @ SX0 @ SX1 ) @ SX2 )
!= ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX3 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(312,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( ( ( ti @ SX1 @ SX5 )
!= ( ti @ SX1 @ SX6 ) ) )
| ( ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX5 ) @ SX3 ) ) @ SX6 ) @ SX4 )
= ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX6 ) @ SX4 ) ) @ SX5 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(313,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ bool ) @ ( hAPP @ SX2 @ ( fun @ SX1 @ ( fun @ SX0 @ bool ) ) @ SX4 @ SX5 ) @ SX6 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ ( hAPP @ ( product_prod @ SX2 @ SX1 ) @ ( fun @ SX0 @ bool ) @ ( hAPP @ ( fun @ SX2 @ ( fun @ SX1 @ ( fun @ SX0 @ bool ) ) ) @ ( fun @ ( product_prod @ SX2 @ SX1 ) @ ( fun @ SX0 @ bool ) ) @ ( product_prod_case @ SX2 @ SX1 @ ( fun @ SX0 @ bool ) ) @ SX4 ) @ ( hAPP @ SX1 @ ( product_prod @ SX2 @ SX1 ) @ ( hAPP @ SX2 @ ( fun @ SX1 @ ( product_prod @ SX2 @ SX1 ) ) @ ( product_Pair @ SX2 @ SX1 ) @ SX5 ) @ SX6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(314,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( ti @ SX1 @ SX4 ) )
| ( ( hAPP @ SX1 @ ( fun @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( fun @ SX0 @ SX1 ) ) @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ SX0 @ ( fun @ SX1 @ ( fun @ SX0 @ SX1 ) ) ) @ ( fun_upd @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 )
= ( ti @ ( fun @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(315,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX1 @ ( fun @ SX0 @ bool ) @ SX2 @ SX3 ) @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SX1 @ SX0 ) @ bool @ ( hAPP @ ( fun @ SX1 @ ( fun @ SX0 @ bool ) ) @ ( fun @ ( product_prod @ SX1 @ SX0 ) @ bool ) @ ( product_prod_case @ SX1 @ SX0 @ bool ) @ SX2 ) @ ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(316,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX0 @ ( option @ SX1 ) @ SX2 @ SX3 )
!= ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX4 ) )
| ( ( hAPP @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) @ ( hAPP @ SX0 @ ( fun @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) ) @ ( hAPP @ ( fun @ SX0 @ ( option @ SX1 ) ) @ ( fun @ SX0 @ ( fun @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) ) ) @ ( fun_upd @ SX0 @ ( option @ SX1 ) ) @ SX2 ) @ SX3 ) @ ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX4 ) )
= ( ti @ ( fun @ SX0 @ ( option @ SX1 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(317,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) )
| ~ ( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(318,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ( ti @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ SX4 )
!= ( hAPP @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ SX5 ) @ ( hAPP @ ( product_prod @ SX2 @ SX3 ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ ( hAPP @ SX1 @ ( fun @ ( product_prod @ SX2 @ SX3 ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) ) @ ( product_Pair @ SX1 @ ( product_prod @ SX2 @ SX3 ) ) @ SX6 ) @ ( hAPP @ SX3 @ ( product_prod @ SX2 @ SX3 ) @ ( hAPP @ SX2 @ ( fun @ SX3 @ ( product_prod @ SX2 @ SX3 ) ) @ ( product_Pair @ SX2 @ SX3 ) @ SX7 ) @ SX8 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(319,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ! [SX3: $i,SX4: $i] :
( ( ti @ ( product_prod @ SX0 @ SX1 ) @ SX2 )
!= ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX3 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ( ti @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) @ SX3 )
!= ( hAPP @ ( product_prod @ SX1 @ SX2 ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ SX2 ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) @ SX4 ) @ ( hAPP @ SX2 @ ( product_prod @ SX1 @ SX2 ) @ ( hAPP @ SX1 @ ( fun @ SX2 @ ( product_prod @ SX1 @ SX2 ) ) @ ( product_Pair @ SX1 @ SX2 ) @ SX5 ) @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(321,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( ( ti @ SX1 @ SX4 )
!= ( ti @ SX1 @ SX5 ) )
| ( ( hAPP @ SX1 @ SX0 @ ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX5 ) @ SX3 ) @ SX4 )
= ( ti @ SX0 @ SX3 ) ) )
| ~ ( ~ ( ( ( ti @ SX1 @ SX4 )
!= ( ti @ SX1 @ SX5 ) ) )
| ( ( hAPP @ SX1 @ SX0 @ ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX5 ) @ SX3 ) @ SX4 )
= ( hAPP @ SX1 @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(322,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ! [SX6: $i,SX7: $i,SX8: $i,SX9: $i,SX10: $i] :
( ( ti @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ SX5 )
!= ( hAPP @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ SX6 ) @ ( hAPP @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( hAPP @ SX1 @ ( fun @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ ( product_Pair @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ SX7 ) @ ( hAPP @ ( product_prod @ SX3 @ SX4 ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ ( hAPP @ SX2 @ ( fun @ ( product_prod @ SX3 @ SX4 ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( product_Pair @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ SX8 ) @ ( hAPP @ SX4 @ ( product_prod @ SX3 @ SX4 ) @ ( hAPP @ SX3 @ ( fun @ SX4 @ ( product_prod @ SX3 @ SX4 ) ) @ ( product_Pair @ SX3 @ SX4 ) @ SX9 ) @ SX10 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(323,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ! [SX5: $i,SX6: $i,SX7: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) @ bool @ SX4 @ ( hAPP @ ( product_prod @ SX1 @ SX2 ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ SX2 ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) @ SX5 ) @ ( hAPP @ SX2 @ ( product_prod @ SX1 @ SX2 ) @ ( hAPP @ SX1 @ ( fun @ SX2 @ ( product_prod @ SX1 @ SX2 ) ) @ ( product_Pair @ SX1 @ SX2 ) @ SX6 ) @ SX7 ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ SX2 ) ) @ bool @ SX4 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(324,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ! [SX7: $i,SX8: $i,SX9: $i,SX10: $i,SX11: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ bool @ SX6 @ ( hAPP @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ SX7 ) @ ( hAPP @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( hAPP @ SX1 @ ( fun @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ ( product_Pair @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ SX8 ) @ ( hAPP @ ( product_prod @ SX3 @ SX4 ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ ( hAPP @ SX2 @ ( fun @ ( product_prod @ SX3 @ SX4 ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) @ ( product_Pair @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) @ SX9 ) @ ( hAPP @ SX4 @ ( product_prod @ SX3 @ SX4 ) @ ( hAPP @ SX3 @ ( fun @ SX4 @ ( product_prod @ SX3 @ SX4 ) ) @ ( product_Pair @ SX3 @ SX4 ) @ SX10 ) @ SX11 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ SX4 ) ) ) ) @ bool @ SX6 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(325,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
~ ( ~ ( ( ( hAPP @ SX0 @ ( option @ SX1 ) @ ( hAPP @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) @ ( hAPP @ SX0 @ ( fun @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) ) @ ( hAPP @ ( fun @ SX0 @ ( option @ SX1 ) ) @ ( fun @ SX0 @ ( fun @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) ) ) @ ( fun_upd @ SX0 @ ( option @ SX1 ) ) @ SX2 ) @ SX3 ) @ ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX4 ) ) @ SX5 )
!= ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX6 ) )
| ~ ( ( ( ti @ SX0 @ SX5 )
!= ( ti @ SX0 @ SX3 ) )
| ( ( ti @ SX1 @ SX4 )
!= ( ti @ SX1 @ SX6 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX5 )
!= ( ti @ SX0 @ SX3 ) ) )
| ( ( hAPP @ SX0 @ ( option @ SX1 ) @ SX2 @ SX5 )
!= ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX6 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SX0 @ SX5 )
!= ( ti @ SX0 @ SX3 ) )
| ( ( ti @ SX1 @ SX4 )
!= ( ti @ SX1 @ SX6 ) ) )
| ~ ( ~ ( ( ( ti @ SX0 @ SX5 )
!= ( ti @ SX0 @ SX3 ) ) )
| ( ( hAPP @ SX0 @ ( option @ SX1 ) @ SX2 @ SX5 )
!= ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX6 ) ) ) )
| ( ( hAPP @ SX0 @ ( option @ SX1 ) @ ( hAPP @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) @ ( hAPP @ SX0 @ ( fun @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) ) @ ( hAPP @ ( fun @ SX0 @ ( option @ SX1 ) ) @ ( fun @ SX0 @ ( fun @ ( option @ SX1 ) @ ( fun @ SX0 @ ( option @ SX1 ) ) ) ) @ ( fun_upd @ SX0 @ ( option @ SX1 ) ) @ SX2 ) @ SX3 ) @ ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX4 ) ) @ SX5 )
= ( hAPP @ SX1 @ ( option @ SX1 ) @ ( some @ SX1 ) @ SX6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(326,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX1 @ ( fun @ SX0 @ bool ) @ SX2 @ SX3 ) @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SX1 @ SX0 ) @ bool @ ( hAPP @ ( fun @ SX1 @ ( fun @ SX0 @ bool ) ) @ ( fun @ ( product_prod @ SX1 @ SX0 ) @ bool ) @ ( product_prod_case @ SX1 @ SX0 @ bool ) @ SX2 ) @ ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(327,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( hAPP @ ( exp @ SX0 ) @ ( exp @ SX0 ) @ ( hAPP @ ( exp @ SX0 ) @ ( fun @ ( exp @ SX0 ) @ ( exp @ SX0 ) ) @ ( seq @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( exp @ SX0 ) @ ( exp @ SX0 ) @ ( hAPP @ ( exp @ SX0 ) @ ( fun @ ( exp @ SX0 ) @ ( exp @ SX0 ) ) @ ( seq @ SX0 ) @ SX3 ) @ SX4 ) )
| ~ ( ( SX1 != SX3 )
| ( SX2 != SX4 ) ) )
| ~ ( ~ ~ ( ( SX1 != SX3 )
| ( SX2 != SX4 ) )
| ( ( hAPP @ ( exp @ SX0 ) @ ( exp @ SX0 ) @ ( hAPP @ ( exp @ SX0 ) @ ( fun @ ( exp @ SX0 ) @ ( exp @ SX0 ) ) @ ( seq @ SX0 ) @ SX1 ) @ SX2 )
= ( hAPP @ ( exp @ SX0 ) @ ( exp @ SX0 ) @ ( hAPP @ ( exp @ SX0 ) @ ( fun @ ( exp @ SX0 ) @ ( exp @ SX0 ) ) @ ( seq @ SX0 ) @ SX3 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(328,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ! [SX8: $i,SX9: $i,SX10: $i,SX11: $i,SX12: $i,SX13: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ bool @ SX7 @ ( hAPP @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ SX8 ) @ ( hAPP @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( hAPP @ SX1 @ ( fun @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ ( product_Pair @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ SX9 ) @ ( hAPP @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( hAPP @ SX2 @ ( fun @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( product_Pair @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ SX10 ) @ ( hAPP @ ( product_prod @ SX4 @ SX5 ) @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ ( hAPP @ SX3 @ ( fun @ ( product_prod @ SX4 @ SX5 ) @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( product_Pair @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ SX11 ) @ ( hAPP @ SX5 @ ( product_prod @ SX4 @ SX5 ) @ ( hAPP @ SX4 @ ( fun @ SX5 @ ( product_prod @ SX4 @ SX5 ) ) @ ( product_Pair @ SX4 @ SX5 ) @ SX12 ) @ SX13 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ bool @ SX7 @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(329,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
~ ! [SX7: $i,SX8: $i,SX9: $i,SX10: $i,SX11: $i,SX12: $i] :
( ( ti @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ SX6 )
!= ( hAPP @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ ( hAPP @ SX0 @ ( fun @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( product_prod @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) ) @ ( product_Pair @ SX0 @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ SX7 ) @ ( hAPP @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( hAPP @ SX1 @ ( fun @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( product_prod @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) ) @ ( product_Pair @ SX1 @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ SX8 ) @ ( hAPP @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( hAPP @ SX2 @ ( fun @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ ( product_prod @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) ) @ ( product_Pair @ SX2 @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ SX9 ) @ ( hAPP @ ( product_prod @ SX4 @ SX5 ) @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ ( hAPP @ SX3 @ ( fun @ ( product_prod @ SX4 @ SX5 ) @ ( product_prod @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) ) @ ( product_Pair @ SX3 @ ( product_prod @ SX4 @ SX5 ) ) @ SX10 ) @ ( hAPP @ SX5 @ ( product_prod @ SX4 @ SX5 ) @ ( hAPP @ SX4 @ ( fun @ SX5 @ ( product_prod @ SX4 @ SX5 ) ) @ ( product_Pair @ SX4 @ SX5 ) @ SX11 ) @ SX12 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(330,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ ( hAPP @ ( fun @ SX0 @ ( fun @ SX1 @ bool ) ) @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ ( product_prod_case @ SX0 @ SX1 @ bool ) @ SX2 ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX3 ) @ SX4 ) ) )
| ( hBOOL @ ( hAPP @ SX1 @ bool @ ( hAPP @ SX0 @ ( fun @ SX1 @ bool ) @ SX2 @ SX3 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(331,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX1 ) @ SX2 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX3 ) @ SX4 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SX5 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SX0 ) @ SX1 ) ) @ SX2 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SX0 ) @ SX3 ) ) @ SX4 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(332,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ! [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 ) ) )
| ~ ( ~ ( 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 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ SX3 )
= ( ti @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ SX2 ) ) )
| ~ ( ( ( 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 ) ) )
| ~ ( ~ ( 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)],[277]) ).
thf(333,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ! [SX4: $i] :
( ( hAPP @ SX0 @ SX1 @ SX2 @ SX4 )
= ( hAPP @ SX0 @ SX1 @ SX3 @ SX4 ) )
| ( ( ti @ ( fun @ SX0 @ SX1 ) @ SX2 )
= ( ti @ ( fun @ SX0 @ SX1 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(334,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( hAPP @ val @ ( exp @ SX0 ) @ ( val_1 @ SX0 ) @ SX1 )
!= ( hAPP @ val @ ( exp @ SX0 ) @ ( val_1 @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ( ( SX1 != SX2 )
| ( ( hAPP @ val @ ( exp @ SX0 ) @ ( val_1 @ SX0 ) @ SX1 )
= ( hAPP @ val @ ( exp @ SX0 ) @ ( val_1 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(335,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ SX3 ) )
| ~ ! [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 ) ) ) )
| ~ ( ~ ~ ! [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 ) ) )
| ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(336,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ ( product_prod @ SX1 @ SX2 ) @ ( fun @ SX0 @ bool ) @ ( hAPP @ ( fun @ SX1 @ ( fun @ SX2 @ ( fun @ SX0 @ bool ) ) ) @ ( fun @ ( product_prod @ SX1 @ SX2 ) @ ( fun @ SX0 @ bool ) ) @ ( product_prod_case @ SX1 @ SX2 @ ( fun @ SX0 @ bool ) ) @ SX3 ) @ ( hAPP @ SX2 @ ( product_prod @ SX1 @ SX2 ) @ ( hAPP @ SX1 @ ( fun @ SX2 @ ( product_prod @ SX1 @ SX2 ) ) @ ( product_Pair @ SX1 @ SX2 ) @ SX4 ) @ SX5 ) ) @ SX6 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX2 @ ( fun @ SX0 @ bool ) @ ( hAPP @ SX1 @ ( fun @ SX2 @ ( fun @ SX0 @ bool ) ) @ SX3 @ SX4 ) @ SX5 ) @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(337,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 ) )
| ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(338,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 ) ) )
| ~ ( ~ ( 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)],[295]) ).
thf(339,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ SX3 ) )
| ! [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 ) ) ) )
| ~ ( ~ ! [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 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(340,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SX0 ) @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX1 ) @ SX2 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX3 ) @ SX4 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SX0 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX1 ) @ SX2 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SX3 ) @ SX4 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SX0 ) @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(341,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SX0 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SX0 ) @ SX2 ) @ SX3 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SX0 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SX0 ) @ SX2 ) @ SX4 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SX0 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SX0 ) @ SX2 ) @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(342,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) @ SX4 )
!= ( ti @ ( fun @ SX1 @ SX0 ) @ SX2 ) )
| ( ( hAPP @ SX1 @ SX0 @ SX2 @ SX3 )
= ( ti @ SX0 @ SX4 ) ) )
| ~ ( ( ( hAPP @ SX1 @ SX0 @ SX2 @ SX3 )
!= ( ti @ SX0 @ SX4 ) )
| ( ( hAPP @ SX0 @ ( fun @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ SX1 @ ( fun @ SX0 @ ( fun @ SX1 @ SX0 ) ) ) @ ( fun_upd @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) @ SX4 )
= ( ti @ ( fun @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(343,plain,
! [SV1: $i] :
( ( ! [SY336: $i] :
( ( ti @ ( fun @ ( fun @ SV1 @ SY336 ) @ ( fun @ SV1 @ ( fun @ SY336 @ ( fun @ SV1 @ SY336 ) ) ) ) @ ( fun_upd @ SV1 @ SY336 ) )
= ( fun_upd @ SV1 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(344,plain,
! [SV2: $i] :
( ( ( ti @ ( fun @ SV2 @ ( option @ SV2 ) ) @ ( some @ SV2 ) )
= ( some @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(345,plain,
! [SV3: $i] :
( ( ! [SY337: $i] :
( ( ti @ ( fun @ SV3 @ ( fun @ SY337 @ ( product_prod @ SV3 @ SY337 ) ) ) @ ( product_Pair @ SV3 @ SY337 ) )
= ( product_Pair @ SV3 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(346,plain,
! [SV4: $i] :
( ( ! [SY338: $i,SY339: $i,SY340: $i] :
( ( hAPP @ SV4 @ SY338 @ ( ti @ ( fun @ SV4 @ SY338 ) @ SY339 ) @ SY340 )
= ( hAPP @ SV4 @ SY338 @ SY339 @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(347,plain,
! [SV5: $i] :
( ( ! [SY341: $i,SY342: $i,SY343: $i] :
( ( hAPP @ SV5 @ SY341 @ SY342 @ ( ti @ SV5 @ SY343 ) )
= ( hAPP @ SV5 @ SY341 @ SY342 @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(348,plain,
! [SV6: $i] :
( ( ! [SY344: $i,SY345: $i,SY346: $i] :
( ( ti @ SV6 @ ( hAPP @ SY344 @ SV6 @ SY345 @ SY346 ) )
= ( hAPP @ SY344 @ SV6 @ SY345 @ SY346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(349,plain,
! [SV7: $i] :
( ( ( ti @ ( fun @ SV7 @ ( fun @ ( fun @ SV7 @ bool ) @ bool ) ) @ ( member @ SV7 ) )
= ( member @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(350,plain,
! [SV8: $i] :
( ( ! [SY347: $i,SY348: $i,SY349: $i] :
( ( hAPP @ SV8 @ ( fun @ SY347 @ SV8 ) @ ( hAPP @ SY347 @ ( fun @ SV8 @ ( fun @ SY347 @ SV8 ) ) @ ( hAPP @ ( fun @ SY347 @ SV8 ) @ ( fun @ SY347 @ ( fun @ SV8 @ ( fun @ SY347 @ SV8 ) ) ) @ ( fun_upd @ SY347 @ SV8 ) @ SY348 ) @ SY349 ) @ ( hAPP @ SY347 @ SV8 @ SY348 @ SY349 ) )
= ( ti @ ( fun @ SY347 @ SV8 ) @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(351,plain,
! [SV9: $i] :
( ( ! [SY350: $i,SY351: $i,SY352: $i,SY353: $i] :
( ( hAPP @ SV9 @ SY350 @ ( hAPP @ SY350 @ ( fun @ SV9 @ SY350 ) @ ( hAPP @ SV9 @ ( fun @ SY350 @ ( fun @ SV9 @ SY350 ) ) @ ( hAPP @ ( fun @ SV9 @ SY350 ) @ ( fun @ SV9 @ ( fun @ SY350 @ ( fun @ SV9 @ SY350 ) ) ) @ ( fun_upd @ SV9 @ SY350 ) @ SY351 ) @ SY352 ) @ SY353 ) @ SY352 )
= ( ti @ SY350 @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(352,plain,
! [SV10: $i] :
( ( ! [SY354: $i,SY355: $i,SY356: $i,SY357: $i,SY358: $i] :
( ( hAPP @ SV10 @ ( fun @ SY354 @ SV10 ) @ ( hAPP @ SY354 @ ( fun @ SV10 @ ( fun @ SY354 @ SV10 ) ) @ ( hAPP @ ( fun @ SY354 @ SV10 ) @ ( fun @ SY354 @ ( fun @ SV10 @ ( fun @ SY354 @ SV10 ) ) ) @ ( fun_upd @ SY354 @ SV10 ) @ ( hAPP @ SV10 @ ( fun @ SY354 @ SV10 ) @ ( hAPP @ SY354 @ ( fun @ SV10 @ ( fun @ SY354 @ SV10 ) ) @ ( hAPP @ ( fun @ SY354 @ SV10 ) @ ( fun @ SY354 @ ( fun @ SV10 @ ( fun @ SY354 @ SV10 ) ) ) @ ( fun_upd @ SY354 @ SV10 ) @ SY355 ) @ SY356 ) @ SY357 ) ) @ SY356 ) @ SY358 )
= ( hAPP @ SV10 @ ( fun @ SY354 @ SV10 ) @ ( hAPP @ SY354 @ ( fun @ SV10 @ ( fun @ SY354 @ SV10 ) ) @ ( hAPP @ ( fun @ SY354 @ SV10 ) @ ( fun @ SY354 @ ( fun @ SV10 @ ( fun @ SY354 @ SV10 ) ) ) @ ( fun_upd @ SY354 @ SV10 ) @ SY355 ) @ SY356 ) @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(353,plain,
! [SV11: $i] :
( ( ! [SY359: $i,SY360: $i] : ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV11 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV11 ) @ SY359 ) @ SY360 ) @ SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(354,plain,
! [SV12: $i] :
( ( ! [SY361: $i,SY362: $i,SY363: $i,SY364: $i,SY365: $i] :
( ( hAPP @ ( product_prod @ SV12 @ SY361 ) @ SY362 @ ( hAPP @ ( fun @ SV12 @ ( fun @ SY361 @ SY362 ) ) @ ( fun @ ( product_prod @ SV12 @ SY361 ) @ SY362 ) @ ( product_prod_rec @ SV12 @ SY361 @ SY362 ) @ SY363 ) @ ( hAPP @ SY361 @ ( product_prod @ SV12 @ SY361 ) @ ( hAPP @ SV12 @ ( fun @ SY361 @ ( product_prod @ SV12 @ SY361 ) ) @ ( product_Pair @ SV12 @ SY361 ) @ SY364 ) @ SY365 ) )
= ( hAPP @ SY361 @ SY362 @ ( hAPP @ SV12 @ ( fun @ SY361 @ SY362 ) @ SY363 @ SY364 ) @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(355,plain,
! [SV13: $i] :
( ( ! [SY366: $i,SY367: $i,SY368: $i,SY369: $i,SY370: $i] :
( ( hAPP @ ( product_prod @ SV13 @ SY366 ) @ SY367 @ ( hAPP @ ( fun @ SV13 @ ( fun @ SY366 @ SY367 ) ) @ ( fun @ ( product_prod @ SV13 @ SY366 ) @ SY367 ) @ ( produc1605651328_split @ SV13 @ SY366 @ SY367 ) @ SY368 ) @ ( hAPP @ SY366 @ ( product_prod @ SV13 @ SY366 ) @ ( hAPP @ SV13 @ ( fun @ SY366 @ ( product_prod @ SV13 @ SY366 ) ) @ ( product_Pair @ SV13 @ SY366 ) @ SY369 ) @ SY370 ) )
= ( hAPP @ SY366 @ SY367 @ ( hAPP @ SV13 @ ( fun @ SY366 @ SY367 ) @ SY368 @ SY369 ) @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(356,plain,
! [SV14: $i] :
( ( ! [SY371: $i,SY372: $i,SY373: $i,SY374: $i,SY375: $i] :
( ( hAPP @ ( product_prod @ SV14 @ SY371 ) @ SY372 @ ( hAPP @ ( fun @ SV14 @ ( fun @ SY371 @ SY372 ) ) @ ( fun @ ( product_prod @ SV14 @ SY371 ) @ SY372 ) @ ( product_prod_case @ SV14 @ SY371 @ SY372 ) @ SY373 ) @ ( hAPP @ SY371 @ ( product_prod @ SV14 @ SY371 ) @ ( hAPP @ SV14 @ ( fun @ SY371 @ ( product_prod @ SV14 @ SY371 ) ) @ ( product_Pair @ SV14 @ SY371 ) @ SY374 ) @ SY375 ) )
= ( hAPP @ SY371 @ SY372 @ ( hAPP @ SV14 @ ( fun @ SY371 @ SY372 ) @ SY373 @ SY374 ) @ SY375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(357,plain,
! [SV15: $i] :
( ( ! [SY376: $i,SY377: $i,SY378: $i,SY379: $i,SY380: $i] :
( ( hAPP @ ( product_prod @ SV15 @ SY376 ) @ SY377 @ ( hAPP @ ( fun @ SV15 @ ( fun @ SY376 @ SY377 ) ) @ ( fun @ ( product_prod @ SV15 @ SY376 ) @ SY377 ) @ ( product_prod_case @ SV15 @ SY376 @ SY377 ) @ SY378 ) @ ( hAPP @ SY376 @ ( product_prod @ SV15 @ SY376 ) @ ( hAPP @ SV15 @ ( fun @ SY376 @ ( product_prod @ SV15 @ SY376 ) ) @ ( product_Pair @ SV15 @ SY376 ) @ SY379 ) @ SY380 ) )
= ( hAPP @ SY376 @ SY377 @ ( hAPP @ SV15 @ ( fun @ SY376 @ SY377 ) @ SY378 @ SY379 ) @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(358,plain,
! [SV16: $i] :
( ( ! [SY381: $i,SY382: $i,SY383: $i,SY384: $i] :
~ ! [SY385: $i] :
( ( hAPP @ SV16 @ ( option @ SY381 ) @ ( hAPP @ ( option @ SY381 ) @ ( fun @ SV16 @ ( option @ SY381 ) ) @ ( hAPP @ SV16 @ ( fun @ ( option @ SY381 ) @ ( fun @ SV16 @ ( option @ SY381 ) ) ) @ ( hAPP @ ( fun @ SV16 @ ( option @ SY381 ) ) @ ( fun @ SV16 @ ( fun @ ( option @ SY381 ) @ ( fun @ SV16 @ ( option @ SY381 ) ) ) ) @ ( fun_upd @ SV16 @ ( option @ SY381 ) ) @ SY382 ) @ SY383 ) @ ( hAPP @ SY381 @ ( option @ SY381 ) @ ( some @ SY381 ) @ SY384 ) ) @ SY385 )
= ( none @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(359,plain,
! [SV17: $i] :
( ( ! [SY386: $i,SY387: $i,SY388: $i,SY389: $i,SY390: $i] :
( ( hAPP @ SV17 @ SY386 @ ( hAPP @ ( fun @ SV17 @ SY387 ) @ ( fun @ SV17 @ SY386 ) @ ( hAPP @ ( fun @ SY387 @ SY386 ) @ ( fun @ ( fun @ SV17 @ SY387 ) @ ( fun @ SV17 @ SY386 ) ) @ ( combb @ SY387 @ SY386 @ SV17 ) @ SY388 ) @ SY389 ) @ SY390 )
= ( hAPP @ SY387 @ SY386 @ SY388 @ ( hAPP @ SV17 @ SY387 @ SY389 @ SY390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(360,plain,
! [SV18: $i] :
( ( ! [SY391: $i,SY392: $i,SY393: $i,SY394: $i,SY395: $i] :
( ( hAPP @ SV18 @ SY391 @ ( hAPP @ SY392 @ ( fun @ SV18 @ SY391 ) @ ( hAPP @ ( fun @ SV18 @ ( fun @ SY392 @ SY391 ) ) @ ( fun @ SY392 @ ( fun @ SV18 @ SY391 ) ) @ ( combc @ SV18 @ SY392 @ SY391 ) @ SY393 ) @ SY394 ) @ SY395 )
= ( hAPP @ SY392 @ SY391 @ ( hAPP @ SV18 @ ( fun @ SY392 @ SY391 ) @ SY393 @ SY395 ) @ SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(361,plain,
! [SV19: $i] :
( ( ! [SY396: $i,SY397: $i,SY398: $i,SY399: $i,SY400: $i] :
( ( hAPP @ SV19 @ SY396 @ ( hAPP @ ( fun @ SV19 @ SY397 ) @ ( fun @ SV19 @ SY396 ) @ ( hAPP @ ( fun @ SV19 @ ( fun @ SY397 @ SY396 ) ) @ ( fun @ ( fun @ SV19 @ SY397 ) @ ( fun @ SV19 @ SY396 ) ) @ ( combs @ SV19 @ SY397 @ SY396 ) @ SY398 ) @ SY399 ) @ SY400 )
= ( hAPP @ SY397 @ SY396 @ ( hAPP @ SV19 @ ( fun @ SY397 @ SY396 ) @ SY398 @ SY400 ) @ ( hAPP @ SV19 @ SY397 @ SY399 @ SY400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(362,plain,
! [SV20: $i] :
( ( ! [SY401: $i] :
( ~ ( hBOOL @ SY401 )
| ~ ( hBOOL @ SV20 )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SY401 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(363,plain,
! [SV21: $i] :
( ( ! [SY402: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV21 ) @ SY402 ) )
| ( hBOOL @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(364,plain,
! [SV22: $i] :
( ( ! [SY403: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV22 ) @ SY403 ) )
| ( hBOOL @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(365,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ea ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ha ) @ ( hAPP @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ val ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ val ) ) @ la ) @ v_1 ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ e_a ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_Pair @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ h_a ) @ l_a ) ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ p ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(366,plain,
! [SV23: $i] :
( ( ! [SY404: $i,SY405: $i,SY406: $i,SY407: $i,SY408: $i] :
~ ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SY404 @ SV23 ) @ ( hAPP @ SY404 @ ( fun @ SV23 @ ( product_prod @ SY404 @ SV23 ) ) @ ( product_Pair @ SY404 @ SV23 ) @ SY405 ) @ SY406 )
!= ( hAPP @ SV23 @ ( product_prod @ SY404 @ SV23 ) @ ( hAPP @ SY404 @ ( fun @ SV23 @ ( product_prod @ SY404 @ SV23 ) ) @ ( product_Pair @ SY404 @ SV23 ) @ SY407 ) @ SY408 ) )
| ~ ( ( ( ti @ SY404 @ SY405 )
!= ( ti @ SY404 @ SY407 ) )
| ( ( ti @ SV23 @ SY406 )
!= ( ti @ SV23 @ SY408 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SY404 @ SY405 )
!= ( ti @ SY404 @ SY407 ) )
| ( ( ti @ SV23 @ SY406 )
!= ( ti @ SV23 @ SY408 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SY404 @ SV23 ) @ ( hAPP @ SY404 @ ( fun @ SV23 @ ( product_prod @ SY404 @ SV23 ) ) @ ( product_Pair @ SY404 @ SV23 ) @ SY405 ) @ SY406 )
= ( hAPP @ SV23 @ ( product_prod @ SY404 @ SV23 ) @ ( hAPP @ SY404 @ ( fun @ SV23 @ ( product_prod @ SY404 @ SV23 ) ) @ ( product_Pair @ SY404 @ SV23 ) @ SY407 ) @ SY408 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(367,plain,
! [SV24: $i] :
( ( ! [SY409: $i,SY410: $i,SY411: $i,SY412: $i,SY413: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY409 ) @ SY410 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY411 ) @ SY412 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY413 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SY409 ) @ SV24 ) ) @ SY410 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SY411 ) @ SV24 ) ) @ SY412 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY413 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(368,plain,
! [SV25: $i] :
( ( ! [SY414: $i,SY415: $i,SY416: $i,SY417: $i,SY418: $i] :
~ ( ~ ( ( ( ti @ SY414 @ SY418 )
!= ( ti @ SY414 @ SY417 ) )
| ( ( hAPP @ SY414 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SY414 @ SV25 ) @ ( hAPP @ SY414 @ ( fun @ SV25 @ ( fun @ SY414 @ SV25 ) ) @ ( hAPP @ ( fun @ SY414 @ SV25 ) @ ( fun @ SY414 @ ( fun @ SV25 @ ( fun @ SY414 @ SV25 ) ) ) @ ( fun_upd @ SY414 @ SV25 ) @ SY415 ) @ SY417 ) @ SY416 ) @ SY418 )
= ( ti @ SV25 @ SY416 ) ) )
| ~ ( ~ ( ( ( ti @ SY414 @ SY418 )
!= ( ti @ SY414 @ SY417 ) ) )
| ( ( hAPP @ SY414 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SY414 @ SV25 ) @ ( hAPP @ SY414 @ ( fun @ SV25 @ ( fun @ SY414 @ SV25 ) ) @ ( hAPP @ ( fun @ SY414 @ SV25 ) @ ( fun @ SY414 @ ( fun @ SV25 @ ( fun @ SY414 @ SV25 ) ) ) @ ( fun_upd @ SY414 @ SV25 ) @ SY415 ) @ SY417 ) @ SY416 ) @ SY418 )
= ( hAPP @ SY414 @ SV25 @ SY415 @ SY418 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(369,plain,
! [SV26: $i] :
( ( ! [SY419: $i,SY420: $i,SY421: $i,SY422: $i,SY423: $i] :
( ~ ! [SY424: $i,SY425: $i,SY426: $i,SY427: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) ) @ bool @ SY423 @ ( hAPP @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) ) @ SY424 ) @ ( hAPP @ ( product_prod @ SY420 @ SY421 ) @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) @ ( hAPP @ SY419 @ ( fun @ ( product_prod @ SY420 @ SY421 ) @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) ) @ ( product_Pair @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) @ SY425 ) @ ( hAPP @ SY421 @ ( product_prod @ SY420 @ SY421 ) @ ( hAPP @ SY420 @ ( fun @ SY421 @ ( product_prod @ SY420 @ SY421 ) ) @ ( product_Pair @ SY420 @ SY421 ) @ SY426 ) @ SY427 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SY419 @ ( product_prod @ SY420 @ SY421 ) ) ) @ bool @ SY423 @ SY422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(370,plain,
! [SV27: $i] :
( ( ! [SY428: $i,SY429: $i,SY430: $i,SY431: $i,SY432: $i] :
( ~ ( ( ( ti @ SY428 @ SY431 )
!= ( ti @ SY428 @ SY432 ) ) )
| ( ( hAPP @ SY428 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SY428 @ SV27 ) @ ( hAPP @ SY428 @ ( fun @ SV27 @ ( fun @ SY428 @ SV27 ) ) @ ( hAPP @ ( fun @ SY428 @ SV27 ) @ ( fun @ SY428 @ ( fun @ SV27 @ ( fun @ SY428 @ SV27 ) ) ) @ ( fun_upd @ SY428 @ SV27 ) @ SY429 ) @ SY432 ) @ SY430 ) @ SY431 )
= ( hAPP @ SY428 @ SV27 @ SY429 @ SY431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(371,plain,
! [SV28: $i] :
( ( ! [SY433: $i,SY434: $i,SY435: $i,SY436: $i,SY437: $i,SY438: $i] :
( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SY433 @ ( option @ SV28 ) ) @ ( hAPP @ SY433 @ ( fun @ ( option @ SV28 ) @ ( fun @ SY433 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SY433 @ ( option @ SV28 ) ) @ ( fun @ SY433 @ ( fun @ ( option @ SV28 ) @ ( fun @ SY433 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SY433 @ ( option @ SV28 ) ) @ SY434 ) @ SY435 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY436 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SY433 @ ( option @ SV28 ) ) @ ( hAPP @ SY433 @ ( fun @ ( option @ SV28 ) @ ( fun @ SY433 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SY433 @ ( option @ SV28 ) ) @ ( fun @ SY433 @ ( fun @ ( option @ SV28 ) @ ( fun @ SY433 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SY433 @ ( option @ SV28 ) ) @ SY437 ) @ SY435 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY438 ) ) )
| ( ( ti @ SV28 @ SY436 )
= ( ti @ SV28 @ SY438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(372,plain,
! [SV29: $i] :
( ( ! [SY439: $i,SY440: $i] :
~ ! [SY441: $i,SY442: $i] :
( ( ti @ ( product_prod @ SV29 @ SY439 ) @ SY440 )
!= ( hAPP @ SY439 @ ( product_prod @ SV29 @ SY439 ) @ ( hAPP @ SV29 @ ( fun @ SY439 @ ( product_prod @ SV29 @ SY439 ) ) @ ( product_Pair @ SV29 @ SY439 ) @ SY441 ) @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(373,plain,
! [SV30: $i] :
( ( ! [SY443: $i,SY444: $i,SY445: $i,SY446: $i,SY447: $i,SY448: $i] :
( ~ ( ( ( ti @ SY443 @ SY447 )
!= ( ti @ SY443 @ SY448 ) ) )
| ( ( hAPP @ SV30 @ ( fun @ SY443 @ SV30 ) @ ( hAPP @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) @ ( hAPP @ ( fun @ SY443 @ SV30 ) @ ( fun @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) ) @ ( fun_upd @ SY443 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SY443 @ SV30 ) @ ( hAPP @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) @ ( hAPP @ ( fun @ SY443 @ SV30 ) @ ( fun @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) ) @ ( fun_upd @ SY443 @ SV30 ) @ SY444 ) @ SY447 ) @ SY445 ) ) @ SY448 ) @ SY446 )
= ( hAPP @ SV30 @ ( fun @ SY443 @ SV30 ) @ ( hAPP @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) @ ( hAPP @ ( fun @ SY443 @ SV30 ) @ ( fun @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) ) @ ( fun_upd @ SY443 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SY443 @ SV30 ) @ ( hAPP @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) @ ( hAPP @ ( fun @ SY443 @ SV30 ) @ ( fun @ SY443 @ ( fun @ SV30 @ ( fun @ SY443 @ SV30 ) ) ) @ ( fun_upd @ SY443 @ SV30 ) @ SY444 ) @ SY448 ) @ SY446 ) ) @ SY447 ) @ SY445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(374,plain,
! [SV31: $i] :
( ( ! [SY449: $i,SY450: $i,SY451: $i,SY452: $i,SY453: $i,SY454: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SY451 ) @ ( hAPP @ SY449 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SY450 @ ( fun @ SY449 @ ( fun @ SV31 @ bool ) ) @ SY452 @ SY453 ) @ SY454 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SY451 ) @ ( hAPP @ ( product_prod @ SY450 @ SY449 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SY450 @ ( fun @ SY449 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SY450 @ SY449 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SY450 @ SY449 @ ( fun @ SV31 @ bool ) ) @ SY452 ) @ ( hAPP @ SY449 @ ( product_prod @ SY450 @ SY449 ) @ ( hAPP @ SY450 @ ( fun @ SY449 @ ( product_prod @ SY450 @ SY449 ) ) @ ( product_Pair @ SY450 @ SY449 ) @ SY453 ) @ SY454 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(375,plain,
! [SV32: $i] :
( ( ! [SY455: $i,SY456: $i,SY457: $i,SY458: $i] :
( ( ( hAPP @ SV32 @ SY455 @ SY456 @ SY457 )
!= ( ti @ SY455 @ SY458 ) )
| ( ( hAPP @ SY455 @ ( fun @ SV32 @ SY455 ) @ ( hAPP @ SV32 @ ( fun @ SY455 @ ( fun @ SV32 @ SY455 ) ) @ ( hAPP @ ( fun @ SV32 @ SY455 ) @ ( fun @ SV32 @ ( fun @ SY455 @ ( fun @ SV32 @ SY455 ) ) ) @ ( fun_upd @ SV32 @ SY455 ) @ SY456 ) @ SY457 ) @ SY458 )
= ( ti @ ( fun @ SV32 @ SY455 ) @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(376,plain,
! [SV33: $i] :
( ( ! [SY459: $i,SY460: $i,SY461: $i,SY462: $i] :
( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SY459 @ ( fun @ SV33 @ bool ) @ SY460 @ SY461 ) @ SY462 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SY459 @ SV33 ) @ bool @ ( hAPP @ ( fun @ SY459 @ ( fun @ SV33 @ bool ) ) @ ( fun @ ( product_prod @ SY459 @ SV33 ) @ bool ) @ ( product_prod_case @ SY459 @ SV33 @ bool ) @ SY460 ) @ ( hAPP @ SV33 @ ( product_prod @ SY459 @ SV33 ) @ ( hAPP @ SY459 @ ( fun @ SV33 @ ( product_prod @ SY459 @ SV33 ) ) @ ( product_Pair @ SY459 @ SV33 ) @ SY461 ) @ SY462 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(377,plain,
! [SV34: $i] :
( ( ! [SY463: $i,SY464: $i,SY465: $i,SY466: $i] :
( ( ( hAPP @ SV34 @ ( option @ SY463 ) @ SY464 @ SY465 )
!= ( hAPP @ SY463 @ ( option @ SY463 ) @ ( some @ SY463 ) @ SY466 ) )
| ( ( hAPP @ ( option @ SY463 ) @ ( fun @ SV34 @ ( option @ SY463 ) ) @ ( hAPP @ SV34 @ ( fun @ ( option @ SY463 ) @ ( fun @ SV34 @ ( option @ SY463 ) ) ) @ ( hAPP @ ( fun @ SV34 @ ( option @ SY463 ) ) @ ( fun @ SV34 @ ( fun @ ( option @ SY463 ) @ ( fun @ SV34 @ ( option @ SY463 ) ) ) ) @ ( fun_upd @ SV34 @ ( option @ SY463 ) ) @ SY464 ) @ SY465 ) @ ( hAPP @ SY463 @ ( option @ SY463 ) @ ( some @ SY463 ) @ SY466 ) )
= ( ti @ ( fun @ SV34 @ ( option @ SY463 ) ) @ SY464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(378,plain,
! [SV35: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( ti @ bool @ SV35 ) )
| ( hBOOL @ SV35 ) )
| ~ ( ~ ( hBOOL @ SV35 )
| ( hBOOL @ ( ti @ bool @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(379,plain,
! [SV36: $i] :
( ( ! [SY467: $i,SY468: $i,SY469: $i,SY470: $i] :
~ ! [SY471: $i,SY472: $i,SY473: $i,SY474: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) ) @ SY470 )
!= ( hAPP @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) ) @ SY471 ) @ ( hAPP @ ( product_prod @ SY468 @ SY469 ) @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) @ ( hAPP @ SY467 @ ( fun @ ( product_prod @ SY468 @ SY469 ) @ ( product_prod @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) ) @ ( product_Pair @ SY467 @ ( product_prod @ SY468 @ SY469 ) ) @ SY472 ) @ ( hAPP @ SY469 @ ( product_prod @ SY468 @ SY469 ) @ ( hAPP @ SY468 @ ( fun @ SY469 @ ( product_prod @ SY468 @ SY469 ) ) @ ( product_Pair @ SY468 @ SY469 ) @ SY473 ) @ SY474 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(380,plain,
! [SV37: $i] :
( ( ! [SY475: $i,SY476: $i] :
~ ! [SY477: $i,SY478: $i] :
( ( ti @ ( product_prod @ SV37 @ SY475 ) @ SY476 )
!= ( hAPP @ SY475 @ ( product_prod @ SV37 @ SY475 ) @ ( hAPP @ SV37 @ ( fun @ SY475 @ ( product_prod @ SV37 @ SY475 ) ) @ ( product_Pair @ SV37 @ SY475 ) @ SY477 ) @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(381,plain,
! [SV38: $i] :
( ( ! [SY479: $i,SY480: $i,SY481: $i] :
~ ! [SY482: $i,SY483: $i,SY484: $i] :
( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SY479 @ SY480 ) ) @ SY481 )
!= ( hAPP @ ( product_prod @ SY479 @ SY480 ) @ ( product_prod @ SV38 @ ( product_prod @ SY479 @ SY480 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SY479 @ SY480 ) @ ( product_prod @ SV38 @ ( product_prod @ SY479 @ SY480 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SY479 @ SY480 ) ) @ SY482 ) @ ( hAPP @ SY480 @ ( product_prod @ SY479 @ SY480 ) @ ( hAPP @ SY479 @ ( fun @ SY480 @ ( product_prod @ SY479 @ SY480 ) ) @ ( product_Pair @ SY479 @ SY480 ) @ SY483 ) @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(382,plain,
! [SV39: $i] :
( ( ! [SY485: $i,SY486: $i,SY487: $i,SY488: $i,SY489: $i] :
~ ( ~ ( ( ( ti @ SY485 @ SY488 )
!= ( ti @ SY485 @ SY489 ) )
| ( ( hAPP @ SY485 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SY485 @ SV39 ) @ ( hAPP @ SY485 @ ( fun @ SV39 @ ( fun @ SY485 @ SV39 ) ) @ ( hAPP @ ( fun @ SY485 @ SV39 ) @ ( fun @ SY485 @ ( fun @ SV39 @ ( fun @ SY485 @ SV39 ) ) ) @ ( fun_upd @ SY485 @ SV39 ) @ SY486 ) @ SY489 ) @ SY487 ) @ SY488 )
= ( ti @ SV39 @ SY487 ) ) )
| ~ ( ~ ( ( ( ti @ SY485 @ SY488 )
!= ( ti @ SY485 @ SY489 ) ) )
| ( ( hAPP @ SY485 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SY485 @ SV39 ) @ ( hAPP @ SY485 @ ( fun @ SV39 @ ( fun @ SY485 @ SV39 ) ) @ ( hAPP @ ( fun @ SY485 @ SV39 ) @ ( fun @ SY485 @ ( fun @ SV39 @ ( fun @ SY485 @ SV39 ) ) ) @ ( fun_upd @ SY485 @ SV39 ) @ SY486 ) @ SY489 ) @ SY487 ) @ SY488 )
= ( hAPP @ SY485 @ SV39 @ SY486 @ SY488 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(383,plain,
! [SV40: $i] :
( ( ! [SY490: $i,SY491: $i,SY492: $i,SY493: $i,SY494: $i] :
~ ! [SY495: $i,SY496: $i,SY497: $i,SY498: $i,SY499: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) ) @ SY494 )
!= ( hAPP @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) ) @ SY495 ) @ ( hAPP @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) @ ( hAPP @ SY490 @ ( fun @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) @ ( product_prod @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) ) @ ( product_Pair @ SY490 @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) @ SY496 ) @ ( hAPP @ ( product_prod @ SY492 @ SY493 ) @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) @ ( hAPP @ SY491 @ ( fun @ ( product_prod @ SY492 @ SY493 ) @ ( product_prod @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) ) @ ( product_Pair @ SY491 @ ( product_prod @ SY492 @ SY493 ) ) @ SY497 ) @ ( hAPP @ SY493 @ ( product_prod @ SY492 @ SY493 ) @ ( hAPP @ SY492 @ ( fun @ SY493 @ ( product_prod @ SY492 @ SY493 ) ) @ ( product_Pair @ SY492 @ SY493 ) @ SY498 ) @ SY499 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(384,plain,
! [SV41: $i] :
( ( ! [SY500: $i,SY501: $i,SY502: $i,SY503: $i] :
( ~ ! [SY504: $i,SY505: $i,SY506: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SY500 @ SY501 ) ) @ bool @ SY503 @ ( hAPP @ ( product_prod @ SY500 @ SY501 ) @ ( product_prod @ SV41 @ ( product_prod @ SY500 @ SY501 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SY500 @ SY501 ) @ ( product_prod @ SV41 @ ( product_prod @ SY500 @ SY501 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SY500 @ SY501 ) ) @ SY504 ) @ ( hAPP @ SY501 @ ( product_prod @ SY500 @ SY501 ) @ ( hAPP @ SY500 @ ( fun @ SY501 @ ( product_prod @ SY500 @ SY501 ) ) @ ( product_Pair @ SY500 @ SY501 ) @ SY505 ) @ SY506 ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SY500 @ SY501 ) ) @ bool @ SY503 @ SY502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(385,plain,
! [SV42: $i] :
( ( ! [SY507: $i,SY508: $i,SY509: $i,SY510: $i,SY511: $i,SY512: $i] :
( ~ ! [SY513: $i,SY514: $i,SY515: $i,SY516: $i,SY517: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) ) @ bool @ SY512 @ ( hAPP @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) ) @ SY513 ) @ ( hAPP @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) @ ( hAPP @ SY507 @ ( fun @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) ) @ ( product_Pair @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) @ SY514 ) @ ( hAPP @ ( product_prod @ SY509 @ SY510 ) @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) @ ( hAPP @ SY508 @ ( fun @ ( product_prod @ SY509 @ SY510 ) @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) @ ( product_Pair @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) @ SY515 ) @ ( hAPP @ SY510 @ ( product_prod @ SY509 @ SY510 ) @ ( hAPP @ SY509 @ ( fun @ SY510 @ ( product_prod @ SY509 @ SY510 ) ) @ ( product_Pair @ SY509 @ SY510 ) @ SY516 ) @ SY517 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SY507 @ ( product_prod @ SY508 @ ( product_prod @ SY509 @ SY510 ) ) ) ) @ bool @ SY512 @ SY511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(386,plain,
! [SV43: $i] :
( ( ! [SY518: $i,SY519: $i,SY520: $i,SY521: $i,SY522: $i,SY523: $i] :
~ ( ~ ( ( ( hAPP @ SV43 @ ( option @ SY518 ) @ ( hAPP @ ( option @ SY518 ) @ ( fun @ SV43 @ ( option @ SY518 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SY518 ) @ ( fun @ SV43 @ ( option @ SY518 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SY518 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SY518 ) @ ( fun @ SV43 @ ( option @ SY518 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SY518 ) ) @ SY519 ) @ SY520 ) @ ( hAPP @ SY518 @ ( option @ SY518 ) @ ( some @ SY518 ) @ SY521 ) ) @ SY522 )
!= ( hAPP @ SY518 @ ( option @ SY518 ) @ ( some @ SY518 ) @ SY523 ) )
| ~ ( ( ( ti @ SV43 @ SY522 )
!= ( ti @ SV43 @ SY520 ) )
| ( ( ti @ SY518 @ SY521 )
!= ( ti @ SY518 @ SY523 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY522 )
!= ( ti @ SV43 @ SY520 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SY518 ) @ SY519 @ SY522 )
!= ( hAPP @ SY518 @ ( option @ SY518 ) @ ( some @ SY518 ) @ SY523 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SY522 )
!= ( ti @ SV43 @ SY520 ) )
| ( ( ti @ SY518 @ SY521 )
!= ( ti @ SY518 @ SY523 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY522 )
!= ( ti @ SV43 @ SY520 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SY518 ) @ SY519 @ SY522 )
!= ( hAPP @ SY518 @ ( option @ SY518 ) @ ( some @ SY518 ) @ SY523 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SY518 ) @ ( hAPP @ ( option @ SY518 ) @ ( fun @ SV43 @ ( option @ SY518 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SY518 ) @ ( fun @ SV43 @ ( option @ SY518 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SY518 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SY518 ) @ ( fun @ SV43 @ ( option @ SY518 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SY518 ) ) @ SY519 ) @ SY520 ) @ ( hAPP @ SY518 @ ( option @ SY518 ) @ ( some @ SY518 ) @ SY521 ) ) @ SY522 )
= ( hAPP @ SY518 @ ( option @ SY518 ) @ ( some @ SY518 ) @ SY523 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(387,plain,
! [SV44: $i] :
( ( ! [SY524: $i,SY525: $i,SY526: $i,SY527: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SY524 @ ( fun @ SV44 @ bool ) @ SY525 @ SY526 ) @ SY527 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SY524 @ SV44 ) @ bool @ ( hAPP @ ( fun @ SY524 @ ( fun @ SV44 @ bool ) ) @ ( fun @ ( product_prod @ SY524 @ SV44 ) @ bool ) @ ( product_prod_case @ SY524 @ SV44 @ bool ) @ SY525 ) @ ( hAPP @ SV44 @ ( product_prod @ SY524 @ SV44 ) @ ( hAPP @ SY524 @ ( fun @ SV44 @ ( product_prod @ SY524 @ SV44 ) ) @ ( product_Pair @ SY524 @ SV44 ) @ SY526 ) @ SY527 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(388,plain,
! [SV45: $i] :
( ( ! [SY528: $i,SY529: $i,SY530: $i,SY531: $i] :
~ ( ~ ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY528 ) @ SY529 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY530 ) @ SY531 ) )
| ~ ( ( SY528 != SY530 )
| ( SY529 != SY531 ) ) )
| ~ ( ~ ~ ( ( SY528 != SY530 )
| ( SY529 != SY531 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY528 ) @ SY529 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY530 ) @ SY531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(389,plain,
! [SV46: $i] :
( ( ! [SY532: $i,SY533: $i,SY534: $i,SY535: $i,SY536: $i,SY537: $i,SY538: $i] :
( ~ ! [SY539: $i,SY540: $i,SY541: $i,SY542: $i,SY543: $i,SY544: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) ) @ bool @ SY538 @ ( hAPP @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) ) @ SY539 ) @ ( hAPP @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) @ ( hAPP @ SY532 @ ( fun @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) ) @ ( product_Pair @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) @ SY540 ) @ ( hAPP @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) @ ( hAPP @ SY533 @ ( fun @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) @ ( product_Pair @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) @ SY541 ) @ ( hAPP @ ( product_prod @ SY535 @ SY536 ) @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) @ ( hAPP @ SY534 @ ( fun @ ( product_prod @ SY535 @ SY536 ) @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) @ ( product_Pair @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) @ SY542 ) @ ( hAPP @ SY536 @ ( product_prod @ SY535 @ SY536 ) @ ( hAPP @ SY535 @ ( fun @ SY536 @ ( product_prod @ SY535 @ SY536 ) ) @ ( product_Pair @ SY535 @ SY536 ) @ SY543 ) @ SY544 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SY532 @ ( product_prod @ SY533 @ ( product_prod @ SY534 @ ( product_prod @ SY535 @ SY536 ) ) ) ) ) @ bool @ SY538 @ SY537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(390,plain,
! [SV47: $i] :
( ( ! [SY545: $i,SY546: $i,SY547: $i,SY548: $i,SY549: $i,SY550: $i] :
~ ! [SY551: $i,SY552: $i,SY553: $i,SY554: $i,SY555: $i,SY556: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) ) @ SY550 )
!= ( hAPP @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) ) @ SY551 ) @ ( hAPP @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) @ ( hAPP @ SY545 @ ( fun @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) @ ( product_prod @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) ) @ ( product_Pair @ SY545 @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) @ SY552 ) @ ( hAPP @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) @ ( hAPP @ SY546 @ ( fun @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) @ ( product_prod @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) ) @ ( product_Pair @ SY546 @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) @ SY553 ) @ ( hAPP @ ( product_prod @ SY548 @ SY549 ) @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) @ ( hAPP @ SY547 @ ( fun @ ( product_prod @ SY548 @ SY549 ) @ ( product_prod @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) ) @ ( product_Pair @ SY547 @ ( product_prod @ SY548 @ SY549 ) ) @ SY554 ) @ ( hAPP @ SY549 @ ( product_prod @ SY548 @ SY549 ) @ ( hAPP @ SY548 @ ( fun @ SY549 @ ( product_prod @ SY548 @ SY549 ) ) @ ( product_Pair @ SY548 @ SY549 ) @ SY555 ) @ SY556 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(391,plain,
! [SV48: $i] :
( ( ! [SY557: $i,SY558: $i,SY559: $i,SY560: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV48 @ SY557 ) @ bool @ ( hAPP @ ( fun @ SV48 @ ( fun @ SY557 @ bool ) ) @ ( fun @ ( product_prod @ SV48 @ SY557 ) @ bool ) @ ( product_prod_case @ SV48 @ SY557 @ bool ) @ SY558 ) @ ( hAPP @ SY557 @ ( product_prod @ SV48 @ SY557 ) @ ( hAPP @ SV48 @ ( fun @ SY557 @ ( product_prod @ SV48 @ SY557 ) ) @ ( product_Pair @ SV48 @ SY557 ) @ SY559 ) @ SY560 ) ) )
| ( hBOOL @ ( hAPP @ SY557 @ bool @ ( hAPP @ SV48 @ ( fun @ SY557 @ bool ) @ SY558 @ SY559 ) @ SY560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(392,plain,
! [SV49: $i] :
( ( ! [SY561: $i,SY562: $i,SY563: $i,SY564: $i,SY565: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY561 ) @ SY562 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY563 ) @ SY564 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY565 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SY561 ) ) @ SY562 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SY563 ) ) @ SY564 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY565 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(393,plain,
! [SV50: $i] :
( ( ! [SY566: $i,SY567: $i,SY568: $i] :
~ ( ~ ( ~ ! [SY569: $i,SY570: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY569 ) @ SY570 ) ) @ SY568 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY569 ) @ SY570 ) ) @ SY567 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY569 ) @ SY570 ) ) @ SY567 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY569 ) @ SY570 ) ) @ SY568 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ SY568 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ SY567 ) ) )
| ~ ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ SY568 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ SY567 ) )
| ! [SY571: $i,SY572: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY571 ) @ SY572 ) ) @ SY568 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY571 ) @ SY572 ) ) @ SY567 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY571 ) @ SY572 ) ) @ SY567 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SY566 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SY566 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SY566 ) ) @ ( hAPP @ SY566 @ ( product_prod @ SV50 @ SY566 ) @ ( hAPP @ SV50 @ ( fun @ SY566 @ ( product_prod @ SV50 @ SY566 ) ) @ ( product_Pair @ SV50 @ SY566 ) @ SY571 ) @ SY572 ) ) @ SY568 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(394,plain,
! [SV51: $i] :
( ( ! [SY573: $i,SY574: $i,SY575: $i] :
( ~ ! [SY576: $i] :
( ( hAPP @ SV51 @ SY573 @ SY574 @ SY576 )
= ( hAPP @ SV51 @ SY573 @ SY575 @ SY576 ) )
| ( ( ti @ ( fun @ SV51 @ SY573 ) @ SY574 )
= ( ti @ ( fun @ SV51 @ SY573 ) @ SY575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(395,plain,
! [SV52: $i] :
( ( ! [SY577: $i,SY578: $i] :
~ ( ~ ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SY577 )
!= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SY578 ) )
| ( SY577 = SY578 ) )
| ~ ( ( SY577 != SY578 )
| ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SY577 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SY578 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(396,plain,
! [SV53: $i] :
( ( ! [SY579: $i,SY580: $i] :
~ ( ~ ( ~ ~ ! [SY581: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SY579 ) @ bool @ SY580 @ SY581 ) )
| ~ ! [SY582: $i] :
~ ~ ! [SY583: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SY579 ) @ bool @ SY580 @ ( hAPP @ SY579 @ ( product_prod @ SV53 @ SY579 ) @ ( hAPP @ SV53 @ ( fun @ SY579 @ ( product_prod @ SV53 @ SY579 ) ) @ ( product_Pair @ SV53 @ SY579 ) @ SY582 ) @ SY583 ) ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ! [SY585: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SY579 ) @ bool @ SY580 @ ( hAPP @ SY579 @ ( product_prod @ SV53 @ SY579 ) @ ( hAPP @ SV53 @ ( fun @ SY579 @ ( product_prod @ SV53 @ SY579 ) ) @ ( product_Pair @ SV53 @ SY579 ) @ SY584 ) @ SY585 ) ) )
| ~ ! [SY586: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SY579 ) @ bool @ SY580 @ SY586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(397,plain,
! [SV54: $i] :
( ( ! [SY587: $i,SY588: $i,SY589: $i,SY590: $i,SY591: $i,SY592: $i] :
( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SY587 @ SY588 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SY587 @ ( fun @ SY588 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SY587 @ SY588 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SY587 @ SY588 @ ( fun @ SV54 @ bool ) ) @ SY589 ) @ ( hAPP @ SY588 @ ( product_prod @ SY587 @ SY588 ) @ ( hAPP @ SY587 @ ( fun @ SY588 @ ( product_prod @ SY587 @ SY588 ) ) @ ( product_Pair @ SY587 @ SY588 ) @ SY590 ) @ SY591 ) ) @ SY592 ) )
| ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SY588 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SY587 @ ( fun @ SY588 @ ( fun @ SV54 @ bool ) ) @ SY589 @ SY590 ) @ SY591 ) @ SY592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(398,plain,
! [SV55: $i] :
( ( ! [SY593: $i,SY594: $i,SY595: $i,SY596: $i,SY597: $i] :
( ( ( hAPP @ SV55 @ ( product_prod @ SY593 @ SV55 ) @ ( hAPP @ SY593 @ ( fun @ SV55 @ ( product_prod @ SY593 @ SV55 ) ) @ ( product_Pair @ SY593 @ SV55 ) @ SY594 ) @ SY595 )
!= ( hAPP @ SV55 @ ( product_prod @ SY593 @ SV55 ) @ ( hAPP @ SY593 @ ( fun @ SV55 @ ( product_prod @ SY593 @ SV55 ) ) @ ( product_Pair @ SY593 @ SV55 ) @ SY596 ) @ SY597 ) )
| ~ ( ( ( ti @ SY593 @ SY594 )
!= ( ti @ SY593 @ SY596 ) )
| ( ( ti @ SV55 @ SY595 )
!= ( ti @ SV55 @ SY597 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(399,plain,
! [SV56: $i] :
( ( ! [SY598: $i,SY599: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SY598 ) @ SY599 ) )
| ( hBOOL @ ( hAPP @ SV56 @ bool @ SY599 @ SY598 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV56 @ bool @ SY599 @ SY598 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SY598 ) @ SY599 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(400,plain,
! [SV57: $i] :
( ( ! [SY600: $i,SY601: $i] :
~ ( ~ ( ~ ! [SY602: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SY600 ) @ bool @ SY601 @ SY602 ) )
| ! [SY603: $i,SY604: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SY600 ) @ bool @ SY601 @ ( hAPP @ SY600 @ ( product_prod @ SV57 @ SY600 ) @ ( hAPP @ SV57 @ ( fun @ SY600 @ ( product_prod @ SV57 @ SY600 ) ) @ ( product_Pair @ SV57 @ SY600 ) @ SY603 ) @ SY604 ) ) ) )
| ~ ( ~ ! [SY605: $i,SY606: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SY600 ) @ bool @ SY601 @ ( hAPP @ SY600 @ ( product_prod @ SV57 @ SY600 ) @ ( hAPP @ SV57 @ ( fun @ SY600 @ ( product_prod @ SV57 @ SY600 ) ) @ ( product_Pair @ SV57 @ SY600 ) @ SY605 ) @ SY606 ) ) )
| ! [SY607: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SY600 ) @ bool @ SY601 @ SY607 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(401,plain,
! [SV58: $i] :
( ( ! [SY608: $i,SY609: $i,SY610: $i,SY611: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SY608 ) @ SY609 ) @ SY610 ) @ SY611 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY608 ) @ SY609 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY610 ) @ SY611 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY608 ) @ SY609 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY610 ) @ SY611 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SY608 ) @ SY609 ) @ SY610 ) @ SY611 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(402,plain,
! [SV59: $i] :
( ( ! [SY612: $i,SY613: $i,SY614: $i,SY615: $i] :
( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SY613 ) @ SY614 ) @ SY615 ) )
| ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SY613 ) @ SY615 ) @ SY612 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SY613 ) @ SY614 ) @ SY612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(403,plain,
! [SV60: $i] :
( ( ! [SY616: $i,SY617: $i,SY618: $i,SY619: $i] :
~ ( ~ ( ( ( hAPP @ SV60 @ ( fun @ SY616 @ SV60 ) @ ( hAPP @ SY616 @ ( fun @ SV60 @ ( fun @ SY616 @ SV60 ) ) @ ( hAPP @ ( fun @ SY616 @ SV60 ) @ ( fun @ SY616 @ ( fun @ SV60 @ ( fun @ SY616 @ SV60 ) ) ) @ ( fun_upd @ SY616 @ SV60 ) @ SY617 ) @ SY618 ) @ SY619 )
!= ( ti @ ( fun @ SY616 @ SV60 ) @ SY617 ) )
| ( ( hAPP @ SY616 @ SV60 @ SY617 @ SY618 )
= ( ti @ SV60 @ SY619 ) ) )
| ~ ( ( ( hAPP @ SY616 @ SV60 @ SY617 @ SY618 )
!= ( ti @ SV60 @ SY619 ) )
| ( ( hAPP @ SV60 @ ( fun @ SY616 @ SV60 ) @ ( hAPP @ SY616 @ ( fun @ SV60 @ ( fun @ SY616 @ SV60 ) ) @ ( hAPP @ ( fun @ SY616 @ SV60 ) @ ( fun @ SY616 @ ( fun @ SV60 @ ( fun @ SY616 @ SV60 ) ) ) @ ( fun_upd @ SY616 @ SV60 ) @ SY617 ) @ SY618 ) @ SY619 )
= ( ti @ ( fun @ SY616 @ SV60 ) @ SY617 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(404,plain,
! [SV61: $i,SV1: $i] :
( ( ( ti @ ( fun @ ( fun @ SV1 @ SV61 ) @ ( fun @ SV1 @ ( fun @ SV61 @ ( fun @ SV1 @ SV61 ) ) ) ) @ ( fun_upd @ SV1 @ SV61 ) )
= ( fun_upd @ SV1 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(405,plain,
! [SV62: $i,SV3: $i] :
( ( ( ti @ ( fun @ SV3 @ ( fun @ SV62 @ ( product_prod @ SV3 @ SV62 ) ) ) @ ( product_Pair @ SV3 @ SV62 ) )
= ( product_Pair @ SV3 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(406,plain,
! [SV63: $i,SV4: $i] :
( ( ! [SY620: $i,SY621: $i] :
( ( hAPP @ SV4 @ SV63 @ ( ti @ ( fun @ SV4 @ SV63 ) @ SY620 ) @ SY621 )
= ( hAPP @ SV4 @ SV63 @ SY620 @ SY621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(407,plain,
! [SV64: $i,SV5: $i] :
( ( ! [SY622: $i,SY623: $i] :
( ( hAPP @ SV5 @ SV64 @ SY622 @ ( ti @ SV5 @ SY623 ) )
= ( hAPP @ SV5 @ SV64 @ SY622 @ SY623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(408,plain,
! [SV65: $i,SV6: $i] :
( ( ! [SY624: $i,SY625: $i] :
( ( ti @ SV6 @ ( hAPP @ SV65 @ SV6 @ SY624 @ SY625 ) )
= ( hAPP @ SV65 @ SV6 @ SY624 @ SY625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(409,plain,
! [SV66: $i,SV8: $i] :
( ( ! [SY626: $i,SY627: $i] :
( ( hAPP @ SV8 @ ( fun @ SV66 @ SV8 ) @ ( hAPP @ SV66 @ ( fun @ SV8 @ ( fun @ SV66 @ SV8 ) ) @ ( hAPP @ ( fun @ SV66 @ SV8 ) @ ( fun @ SV66 @ ( fun @ SV8 @ ( fun @ SV66 @ SV8 ) ) ) @ ( fun_upd @ SV66 @ SV8 ) @ SY626 ) @ SY627 ) @ ( hAPP @ SV66 @ SV8 @ SY626 @ SY627 ) )
= ( ti @ ( fun @ SV66 @ SV8 ) @ SY626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(410,plain,
! [SV67: $i,SV9: $i] :
( ( ! [SY628: $i,SY629: $i,SY630: $i] :
( ( hAPP @ SV9 @ SV67 @ ( hAPP @ SV67 @ ( fun @ SV9 @ SV67 ) @ ( hAPP @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) @ ( hAPP @ ( fun @ SV9 @ SV67 ) @ ( fun @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) ) @ ( fun_upd @ SV9 @ SV67 ) @ SY628 ) @ SY629 ) @ SY630 ) @ SY629 )
= ( ti @ SV67 @ SY630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(411,plain,
! [SV68: $i,SV10: $i] :
( ( ! [SY631: $i,SY632: $i,SY633: $i,SY634: $i] :
( ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SY631 ) @ SY632 ) @ SY633 ) ) @ SY632 ) @ SY634 )
= ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SY631 ) @ SY632 ) @ SY634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(412,plain,
! [SV69: $i,SV11: $i] :
( ( ! [SY635: $i] : ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV11 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV11 ) @ SV69 ) @ SY635 ) @ SY635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(413,plain,
! [SV70: $i,SV12: $i] :
( ( ! [SY636: $i,SY637: $i,SY638: $i,SY639: $i] :
( ( hAPP @ ( product_prod @ SV12 @ SV70 ) @ SY636 @ ( hAPP @ ( fun @ SV12 @ ( fun @ SV70 @ SY636 ) ) @ ( fun @ ( product_prod @ SV12 @ SV70 ) @ SY636 ) @ ( product_prod_rec @ SV12 @ SV70 @ SY636 ) @ SY637 ) @ ( hAPP @ SV70 @ ( product_prod @ SV12 @ SV70 ) @ ( hAPP @ SV12 @ ( fun @ SV70 @ ( product_prod @ SV12 @ SV70 ) ) @ ( product_Pair @ SV12 @ SV70 ) @ SY638 ) @ SY639 ) )
= ( hAPP @ SV70 @ SY636 @ ( hAPP @ SV12 @ ( fun @ SV70 @ SY636 ) @ SY637 @ SY638 ) @ SY639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(414,plain,
! [SV71: $i,SV13: $i] :
( ( ! [SY640: $i,SY641: $i,SY642: $i,SY643: $i] :
( ( hAPP @ ( product_prod @ SV13 @ SV71 ) @ SY640 @ ( hAPP @ ( fun @ SV13 @ ( fun @ SV71 @ SY640 ) ) @ ( fun @ ( product_prod @ SV13 @ SV71 ) @ SY640 ) @ ( produc1605651328_split @ SV13 @ SV71 @ SY640 ) @ SY641 ) @ ( hAPP @ SV71 @ ( product_prod @ SV13 @ SV71 ) @ ( hAPP @ SV13 @ ( fun @ SV71 @ ( product_prod @ SV13 @ SV71 ) ) @ ( product_Pair @ SV13 @ SV71 ) @ SY642 ) @ SY643 ) )
= ( hAPP @ SV71 @ SY640 @ ( hAPP @ SV13 @ ( fun @ SV71 @ SY640 ) @ SY641 @ SY642 ) @ SY643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(415,plain,
! [SV72: $i,SV14: $i] :
( ( ! [SY644: $i,SY645: $i,SY646: $i,SY647: $i] :
( ( hAPP @ ( product_prod @ SV14 @ SV72 ) @ SY644 @ ( hAPP @ ( fun @ SV14 @ ( fun @ SV72 @ SY644 ) ) @ ( fun @ ( product_prod @ SV14 @ SV72 ) @ SY644 ) @ ( product_prod_case @ SV14 @ SV72 @ SY644 ) @ SY645 ) @ ( hAPP @ SV72 @ ( product_prod @ SV14 @ SV72 ) @ ( hAPP @ SV14 @ ( fun @ SV72 @ ( product_prod @ SV14 @ SV72 ) ) @ ( product_Pair @ SV14 @ SV72 ) @ SY646 ) @ SY647 ) )
= ( hAPP @ SV72 @ SY644 @ ( hAPP @ SV14 @ ( fun @ SV72 @ SY644 ) @ SY645 @ SY646 ) @ SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(416,plain,
! [SV73: $i,SV15: $i] :
( ( ! [SY648: $i,SY649: $i,SY650: $i,SY651: $i] :
( ( hAPP @ ( product_prod @ SV15 @ SV73 ) @ SY648 @ ( hAPP @ ( fun @ SV15 @ ( fun @ SV73 @ SY648 ) ) @ ( fun @ ( product_prod @ SV15 @ SV73 ) @ SY648 ) @ ( product_prod_case @ SV15 @ SV73 @ SY648 ) @ SY649 ) @ ( hAPP @ SV73 @ ( product_prod @ SV15 @ SV73 ) @ ( hAPP @ SV15 @ ( fun @ SV73 @ ( product_prod @ SV15 @ SV73 ) ) @ ( product_Pair @ SV15 @ SV73 ) @ SY650 ) @ SY651 ) )
= ( hAPP @ SV73 @ SY648 @ ( hAPP @ SV15 @ ( fun @ SV73 @ SY648 ) @ SY649 @ SY650 ) @ SY651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(417,plain,
! [SV74: $i,SV16: $i] :
( ( ! [SY652: $i,SY653: $i,SY654: $i] :
~ ! [SY655: $i] :
( ( hAPP @ SV16 @ ( option @ SV74 ) @ ( hAPP @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( hAPP @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) @ ( hAPP @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( fun @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) ) @ ( fun_upd @ SV16 @ ( option @ SV74 ) ) @ SY652 ) @ SY653 ) @ ( hAPP @ SV74 @ ( option @ SV74 ) @ ( some @ SV74 ) @ SY654 ) ) @ SY655 )
= ( none @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(418,plain,
! [SV75: $i,SV17: $i] :
( ( ! [SY656: $i,SY657: $i,SY658: $i,SY659: $i] :
( ( hAPP @ SV17 @ SV75 @ ( hAPP @ ( fun @ SV17 @ SY656 ) @ ( fun @ SV17 @ SV75 ) @ ( hAPP @ ( fun @ SY656 @ SV75 ) @ ( fun @ ( fun @ SV17 @ SY656 ) @ ( fun @ SV17 @ SV75 ) ) @ ( combb @ SY656 @ SV75 @ SV17 ) @ SY657 ) @ SY658 ) @ SY659 )
= ( hAPP @ SY656 @ SV75 @ SY657 @ ( hAPP @ SV17 @ SY656 @ SY658 @ SY659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(419,plain,
! [SV76: $i,SV18: $i] :
( ( ! [SY660: $i,SY661: $i,SY662: $i,SY663: $i] :
( ( hAPP @ SV18 @ SV76 @ ( hAPP @ SY660 @ ( fun @ SV18 @ SV76 ) @ ( hAPP @ ( fun @ SV18 @ ( fun @ SY660 @ SV76 ) ) @ ( fun @ SY660 @ ( fun @ SV18 @ SV76 ) ) @ ( combc @ SV18 @ SY660 @ SV76 ) @ SY661 ) @ SY662 ) @ SY663 )
= ( hAPP @ SY660 @ SV76 @ ( hAPP @ SV18 @ ( fun @ SY660 @ SV76 ) @ SY661 @ SY663 ) @ SY662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(420,plain,
! [SV77: $i,SV19: $i] :
( ( ! [SY664: $i,SY665: $i,SY666: $i,SY667: $i] :
( ( hAPP @ SV19 @ SV77 @ ( hAPP @ ( fun @ SV19 @ SY664 ) @ ( fun @ SV19 @ SV77 ) @ ( hAPP @ ( fun @ SV19 @ ( fun @ SY664 @ SV77 ) ) @ ( fun @ ( fun @ SV19 @ SY664 ) @ ( fun @ SV19 @ SV77 ) ) @ ( combs @ SV19 @ SY664 @ SV77 ) @ SY665 ) @ SY666 ) @ SY667 )
= ( hAPP @ SY664 @ SV77 @ ( hAPP @ SV19 @ ( fun @ SY664 @ SV77 ) @ SY665 @ SY667 ) @ ( hAPP @ SV19 @ SY664 @ SY666 @ SY667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(421,plain,
! [SV20: $i,SV78: $i] :
( ( ~ ( hBOOL @ SV78 )
| ~ ( hBOOL @ SV20 )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV78 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(422,plain,
! [SV79: $i,SV21: $i] :
( ( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV21 ) @ SV79 ) )
| ( hBOOL @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(423,plain,
! [SV80: $i,SV22: $i] :
( ( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV22 ) @ SV80 ) )
| ( hBOOL @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(424,plain,
! [SV81: $i,SV23: $i] :
( ( ! [SY668: $i,SY669: $i,SY670: $i,SY671: $i] :
~ ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY668 ) @ SY669 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY670 ) @ SY671 ) )
| ~ ( ( ( ti @ SV81 @ SY668 )
!= ( ti @ SV81 @ SY670 ) )
| ( ( ti @ SV23 @ SY669 )
!= ( ti @ SV23 @ SY671 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV81 @ SY668 )
!= ( ti @ SV81 @ SY670 ) )
| ( ( ti @ SV23 @ SY669 )
!= ( ti @ SV23 @ SY671 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY668 ) @ SY669 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY670 ) @ SY671 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(425,plain,
! [SV24: $i,SV82: $i] :
( ( ! [SY672: $i,SY673: $i,SY674: $i,SY675: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV82 ) @ SY672 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY673 ) @ SY674 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY675 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV82 ) @ SV24 ) ) @ SY672 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SY673 ) @ SV24 ) ) @ SY674 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY675 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(426,plain,
! [SV25: $i,SV83: $i] :
( ( ! [SY676: $i,SY677: $i,SY678: $i,SY679: $i] :
~ ( ~ ( ( ( ti @ SV83 @ SY679 )
!= ( ti @ SV83 @ SY678 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SY676 ) @ SY678 ) @ SY677 ) @ SY679 )
= ( ti @ SV25 @ SY677 ) ) )
| ~ ( ~ ( ( ( ti @ SV83 @ SY679 )
!= ( ti @ SV83 @ SY678 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SY676 ) @ SY678 ) @ SY677 ) @ SY679 )
= ( hAPP @ SV83 @ SV25 @ SY676 @ SY679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(427,plain,
! [SV84: $i,SV26: $i] :
( ( ! [SY680: $i,SY681: $i,SY682: $i,SY683: $i] :
( ~ ! [SY684: $i,SY685: $i,SY686: $i,SY687: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) ) @ bool @ SY683 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) ) @ SY684 ) @ ( hAPP @ ( product_prod @ SY680 @ SY681 ) @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SY680 @ SY681 ) @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) @ SY685 ) @ ( hAPP @ SY681 @ ( product_prod @ SY680 @ SY681 ) @ ( hAPP @ SY680 @ ( fun @ SY681 @ ( product_prod @ SY680 @ SY681 ) ) @ ( product_Pair @ SY680 @ SY681 ) @ SY686 ) @ SY687 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SY680 @ SY681 ) ) ) @ bool @ SY683 @ SY682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(428,plain,
! [SV27: $i,SV85: $i] :
( ( ! [SY688: $i,SY689: $i,SY690: $i,SY691: $i] :
( ~ ( ( ( ti @ SV85 @ SY690 )
!= ( ti @ SV85 @ SY691 ) ) )
| ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SY688 ) @ SY691 ) @ SY689 ) @ SY690 )
= ( hAPP @ SV85 @ SV27 @ SY688 @ SY690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(429,plain,
! [SV86: $i,SV28: $i] :
( ( ! [SY692: $i,SY693: $i,SY694: $i,SY695: $i,SY696: $i] :
( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SY692 ) @ SY693 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY694 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SY695 ) @ SY693 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY696 ) ) )
| ( ( ti @ SV28 @ SY694 )
= ( ti @ SV28 @ SY696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(430,plain,
! [SV87: $i,SV29: $i] :
( ( ! [SY697: $i] :
~ ! [SY698: $i,SY699: $i] :
( ( ti @ ( product_prod @ SV29 @ SV87 ) @ SY697 )
!= ( hAPP @ SV87 @ ( product_prod @ SV29 @ SV87 ) @ ( hAPP @ SV29 @ ( fun @ SV87 @ ( product_prod @ SV29 @ SV87 ) ) @ ( product_Pair @ SV29 @ SV87 ) @ SY698 ) @ SY699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(431,plain,
! [SV30: $i,SV88: $i] :
( ( ! [SY700: $i,SY701: $i,SY702: $i,SY703: $i,SY704: $i] :
( ~ ( ( ( ti @ SV88 @ SY703 )
!= ( ti @ SV88 @ SY704 ) ) )
| ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SY700 ) @ SY703 ) @ SY701 ) ) @ SY704 ) @ SY702 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SY700 ) @ SY704 ) @ SY702 ) ) @ SY703 ) @ SY701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(432,plain,
! [SV89: $i,SV31: $i] :
( ( ! [SY705: $i,SY706: $i,SY707: $i,SY708: $i,SY709: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SY706 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SY705 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SY707 @ SY708 ) @ SY709 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SY706 ) @ ( hAPP @ ( product_prod @ SY705 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SY705 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SY705 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SY705 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SY707 ) @ ( hAPP @ SV89 @ ( product_prod @ SY705 @ SV89 ) @ ( hAPP @ SY705 @ ( fun @ SV89 @ ( product_prod @ SY705 @ SV89 ) ) @ ( product_Pair @ SY705 @ SV89 ) @ SY708 ) @ SY709 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(433,plain,
! [SV90: $i,SV32: $i] :
( ( ! [SY710: $i,SY711: $i,SY712: $i] :
( ( ( hAPP @ SV32 @ SV90 @ SY710 @ SY711 )
!= ( ti @ SV90 @ SY712 ) )
| ( ( hAPP @ SV90 @ ( fun @ SV32 @ SV90 ) @ ( hAPP @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) @ ( hAPP @ ( fun @ SV32 @ SV90 ) @ ( fun @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) ) @ ( fun_upd @ SV32 @ SV90 ) @ SY710 ) @ SY711 ) @ SY712 )
= ( ti @ ( fun @ SV32 @ SV90 ) @ SY710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(434,plain,
! [SV91: $i,SV33: $i] :
( ( ! [SY713: $i,SY714: $i,SY715: $i] :
( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV91 @ ( fun @ SV33 @ bool ) @ SY713 @ SY714 ) @ SY715 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV91 @ SV33 ) @ bool @ ( hAPP @ ( fun @ SV91 @ ( fun @ SV33 @ bool ) ) @ ( fun @ ( product_prod @ SV91 @ SV33 ) @ bool ) @ ( product_prod_case @ SV91 @ SV33 @ bool ) @ SY713 ) @ ( hAPP @ SV33 @ ( product_prod @ SV91 @ SV33 ) @ ( hAPP @ SV91 @ ( fun @ SV33 @ ( product_prod @ SV91 @ SV33 ) ) @ ( product_Pair @ SV91 @ SV33 ) @ SY714 ) @ SY715 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(435,plain,
! [SV92: $i,SV34: $i] :
( ( ! [SY716: $i,SY717: $i,SY718: $i] :
( ( ( hAPP @ SV34 @ ( option @ SV92 ) @ SY716 @ SY717 )
!= ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SY718 ) )
| ( ( hAPP @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( hAPP @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) @ ( hAPP @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( fun @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) ) @ ( fun_upd @ SV34 @ ( option @ SV92 ) ) @ SY716 ) @ SY717 ) @ ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SY718 ) )
= ( ti @ ( fun @ SV34 @ ( option @ SV92 ) ) @ SY716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(436,plain,
! [SV35: $i] :
( ( ~ ( ~ ( hBOOL @ ( ti @ bool @ SV35 ) )
| ( hBOOL @ SV35 ) )
| ~ ( ~ ( hBOOL @ SV35 )
| ( hBOOL @ ( ti @ bool @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(437,plain,
! [SV93: $i,SV36: $i] :
( ( ! [SY719: $i,SY720: $i,SY721: $i] :
~ ! [SY722: $i,SY723: $i,SY724: $i,SY725: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) ) @ SY721 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) ) @ SY722 ) @ ( hAPP @ ( product_prod @ SY719 @ SY720 ) @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SY719 @ SY720 ) @ ( product_prod @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SY719 @ SY720 ) ) @ SY723 ) @ ( hAPP @ SY720 @ ( product_prod @ SY719 @ SY720 ) @ ( hAPP @ SY719 @ ( fun @ SY720 @ ( product_prod @ SY719 @ SY720 ) ) @ ( product_Pair @ SY719 @ SY720 ) @ SY724 ) @ SY725 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(438,plain,
! [SV94: $i,SV37: $i] :
( ( ! [SY726: $i] :
~ ! [SY727: $i,SY728: $i] :
( ( ti @ ( product_prod @ SV37 @ SV94 ) @ SY726 )
!= ( hAPP @ SV94 @ ( product_prod @ SV37 @ SV94 ) @ ( hAPP @ SV37 @ ( fun @ SV94 @ ( product_prod @ SV37 @ SV94 ) ) @ ( product_Pair @ SV37 @ SV94 ) @ SY727 ) @ SY728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(439,plain,
! [SV95: $i,SV38: $i] :
( ( ! [SY729: $i,SY730: $i] :
~ ! [SY731: $i,SY732: $i,SY733: $i] :
( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SY729 ) ) @ SY730 )
!= ( hAPP @ ( product_prod @ SV95 @ SY729 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SY729 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SY729 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SY729 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SY729 ) ) @ SY731 ) @ ( hAPP @ SY729 @ ( product_prod @ SV95 @ SY729 ) @ ( hAPP @ SV95 @ ( fun @ SY729 @ ( product_prod @ SV95 @ SY729 ) ) @ ( product_Pair @ SV95 @ SY729 ) @ SY732 ) @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(440,plain,
! [SV39: $i,SV96: $i] :
( ( ! [SY734: $i,SY735: $i,SY736: $i,SY737: $i] :
~ ( ~ ( ( ( ti @ SV96 @ SY736 )
!= ( ti @ SV96 @ SY737 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SY734 ) @ SY737 ) @ SY735 ) @ SY736 )
= ( ti @ SV39 @ SY735 ) ) )
| ~ ( ~ ( ( ( ti @ SV96 @ SY736 )
!= ( ti @ SV96 @ SY737 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SY734 ) @ SY737 ) @ SY735 ) @ SY736 )
= ( hAPP @ SV96 @ SV39 @ SY734 @ SY736 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(441,plain,
! [SV97: $i,SV40: $i] :
( ( ! [SY738: $i,SY739: $i,SY740: $i,SY741: $i] :
~ ! [SY742: $i,SY743: $i,SY744: $i,SY745: $i,SY746: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) ) @ SY741 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) ) @ SY742 ) @ ( hAPP @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) @ SY743 ) @ ( hAPP @ ( product_prod @ SY739 @ SY740 ) @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) @ ( hAPP @ SY738 @ ( fun @ ( product_prod @ SY739 @ SY740 ) @ ( product_prod @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) ) @ ( product_Pair @ SY738 @ ( product_prod @ SY739 @ SY740 ) ) @ SY744 ) @ ( hAPP @ SY740 @ ( product_prod @ SY739 @ SY740 ) @ ( hAPP @ SY739 @ ( fun @ SY740 @ ( product_prod @ SY739 @ SY740 ) ) @ ( product_Pair @ SY739 @ SY740 ) @ SY745 ) @ SY746 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(442,plain,
! [SV98: $i,SV41: $i] :
( ( ! [SY747: $i,SY748: $i,SY749: $i] :
( ~ ! [SY750: $i,SY751: $i,SY752: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SY747 ) ) @ bool @ SY749 @ ( hAPP @ ( product_prod @ SV98 @ SY747 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SY747 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SY747 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SY747 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SY747 ) ) @ SY750 ) @ ( hAPP @ SY747 @ ( product_prod @ SV98 @ SY747 ) @ ( hAPP @ SV98 @ ( fun @ SY747 @ ( product_prod @ SV98 @ SY747 ) ) @ ( product_Pair @ SV98 @ SY747 ) @ SY751 ) @ SY752 ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SY747 ) ) @ bool @ SY749 @ SY748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(443,plain,
! [SV99: $i,SV42: $i] :
( ( ! [SY753: $i,SY754: $i,SY755: $i,SY756: $i,SY757: $i] :
( ~ ! [SY758: $i,SY759: $i,SY760: $i,SY761: $i,SY762: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) ) @ bool @ SY757 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) ) @ SY758 ) @ ( hAPP @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) @ SY759 ) @ ( hAPP @ ( product_prod @ SY754 @ SY755 ) @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) @ ( hAPP @ SY753 @ ( fun @ ( product_prod @ SY754 @ SY755 ) @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) @ ( product_Pair @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) @ SY760 ) @ ( hAPP @ SY755 @ ( product_prod @ SY754 @ SY755 ) @ ( hAPP @ SY754 @ ( fun @ SY755 @ ( product_prod @ SY754 @ SY755 ) ) @ ( product_Pair @ SY754 @ SY755 ) @ SY761 ) @ SY762 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SY753 @ ( product_prod @ SY754 @ SY755 ) ) ) ) @ bool @ SY757 @ SY756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(444,plain,
! [SV100: $i,SV43: $i] :
( ( ! [SY763: $i,SY764: $i,SY765: $i,SY766: $i,SY767: $i] :
~ ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SY763 ) @ SY764 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY765 ) ) @ SY766 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY767 ) )
| ~ ( ( ( ti @ SV43 @ SY766 )
!= ( ti @ SV43 @ SY764 ) )
| ( ( ti @ SV100 @ SY765 )
!= ( ti @ SV100 @ SY767 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY766 )
!= ( ti @ SV43 @ SY764 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SY763 @ SY766 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY767 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SY766 )
!= ( ti @ SV43 @ SY764 ) )
| ( ( ti @ SV100 @ SY765 )
!= ( ti @ SV100 @ SY767 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY766 )
!= ( ti @ SV43 @ SY764 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SY763 @ SY766 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY767 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SY763 ) @ SY764 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY765 ) ) @ SY766 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY767 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(445,plain,
! [SV101: $i,SV44: $i] :
( ( ! [SY768: $i,SY769: $i,SY770: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV101 @ ( fun @ SV44 @ bool ) @ SY768 @ SY769 ) @ SY770 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV44 ) @ bool @ ( hAPP @ ( fun @ SV101 @ ( fun @ SV44 @ bool ) ) @ ( fun @ ( product_prod @ SV101 @ SV44 ) @ bool ) @ ( product_prod_case @ SV101 @ SV44 @ bool ) @ SY768 ) @ ( hAPP @ SV44 @ ( product_prod @ SV101 @ SV44 ) @ ( hAPP @ SV101 @ ( fun @ SV44 @ ( product_prod @ SV101 @ SV44 ) ) @ ( product_Pair @ SV101 @ SV44 ) @ SY769 ) @ SY770 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(446,plain,
! [SV102: $i,SV45: $i] :
( ( ! [SY771: $i,SY772: $i,SY773: $i] :
~ ( ~ ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SY771 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY772 ) @ SY773 ) )
| ~ ( ( SV102 != SY772 )
| ( SY771 != SY773 ) ) )
| ~ ( ~ ~ ( ( SV102 != SY772 )
| ( SY771 != SY773 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SY771 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY772 ) @ SY773 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(447,plain,
! [SV103: $i,SV46: $i] :
( ( ! [SY774: $i,SY775: $i,SY776: $i,SY777: $i,SY778: $i,SY779: $i] :
( ~ ! [SY780: $i,SY781: $i,SY782: $i,SY783: $i,SY784: $i,SY785: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) ) @ bool @ SY779 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) ) @ SY780 ) @ ( hAPP @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) @ SY781 ) @ ( hAPP @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) @ ( hAPP @ SY774 @ ( fun @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) @ ( product_Pair @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) @ SY782 ) @ ( hAPP @ ( product_prod @ SY776 @ SY777 ) @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) @ ( hAPP @ SY775 @ ( fun @ ( product_prod @ SY776 @ SY777 ) @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) @ ( product_Pair @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) @ SY783 ) @ ( hAPP @ SY777 @ ( product_prod @ SY776 @ SY777 ) @ ( hAPP @ SY776 @ ( fun @ SY777 @ ( product_prod @ SY776 @ SY777 ) ) @ ( product_Pair @ SY776 @ SY777 ) @ SY784 ) @ SY785 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SY774 @ ( product_prod @ SY775 @ ( product_prod @ SY776 @ SY777 ) ) ) ) ) @ bool @ SY779 @ SY778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(448,plain,
! [SV104: $i,SV47: $i] :
( ( ! [SY786: $i,SY787: $i,SY788: $i,SY789: $i,SY790: $i] :
~ ! [SY791: $i,SY792: $i,SY793: $i,SY794: $i,SY795: $i,SY796: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) ) @ SY790 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) ) @ SY791 ) @ ( hAPP @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) @ SY792 ) @ ( hAPP @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) @ ( hAPP @ SY786 @ ( fun @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) @ ( product_prod @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) ) @ ( product_Pair @ SY786 @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) @ SY793 ) @ ( hAPP @ ( product_prod @ SY788 @ SY789 ) @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) @ ( hAPP @ SY787 @ ( fun @ ( product_prod @ SY788 @ SY789 ) @ ( product_prod @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) ) @ ( product_Pair @ SY787 @ ( product_prod @ SY788 @ SY789 ) ) @ SY794 ) @ ( hAPP @ SY789 @ ( product_prod @ SY788 @ SY789 ) @ ( hAPP @ SY788 @ ( fun @ SY789 @ ( product_prod @ SY788 @ SY789 ) ) @ ( product_Pair @ SY788 @ SY789 ) @ SY795 ) @ SY796 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(449,plain,
! [SV105: $i,SV48: $i] :
( ( ! [SY797: $i,SY798: $i,SY799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV48 @ SV105 ) @ bool @ ( hAPP @ ( fun @ SV48 @ ( fun @ SV105 @ bool ) ) @ ( fun @ ( product_prod @ SV48 @ SV105 ) @ bool ) @ ( product_prod_case @ SV48 @ SV105 @ bool ) @ SY797 ) @ ( hAPP @ SV105 @ ( product_prod @ SV48 @ SV105 ) @ ( hAPP @ SV48 @ ( fun @ SV105 @ ( product_prod @ SV48 @ SV105 ) ) @ ( product_Pair @ SV48 @ SV105 ) @ SY798 ) @ SY799 ) ) )
| ( hBOOL @ ( hAPP @ SV105 @ bool @ ( hAPP @ SV48 @ ( fun @ SV105 @ bool ) @ SY797 @ SY798 ) @ SY799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(450,plain,
! [SV49: $i,SV106: $i] :
( ( ! [SY800: $i,SY801: $i,SY802: $i,SY803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV106 ) @ SY800 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY801 ) @ SY802 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY803 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV106 ) ) @ SY800 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SY801 ) ) @ SY802 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY803 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(451,plain,
! [SV107: $i,SV50: $i] :
( ( ! [SY804: $i,SY805: $i] :
~ ( ~ ( ~ ! [SY806: $i,SY807: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY806 ) @ SY807 ) ) @ SY805 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY806 ) @ SY807 ) ) @ SY804 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY806 ) @ SY807 ) ) @ SY804 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY806 ) @ SY807 ) ) @ SY805 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SY805 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SY804 ) ) )
| ~ ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SY805 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SY804 ) )
| ! [SY808: $i,SY809: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY808 ) @ SY809 ) ) @ SY805 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY808 ) @ SY809 ) ) @ SY804 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY808 ) @ SY809 ) ) @ SY804 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY808 ) @ SY809 ) ) @ SY805 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(452,plain,
! [SV108: $i,SV51: $i] :
( ( ! [SY810: $i,SY811: $i] :
( ~ ! [SY812: $i] :
( ( hAPP @ SV51 @ SV108 @ SY810 @ SY812 )
= ( hAPP @ SV51 @ SV108 @ SY811 @ SY812 ) )
| ( ( ti @ ( fun @ SV51 @ SV108 ) @ SY810 )
= ( ti @ ( fun @ SV51 @ SV108 ) @ SY811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(453,plain,
! [SV109: $i,SV52: $i] :
( ( ! [SY813: $i] :
~ ( ~ ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
!= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SY813 ) )
| ( SV109 = SY813 ) )
| ~ ( ( SV109 != SY813 )
| ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SY813 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(454,plain,
! [SV110: $i,SV53: $i] :
( ( ! [SY814: $i] :
~ ( ~ ( ~ ~ ! [SY815: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SY814 @ SY815 ) )
| ~ ! [SY816: $i] :
~ ~ ! [SY817: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SY814 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY816 ) @ SY817 ) ) ) )
| ~ ( ~ ~ ! [SY818: $i] :
~ ~ ! [SY819: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SY814 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY818 ) @ SY819 ) ) )
| ~ ! [SY820: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SY814 @ SY820 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(455,plain,
! [SV111: $i,SV54: $i] :
( ( ! [SY821: $i,SY822: $i,SY823: $i,SY824: $i,SY825: $i] :
( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SY821 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SY821 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SY821 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SY821 @ ( fun @ SV54 @ bool ) ) @ SY822 ) @ ( hAPP @ SY821 @ ( product_prod @ SV111 @ SY821 ) @ ( hAPP @ SV111 @ ( fun @ SY821 @ ( product_prod @ SV111 @ SY821 ) ) @ ( product_Pair @ SV111 @ SY821 ) @ SY823 ) @ SY824 ) ) @ SY825 ) )
| ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SY821 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SY821 @ ( fun @ SV54 @ bool ) ) @ SY822 @ SY823 ) @ SY824 ) @ SY825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(456,plain,
! [SV112: $i,SV55: $i] :
( ( ! [SY826: $i,SY827: $i,SY828: $i,SY829: $i] :
( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SY826 ) @ SY827 )
!= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SY828 ) @ SY829 ) )
| ~ ( ( ( ti @ SV112 @ SY826 )
!= ( ti @ SV112 @ SY828 ) )
| ( ( ti @ SV55 @ SY827 )
!= ( ti @ SV55 @ SY829 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(457,plain,
! [SV113: $i,SV56: $i] :
( ( ! [SY830: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SY830 ) )
| ( hBOOL @ ( hAPP @ SV56 @ bool @ SY830 @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV56 @ bool @ SY830 @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SY830 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(458,plain,
! [SV114: $i,SV57: $i] :
( ( ! [SY831: $i] :
~ ( ~ ( ~ ! [SY832: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SY831 @ SY832 ) )
| ! [SY833: $i,SY834: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SY831 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY833 ) @ SY834 ) ) ) )
| ~ ( ~ ! [SY835: $i,SY836: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SY831 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY835 ) @ SY836 ) ) )
| ! [SY837: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SY831 @ SY837 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(459,plain,
! [SV115: $i,SV58: $i] :
( ( ! [SY838: $i,SY839: $i,SY840: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SY838 ) @ SY839 ) @ SY840 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SY838 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY839 ) @ SY840 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SY838 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY839 ) @ SY840 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SY838 ) @ SY839 ) @ SY840 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(460,plain,
! [SV116: $i,SV59: $i] :
( ( ! [SY841: $i,SY842: $i,SY843: $i] :
( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SY841 ) @ SY842 ) @ SY843 ) )
| ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SY841 ) @ SY843 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SY841 ) @ SY842 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(461,plain,
! [SV117: $i,SV60: $i] :
( ( ! [SY844: $i,SY845: $i,SY846: $i] :
~ ( ~ ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SY844 ) @ SY845 ) @ SY846 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SY844 ) )
| ( ( hAPP @ SV117 @ SV60 @ SY844 @ SY845 )
= ( ti @ SV60 @ SY846 ) ) )
| ~ ( ( ( hAPP @ SV117 @ SV60 @ SY844 @ SY845 )
!= ( ti @ SV60 @ SY846 ) )
| ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SY844 ) @ SY845 ) @ SY846 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SY844 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(462,plain,
! [SV118: $i,SV63: $i,SV4: $i] :
( ( ! [SY847: $i] :
( ( hAPP @ SV4 @ SV63 @ ( ti @ ( fun @ SV4 @ SV63 ) @ SV118 ) @ SY847 )
= ( hAPP @ SV4 @ SV63 @ SV118 @ SY847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(463,plain,
! [SV119: $i,SV64: $i,SV5: $i] :
( ( ! [SY848: $i] :
( ( hAPP @ SV5 @ SV64 @ SV119 @ ( ti @ SV5 @ SY848 ) )
= ( hAPP @ SV5 @ SV64 @ SV119 @ SY848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(464,plain,
! [SV120: $i,SV65: $i,SV6: $i] :
( ( ! [SY849: $i] :
( ( ti @ SV6 @ ( hAPP @ SV65 @ SV6 @ SV120 @ SY849 ) )
= ( hAPP @ SV65 @ SV6 @ SV120 @ SY849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(465,plain,
! [SV121: $i,SV66: $i,SV8: $i] :
( ( ! [SY850: $i] :
( ( hAPP @ SV8 @ ( fun @ SV66 @ SV8 ) @ ( hAPP @ SV66 @ ( fun @ SV8 @ ( fun @ SV66 @ SV8 ) ) @ ( hAPP @ ( fun @ SV66 @ SV8 ) @ ( fun @ SV66 @ ( fun @ SV8 @ ( fun @ SV66 @ SV8 ) ) ) @ ( fun_upd @ SV66 @ SV8 ) @ SV121 ) @ SY850 ) @ ( hAPP @ SV66 @ SV8 @ SV121 @ SY850 ) )
= ( ti @ ( fun @ SV66 @ SV8 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(466,plain,
! [SV122: $i,SV67: $i,SV9: $i] :
( ( ! [SY851: $i,SY852: $i] :
( ( hAPP @ SV9 @ SV67 @ ( hAPP @ SV67 @ ( fun @ SV9 @ SV67 ) @ ( hAPP @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) @ ( hAPP @ ( fun @ SV9 @ SV67 ) @ ( fun @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) ) @ ( fun_upd @ SV9 @ SV67 ) @ SV122 ) @ SY851 ) @ SY852 ) @ SY851 )
= ( ti @ SV67 @ SY852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(467,plain,
! [SV123: $i,SV68: $i,SV10: $i] :
( ( ! [SY853: $i,SY854: $i,SY855: $i] :
( ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SY853 ) @ SY854 ) ) @ SY853 ) @ SY855 )
= ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SY853 ) @ SY855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(468,plain,
! [SV124: $i,SV69: $i,SV11: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV11 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV11 ) @ SV69 ) @ SV124 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(469,plain,
! [SV125: $i,SV70: $i,SV12: $i] :
( ( ! [SY856: $i,SY857: $i,SY858: $i] :
( ( hAPP @ ( product_prod @ SV12 @ SV70 ) @ SV125 @ ( hAPP @ ( fun @ SV12 @ ( fun @ SV70 @ SV125 ) ) @ ( fun @ ( product_prod @ SV12 @ SV70 ) @ SV125 ) @ ( product_prod_rec @ SV12 @ SV70 @ SV125 ) @ SY856 ) @ ( hAPP @ SV70 @ ( product_prod @ SV12 @ SV70 ) @ ( hAPP @ SV12 @ ( fun @ SV70 @ ( product_prod @ SV12 @ SV70 ) ) @ ( product_Pair @ SV12 @ SV70 ) @ SY857 ) @ SY858 ) )
= ( hAPP @ SV70 @ SV125 @ ( hAPP @ SV12 @ ( fun @ SV70 @ SV125 ) @ SY856 @ SY857 ) @ SY858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(470,plain,
! [SV126: $i,SV71: $i,SV13: $i] :
( ( ! [SY859: $i,SY860: $i,SY861: $i] :
( ( hAPP @ ( product_prod @ SV13 @ SV71 ) @ SV126 @ ( hAPP @ ( fun @ SV13 @ ( fun @ SV71 @ SV126 ) ) @ ( fun @ ( product_prod @ SV13 @ SV71 ) @ SV126 ) @ ( produc1605651328_split @ SV13 @ SV71 @ SV126 ) @ SY859 ) @ ( hAPP @ SV71 @ ( product_prod @ SV13 @ SV71 ) @ ( hAPP @ SV13 @ ( fun @ SV71 @ ( product_prod @ SV13 @ SV71 ) ) @ ( product_Pair @ SV13 @ SV71 ) @ SY860 ) @ SY861 ) )
= ( hAPP @ SV71 @ SV126 @ ( hAPP @ SV13 @ ( fun @ SV71 @ SV126 ) @ SY859 @ SY860 ) @ SY861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(471,plain,
! [SV127: $i,SV72: $i,SV14: $i] :
( ( ! [SY862: $i,SY863: $i,SY864: $i] :
( ( hAPP @ ( product_prod @ SV14 @ SV72 ) @ SV127 @ ( hAPP @ ( fun @ SV14 @ ( fun @ SV72 @ SV127 ) ) @ ( fun @ ( product_prod @ SV14 @ SV72 ) @ SV127 ) @ ( product_prod_case @ SV14 @ SV72 @ SV127 ) @ SY862 ) @ ( hAPP @ SV72 @ ( product_prod @ SV14 @ SV72 ) @ ( hAPP @ SV14 @ ( fun @ SV72 @ ( product_prod @ SV14 @ SV72 ) ) @ ( product_Pair @ SV14 @ SV72 ) @ SY863 ) @ SY864 ) )
= ( hAPP @ SV72 @ SV127 @ ( hAPP @ SV14 @ ( fun @ SV72 @ SV127 ) @ SY862 @ SY863 ) @ SY864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(472,plain,
! [SV128: $i,SV73: $i,SV15: $i] :
( ( ! [SY865: $i,SY866: $i,SY867: $i] :
( ( hAPP @ ( product_prod @ SV15 @ SV73 ) @ SV128 @ ( hAPP @ ( fun @ SV15 @ ( fun @ SV73 @ SV128 ) ) @ ( fun @ ( product_prod @ SV15 @ SV73 ) @ SV128 ) @ ( product_prod_case @ SV15 @ SV73 @ SV128 ) @ SY865 ) @ ( hAPP @ SV73 @ ( product_prod @ SV15 @ SV73 ) @ ( hAPP @ SV15 @ ( fun @ SV73 @ ( product_prod @ SV15 @ SV73 ) ) @ ( product_Pair @ SV15 @ SV73 ) @ SY866 ) @ SY867 ) )
= ( hAPP @ SV73 @ SV128 @ ( hAPP @ SV15 @ ( fun @ SV73 @ SV128 ) @ SY865 @ SY866 ) @ SY867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(473,plain,
! [SV129: $i,SV74: $i,SV16: $i] :
( ( ! [SY868: $i,SY869: $i] :
~ ! [SY870: $i] :
( ( hAPP @ SV16 @ ( option @ SV74 ) @ ( hAPP @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( hAPP @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) @ ( hAPP @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( fun @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) ) @ ( fun_upd @ SV16 @ ( option @ SV74 ) ) @ SV129 ) @ SY868 ) @ ( hAPP @ SV74 @ ( option @ SV74 ) @ ( some @ SV74 ) @ SY869 ) ) @ SY870 )
= ( none @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(474,plain,
! [SV130: $i,SV75: $i,SV17: $i] :
( ( ! [SY871: $i,SY872: $i,SY873: $i] :
( ( hAPP @ SV17 @ SV75 @ ( hAPP @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) @ ( hAPP @ ( fun @ SV130 @ SV75 ) @ ( fun @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) ) @ ( combb @ SV130 @ SV75 @ SV17 ) @ SY871 ) @ SY872 ) @ SY873 )
= ( hAPP @ SV130 @ SV75 @ SY871 @ ( hAPP @ SV17 @ SV130 @ SY872 @ SY873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(475,plain,
! [SV131: $i,SV76: $i,SV18: $i] :
( ( ! [SY874: $i,SY875: $i,SY876: $i] :
( ( hAPP @ SV18 @ SV76 @ ( hAPP @ SV131 @ ( fun @ SV18 @ SV76 ) @ ( hAPP @ ( fun @ SV18 @ ( fun @ SV131 @ SV76 ) ) @ ( fun @ SV131 @ ( fun @ SV18 @ SV76 ) ) @ ( combc @ SV18 @ SV131 @ SV76 ) @ SY874 ) @ SY875 ) @ SY876 )
= ( hAPP @ SV131 @ SV76 @ ( hAPP @ SV18 @ ( fun @ SV131 @ SV76 ) @ SY874 @ SY876 ) @ SY875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(476,plain,
! [SV132: $i,SV77: $i,SV19: $i] :
( ( ! [SY877: $i,SY878: $i,SY879: $i] :
( ( hAPP @ SV19 @ SV77 @ ( hAPP @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) @ ( hAPP @ ( fun @ SV19 @ ( fun @ SV132 @ SV77 ) ) @ ( fun @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) ) @ ( combs @ SV19 @ SV132 @ SV77 ) @ SY877 ) @ SY878 ) @ SY879 )
= ( hAPP @ SV132 @ SV77 @ ( hAPP @ SV19 @ ( fun @ SV132 @ SV77 ) @ SY877 @ SY879 ) @ ( hAPP @ SV19 @ SV132 @ SY878 @ SY879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(477,plain,
! [SV20: $i,SV78: $i] :
( ( ( ~ ( hBOOL @ SV78 )
| ~ ( hBOOL @ SV20 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV78 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(478,plain,
! [SV79: $i,SV21: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV21 ) @ SV79 ) ) )
= $true )
| ( ( hBOOL @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(479,plain,
! [SV80: $i,SV22: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV22 ) @ SV80 ) ) )
= $true )
| ( ( hBOOL @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(480,plain,
! [SV133: $i,SV81: $i,SV23: $i] :
( ( ! [SY880: $i,SY881: $i,SY882: $i] :
~ ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SY880 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY881 ) @ SY882 ) )
| ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SY881 ) )
| ( ( ti @ SV23 @ SY880 )
!= ( ti @ SV23 @ SY882 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SY881 ) )
| ( ( ti @ SV23 @ SY880 )
!= ( ti @ SV23 @ SY882 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SY880 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY881 ) @ SY882 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(481,plain,
! [SV24: $i,SV134: $i,SV82: $i] :
( ( ! [SY883: $i,SY884: $i,SY885: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV82 ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY883 ) @ SY884 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY885 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV82 ) @ SV24 ) ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SY883 ) @ SV24 ) ) @ SY884 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY885 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(482,plain,
! [SV135: $i,SV25: $i,SV83: $i] :
( ( ! [SY886: $i,SY887: $i,SY888: $i] :
~ ( ~ ( ( ( ti @ SV83 @ SY888 )
!= ( ti @ SV83 @ SY887 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SY887 ) @ SY886 ) @ SY888 )
= ( ti @ SV25 @ SY886 ) ) )
| ~ ( ~ ( ( ( ti @ SV83 @ SY888 )
!= ( ti @ SV83 @ SY887 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SY887 ) @ SY886 ) @ SY888 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SY888 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(483,plain,
! [SV136: $i,SV84: $i,SV26: $i] :
( ( ! [SY889: $i,SY890: $i,SY891: $i] :
( ~ ! [SY892: $i,SY893: $i,SY894: $i,SY895: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) ) @ bool @ SY891 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) ) @ SY892 ) @ ( hAPP @ ( product_prod @ SV136 @ SY889 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SY889 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) @ SY893 ) @ ( hAPP @ SY889 @ ( product_prod @ SV136 @ SY889 ) @ ( hAPP @ SV136 @ ( fun @ SY889 @ ( product_prod @ SV136 @ SY889 ) ) @ ( product_Pair @ SV136 @ SY889 ) @ SY894 ) @ SY895 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SY889 ) ) ) @ bool @ SY891 @ SY890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(484,plain,
! [SV137: $i,SV27: $i,SV85: $i] :
( ( ! [SY896: $i,SY897: $i,SY898: $i] :
( ~ ( ( ( ti @ SV85 @ SY897 )
!= ( ti @ SV85 @ SY898 ) ) )
| ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SV137 ) @ SY898 ) @ SY896 ) @ SY897 )
= ( hAPP @ SV85 @ SV27 @ SV137 @ SY897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(485,plain,
! [SV138: $i,SV86: $i,SV28: $i] :
( ( ! [SY899: $i,SY900: $i,SY901: $i,SY902: $i] :
( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV138 ) @ SY899 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY900 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SY901 ) @ SY899 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY902 ) ) )
| ( ( ti @ SV28 @ SY900 )
= ( ti @ SV28 @ SY902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(486,plain,
! [SV139: $i,SV87: $i,SV29: $i] :
( ( ~ ! [SY903: $i,SY904: $i] :
( ( ti @ ( product_prod @ SV29 @ SV87 ) @ SV139 )
!= ( hAPP @ SV87 @ ( product_prod @ SV29 @ SV87 ) @ ( hAPP @ SV29 @ ( fun @ SV87 @ ( product_prod @ SV29 @ SV87 ) ) @ ( product_Pair @ SV29 @ SV87 ) @ SY903 ) @ SY904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(487,plain,
! [SV140: $i,SV30: $i,SV88: $i] :
( ( ! [SY905: $i,SY906: $i,SY907: $i,SY908: $i] :
( ~ ( ( ( ti @ SV88 @ SY907 )
!= ( ti @ SV88 @ SY908 ) ) )
| ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SY907 ) @ SY905 ) ) @ SY908 ) @ SY906 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SY908 ) @ SY906 ) ) @ SY907 ) @ SY905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(488,plain,
! [SV141: $i,SV89: $i,SV31: $i] :
( ( ! [SY909: $i,SY910: $i,SY911: $i,SY912: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SY909 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SY910 @ SY911 ) @ SY912 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SY909 ) @ ( hAPP @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SV141 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SY910 ) @ ( hAPP @ SV89 @ ( product_prod @ SV141 @ SV89 ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( product_prod @ SV141 @ SV89 ) ) @ ( product_Pair @ SV141 @ SV89 ) @ SY911 ) @ SY912 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(489,plain,
! [SV142: $i,SV90: $i,SV32: $i] :
( ( ! [SY913: $i,SY914: $i] :
( ( ( hAPP @ SV32 @ SV90 @ SV142 @ SY913 )
!= ( ti @ SV90 @ SY914 ) )
| ( ( hAPP @ SV90 @ ( fun @ SV32 @ SV90 ) @ ( hAPP @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) @ ( hAPP @ ( fun @ SV32 @ SV90 ) @ ( fun @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) ) @ ( fun_upd @ SV32 @ SV90 ) @ SV142 ) @ SY913 ) @ SY914 )
= ( ti @ ( fun @ SV32 @ SV90 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(490,plain,
! [SV143: $i,SV91: $i,SV33: $i] :
( ( ! [SY915: $i,SY916: $i] :
( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV91 @ ( fun @ SV33 @ bool ) @ SV143 @ SY915 ) @ SY916 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV91 @ SV33 ) @ bool @ ( hAPP @ ( fun @ SV91 @ ( fun @ SV33 @ bool ) ) @ ( fun @ ( product_prod @ SV91 @ SV33 ) @ bool ) @ ( product_prod_case @ SV91 @ SV33 @ bool ) @ SV143 ) @ ( hAPP @ SV33 @ ( product_prod @ SV91 @ SV33 ) @ ( hAPP @ SV91 @ ( fun @ SV33 @ ( product_prod @ SV91 @ SV33 ) ) @ ( product_Pair @ SV91 @ SV33 ) @ SY915 ) @ SY916 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(491,plain,
! [SV144: $i,SV92: $i,SV34: $i] :
( ( ! [SY917: $i,SY918: $i] :
( ( ( hAPP @ SV34 @ ( option @ SV92 ) @ SV144 @ SY917 )
!= ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SY918 ) )
| ( ( hAPP @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( hAPP @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) @ ( hAPP @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( fun @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) ) @ ( fun_upd @ SV34 @ ( option @ SV92 ) ) @ SV144 ) @ SY917 ) @ ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SY918 ) )
= ( ti @ ( fun @ SV34 @ ( option @ SV92 ) ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(492,plain,
! [SV35: $i] :
( ( ~ ( ~ ( hBOOL @ ( ti @ bool @ SV35 ) )
| ( hBOOL @ SV35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(493,plain,
! [SV35: $i] :
( ( ~ ( ~ ( hBOOL @ SV35 )
| ( hBOOL @ ( ti @ bool @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(494,plain,
! [SV145: $i,SV93: $i,SV36: $i] :
( ( ! [SY919: $i,SY920: $i] :
~ ! [SY921: $i,SY922: $i,SY923: $i,SY924: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) ) @ SY920 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) ) @ SY921 ) @ ( hAPP @ ( product_prod @ SV145 @ SY919 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SY919 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SY919 ) ) @ SY922 ) @ ( hAPP @ SY919 @ ( product_prod @ SV145 @ SY919 ) @ ( hAPP @ SV145 @ ( fun @ SY919 @ ( product_prod @ SV145 @ SY919 ) ) @ ( product_Pair @ SV145 @ SY919 ) @ SY923 ) @ SY924 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(495,plain,
! [SV146: $i,SV94: $i,SV37: $i] :
( ( ~ ! [SY925: $i,SY926: $i] :
( ( ti @ ( product_prod @ SV37 @ SV94 ) @ SV146 )
!= ( hAPP @ SV94 @ ( product_prod @ SV37 @ SV94 ) @ ( hAPP @ SV37 @ ( fun @ SV94 @ ( product_prod @ SV37 @ SV94 ) ) @ ( product_Pair @ SV37 @ SV94 ) @ SY925 ) @ SY926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(496,plain,
! [SV147: $i,SV95: $i,SV38: $i] :
( ( ! [SY927: $i] :
~ ! [SY928: $i,SY929: $i,SY930: $i] :
( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SY927 )
!= ( hAPP @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SY928 ) @ ( hAPP @ SV147 @ ( product_prod @ SV95 @ SV147 ) @ ( hAPP @ SV95 @ ( fun @ SV147 @ ( product_prod @ SV95 @ SV147 ) ) @ ( product_Pair @ SV95 @ SV147 ) @ SY929 ) @ SY930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(497,plain,
! [SV148: $i,SV39: $i,SV96: $i] :
( ( ! [SY931: $i,SY932: $i,SY933: $i] :
~ ( ~ ( ( ( ti @ SV96 @ SY932 )
!= ( ti @ SV96 @ SY933 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SY933 ) @ SY931 ) @ SY932 )
= ( ti @ SV39 @ SY931 ) ) )
| ~ ( ~ ( ( ( ti @ SV96 @ SY932 )
!= ( ti @ SV96 @ SY933 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SY933 ) @ SY931 ) @ SY932 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SY932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(498,plain,
! [SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY934: $i,SY935: $i,SY936: $i] :
~ ! [SY937: $i,SY938: $i,SY939: $i,SY940: $i,SY941: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) ) @ SY936 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) ) @ SY937 ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) @ SY938 ) @ ( hAPP @ ( product_prod @ SY934 @ SY935 ) @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SY934 @ SY935 ) @ ( product_prod @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SY934 @ SY935 ) ) @ SY939 ) @ ( hAPP @ SY935 @ ( product_prod @ SY934 @ SY935 ) @ ( hAPP @ SY934 @ ( fun @ SY935 @ ( product_prod @ SY934 @ SY935 ) ) @ ( product_Pair @ SY934 @ SY935 ) @ SY940 ) @ SY941 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(499,plain,
! [SV150: $i,SV98: $i,SV41: $i] :
( ( ! [SY942: $i,SY943: $i] :
( ~ ! [SY944: $i,SY945: $i,SY946: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SY943 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ SY944 ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ SY945 ) @ SY946 ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SY943 @ SY942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(500,plain,
! [SV151: $i,SV99: $i,SV42: $i] :
( ( ! [SY947: $i,SY948: $i,SY949: $i,SY950: $i] :
( ~ ! [SY951: $i,SY952: $i,SY953: $i,SY954: $i,SY955: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) ) @ bool @ SY950 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) ) @ SY951 ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) @ SY952 ) @ ( hAPP @ ( product_prod @ SY947 @ SY948 ) @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SY947 @ SY948 ) @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) @ SY953 ) @ ( hAPP @ SY948 @ ( product_prod @ SY947 @ SY948 ) @ ( hAPP @ SY947 @ ( fun @ SY948 @ ( product_prod @ SY947 @ SY948 ) ) @ ( product_Pair @ SY947 @ SY948 ) @ SY954 ) @ SY955 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SY947 @ SY948 ) ) ) ) @ bool @ SY950 @ SY949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(501,plain,
! [SV152: $i,SV100: $i,SV43: $i] :
( ( ! [SY956: $i,SY957: $i,SY958: $i,SY959: $i] :
~ ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SY956 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY957 ) ) @ SY958 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY959 ) )
| ~ ( ( ( ti @ SV43 @ SY958 )
!= ( ti @ SV43 @ SY956 ) )
| ( ( ti @ SV100 @ SY957 )
!= ( ti @ SV100 @ SY959 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY958 )
!= ( ti @ SV43 @ SY956 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SY958 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY959 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SY958 )
!= ( ti @ SV43 @ SY956 ) )
| ( ( ti @ SV100 @ SY957 )
!= ( ti @ SV100 @ SY959 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY958 )
!= ( ti @ SV43 @ SY956 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SY958 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY959 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SY956 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY957 ) ) @ SY958 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY959 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(502,plain,
! [SV153: $i,SV101: $i,SV44: $i] :
( ( ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV101 @ ( fun @ SV44 @ bool ) @ SV153 @ SY960 ) @ SY961 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV44 ) @ bool @ ( hAPP @ ( fun @ SV101 @ ( fun @ SV44 @ bool ) ) @ ( fun @ ( product_prod @ SV101 @ SV44 ) @ bool ) @ ( product_prod_case @ SV101 @ SV44 @ bool ) @ SV153 ) @ ( hAPP @ SV44 @ ( product_prod @ SV101 @ SV44 ) @ ( hAPP @ SV101 @ ( fun @ SV44 @ ( product_prod @ SV101 @ SV44 ) ) @ ( product_Pair @ SV101 @ SV44 ) @ SY960 ) @ SY961 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(503,plain,
! [SV154: $i,SV102: $i,SV45: $i] :
( ( ! [SY962: $i,SY963: $i] :
~ ( ~ ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY962 ) @ SY963 ) )
| ~ ( ( SV102 != SY962 )
| ( SV154 != SY963 ) ) )
| ~ ( ~ ~ ( ( SV102 != SY962 )
| ( SV154 != SY963 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SY962 ) @ SY963 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(504,plain,
! [SV155: $i,SV103: $i,SV46: $i] :
( ( ! [SY964: $i,SY965: $i,SY966: $i,SY967: $i,SY968: $i] :
( ~ ! [SY969: $i,SY970: $i,SY971: $i,SY972: $i,SY973: $i,SY974: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) ) @ bool @ SY968 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) ) @ SY969 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) @ SY970 ) @ ( hAPP @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) @ SY971 ) @ ( hAPP @ ( product_prod @ SY965 @ SY966 ) @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) @ ( hAPP @ SY964 @ ( fun @ ( product_prod @ SY965 @ SY966 ) @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) @ ( product_Pair @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) @ SY972 ) @ ( hAPP @ SY966 @ ( product_prod @ SY965 @ SY966 ) @ ( hAPP @ SY965 @ ( fun @ SY966 @ ( product_prod @ SY965 @ SY966 ) ) @ ( product_Pair @ SY965 @ SY966 ) @ SY973 ) @ SY974 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SY964 @ ( product_prod @ SY965 @ SY966 ) ) ) ) ) @ bool @ SY968 @ SY967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(505,plain,
! [SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY975: $i,SY976: $i,SY977: $i,SY978: $i] :
~ ! [SY979: $i,SY980: $i,SY981: $i,SY982: $i,SY983: $i,SY984: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) ) @ SY978 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) ) @ SY979 ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) @ SY980 ) @ ( hAPP @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) @ SY981 ) @ ( hAPP @ ( product_prod @ SY976 @ SY977 ) @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) @ ( hAPP @ SY975 @ ( fun @ ( product_prod @ SY976 @ SY977 ) @ ( product_prod @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) ) @ ( product_Pair @ SY975 @ ( product_prod @ SY976 @ SY977 ) ) @ SY982 ) @ ( hAPP @ SY977 @ ( product_prod @ SY976 @ SY977 ) @ ( hAPP @ SY976 @ ( fun @ SY977 @ ( product_prod @ SY976 @ SY977 ) ) @ ( product_Pair @ SY976 @ SY977 ) @ SY983 ) @ SY984 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(506,plain,
! [SV157: $i,SV105: $i,SV48: $i] :
( ( ! [SY985: $i,SY986: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV48 @ SV105 ) @ bool @ ( hAPP @ ( fun @ SV48 @ ( fun @ SV105 @ bool ) ) @ ( fun @ ( product_prod @ SV48 @ SV105 ) @ bool ) @ ( product_prod_case @ SV48 @ SV105 @ bool ) @ SV157 ) @ ( hAPP @ SV105 @ ( product_prod @ SV48 @ SV105 ) @ ( hAPP @ SV48 @ ( fun @ SV105 @ ( product_prod @ SV48 @ SV105 ) ) @ ( product_Pair @ SV48 @ SV105 ) @ SY985 ) @ SY986 ) ) )
| ( hBOOL @ ( hAPP @ SV105 @ bool @ ( hAPP @ SV48 @ ( fun @ SV105 @ bool ) @ SV157 @ SY985 ) @ SY986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(507,plain,
! [SV49: $i,SV158: $i,SV106: $i] :
( ( ! [SY987: $i,SY988: $i,SY989: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV106 ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY987 ) @ SY988 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY989 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV106 ) ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SY987 ) ) @ SY988 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY989 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(508,plain,
! [SV159: $i,SV107: $i,SV50: $i] :
( ( ! [SY990: $i] :
~ ( ~ ( ~ ! [SY991: $i,SY992: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY991 ) @ SY992 ) ) @ SY990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY991 ) @ SY992 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY991 ) @ SY992 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY991 ) @ SY992 ) ) @ SY990 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SY990 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) ) )
| ~ ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SY990 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
| ! [SY993: $i,SY994: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY993 ) @ SY994 ) ) @ SY990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY993 ) @ SY994 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY993 ) @ SY994 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY993 ) @ SY994 ) ) @ SY990 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(509,plain,
! [SV160: $i,SV108: $i,SV51: $i] :
( ( ! [SY995: $i] :
( ~ ! [SY996: $i] :
( ( hAPP @ SV51 @ SV108 @ SV160 @ SY996 )
= ( hAPP @ SV51 @ SV108 @ SY995 @ SY996 ) )
| ( ( ti @ ( fun @ SV51 @ SV108 ) @ SV160 )
= ( ti @ ( fun @ SV51 @ SV108 ) @ SY995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(510,plain,
! [SV161: $i,SV109: $i,SV52: $i] :
( ( ~ ( ~ ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
!= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
| ( SV109 = SV161 ) )
| ~ ( ( SV109 != SV161 )
| ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(511,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ~ ( ~ ( ~ ~ ! [SY997: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY997 ) )
| ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
| ~ ( ~ ~ ! [SY1000: $i] :
~ ~ ! [SY1001: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY1000 ) @ SY1001 ) ) )
| ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(512,plain,
! [SV163: $i,SV111: $i,SV54: $i] :
( ( ! [SY1003: $i,SY1004: $i,SY1005: $i,SY1006: $i] :
( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SV163 @ ( fun @ SV54 @ bool ) ) @ SY1003 ) @ ( hAPP @ SV163 @ ( product_prod @ SV111 @ SV163 ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( product_prod @ SV111 @ SV163 ) ) @ ( product_Pair @ SV111 @ SV163 ) @ SY1004 ) @ SY1005 ) ) @ SY1006 ) )
| ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SV163 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) @ SY1003 @ SY1004 ) @ SY1005 ) @ SY1006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(513,plain,
! [SV164: $i,SV112: $i,SV55: $i] :
( ( ! [SY1007: $i,SY1008: $i,SY1009: $i] :
( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SY1007 )
!= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SY1008 ) @ SY1009 ) )
| ~ ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SY1008 ) )
| ( ( ti @ SV55 @ SY1007 )
!= ( ti @ SV55 @ SY1009 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(514,plain,
! [SV165: $i,SV113: $i,SV56: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) )
| ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(515,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ~ ( ~ ( ~ ! [SY1010: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1010 ) )
| ! [SY1011: $i,SY1012: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1011 ) @ SY1012 ) ) ) )
| ~ ( ~ ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1013 ) @ SY1014 ) ) )
| ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(516,plain,
! [SV167: $i,SV115: $i,SV58: $i] :
( ( ! [SY1016: $i,SY1017: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SY1016 ) @ SY1017 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY1016 ) @ SY1017 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SY1016 ) @ SY1017 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SY1016 ) @ SY1017 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(517,plain,
! [SV116: $i,SV168: $i,SV59: $i] :
( ( ! [SY1018: $i,SY1019: $i] :
( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SY1018 ) @ SY1019 ) )
| ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SY1019 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SY1018 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(518,plain,
! [SV169: $i,SV117: $i,SV60: $i] :
( ( ! [SY1020: $i,SY1021: $i] :
~ ( ~ ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SY1020 ) @ SY1021 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
| ( ( hAPP @ SV117 @ SV60 @ SV169 @ SY1020 )
= ( ti @ SV60 @ SY1021 ) ) )
| ~ ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SY1020 )
!= ( ti @ SV60 @ SY1021 ) )
| ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SY1020 ) @ SY1021 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(519,plain,
! [SV170: $i,SV118: $i,SV63: $i,SV4: $i] :
( ( ( hAPP @ SV4 @ SV63 @ ( ti @ ( fun @ SV4 @ SV63 ) @ SV118 ) @ SV170 )
= ( hAPP @ SV4 @ SV63 @ SV118 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(520,plain,
! [SV171: $i,SV119: $i,SV64: $i,SV5: $i] :
( ( ( hAPP @ SV5 @ SV64 @ SV119 @ ( ti @ SV5 @ SV171 ) )
= ( hAPP @ SV5 @ SV64 @ SV119 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(521,plain,
! [SV172: $i,SV120: $i,SV65: $i,SV6: $i] :
( ( ( ti @ SV6 @ ( hAPP @ SV65 @ SV6 @ SV120 @ SV172 ) )
= ( hAPP @ SV65 @ SV6 @ SV120 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(522,plain,
! [SV173: $i,SV121: $i,SV66: $i,SV8: $i] :
( ( ( hAPP @ SV8 @ ( fun @ SV66 @ SV8 ) @ ( hAPP @ SV66 @ ( fun @ SV8 @ ( fun @ SV66 @ SV8 ) ) @ ( hAPP @ ( fun @ SV66 @ SV8 ) @ ( fun @ SV66 @ ( fun @ SV8 @ ( fun @ SV66 @ SV8 ) ) ) @ ( fun_upd @ SV66 @ SV8 ) @ SV121 ) @ SV173 ) @ ( hAPP @ SV66 @ SV8 @ SV121 @ SV173 ) )
= ( ti @ ( fun @ SV66 @ SV8 ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(523,plain,
! [SV174: $i,SV122: $i,SV67: $i,SV9: $i] :
( ( ! [SY1022: $i] :
( ( hAPP @ SV9 @ SV67 @ ( hAPP @ SV67 @ ( fun @ SV9 @ SV67 ) @ ( hAPP @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) @ ( hAPP @ ( fun @ SV9 @ SV67 ) @ ( fun @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) ) @ ( fun_upd @ SV9 @ SV67 ) @ SV122 ) @ SV174 ) @ SY1022 ) @ SV174 )
= ( ti @ SV67 @ SY1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(524,plain,
! [SV175: $i,SV123: $i,SV68: $i,SV10: $i] :
( ( ! [SY1023: $i,SY1024: $i] :
( ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SV175 ) @ SY1023 ) ) @ SV175 ) @ SY1024 )
= ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SV175 ) @ SY1024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(525,plain,
! [SV176: $i,SV125: $i,SV70: $i,SV12: $i] :
( ( ! [SY1025: $i,SY1026: $i] :
( ( hAPP @ ( product_prod @ SV12 @ SV70 ) @ SV125 @ ( hAPP @ ( fun @ SV12 @ ( fun @ SV70 @ SV125 ) ) @ ( fun @ ( product_prod @ SV12 @ SV70 ) @ SV125 ) @ ( product_prod_rec @ SV12 @ SV70 @ SV125 ) @ SV176 ) @ ( hAPP @ SV70 @ ( product_prod @ SV12 @ SV70 ) @ ( hAPP @ SV12 @ ( fun @ SV70 @ ( product_prod @ SV12 @ SV70 ) ) @ ( product_Pair @ SV12 @ SV70 ) @ SY1025 ) @ SY1026 ) )
= ( hAPP @ SV70 @ SV125 @ ( hAPP @ SV12 @ ( fun @ SV70 @ SV125 ) @ SV176 @ SY1025 ) @ SY1026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(526,plain,
! [SV177: $i,SV126: $i,SV71: $i,SV13: $i] :
( ( ! [SY1027: $i,SY1028: $i] :
( ( hAPP @ ( product_prod @ SV13 @ SV71 ) @ SV126 @ ( hAPP @ ( fun @ SV13 @ ( fun @ SV71 @ SV126 ) ) @ ( fun @ ( product_prod @ SV13 @ SV71 ) @ SV126 ) @ ( produc1605651328_split @ SV13 @ SV71 @ SV126 ) @ SV177 ) @ ( hAPP @ SV71 @ ( product_prod @ SV13 @ SV71 ) @ ( hAPP @ SV13 @ ( fun @ SV71 @ ( product_prod @ SV13 @ SV71 ) ) @ ( product_Pair @ SV13 @ SV71 ) @ SY1027 ) @ SY1028 ) )
= ( hAPP @ SV71 @ SV126 @ ( hAPP @ SV13 @ ( fun @ SV71 @ SV126 ) @ SV177 @ SY1027 ) @ SY1028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(527,plain,
! [SV178: $i,SV127: $i,SV72: $i,SV14: $i] :
( ( ! [SY1029: $i,SY1030: $i] :
( ( hAPP @ ( product_prod @ SV14 @ SV72 ) @ SV127 @ ( hAPP @ ( fun @ SV14 @ ( fun @ SV72 @ SV127 ) ) @ ( fun @ ( product_prod @ SV14 @ SV72 ) @ SV127 ) @ ( product_prod_case @ SV14 @ SV72 @ SV127 ) @ SV178 ) @ ( hAPP @ SV72 @ ( product_prod @ SV14 @ SV72 ) @ ( hAPP @ SV14 @ ( fun @ SV72 @ ( product_prod @ SV14 @ SV72 ) ) @ ( product_Pair @ SV14 @ SV72 ) @ SY1029 ) @ SY1030 ) )
= ( hAPP @ SV72 @ SV127 @ ( hAPP @ SV14 @ ( fun @ SV72 @ SV127 ) @ SV178 @ SY1029 ) @ SY1030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(528,plain,
! [SV179: $i,SV128: $i,SV73: $i,SV15: $i] :
( ( ! [SY1031: $i,SY1032: $i] :
( ( hAPP @ ( product_prod @ SV15 @ SV73 ) @ SV128 @ ( hAPP @ ( fun @ SV15 @ ( fun @ SV73 @ SV128 ) ) @ ( fun @ ( product_prod @ SV15 @ SV73 ) @ SV128 ) @ ( product_prod_case @ SV15 @ SV73 @ SV128 ) @ SV179 ) @ ( hAPP @ SV73 @ ( product_prod @ SV15 @ SV73 ) @ ( hAPP @ SV15 @ ( fun @ SV73 @ ( product_prod @ SV15 @ SV73 ) ) @ ( product_Pair @ SV15 @ SV73 ) @ SY1031 ) @ SY1032 ) )
= ( hAPP @ SV73 @ SV128 @ ( hAPP @ SV15 @ ( fun @ SV73 @ SV128 ) @ SV179 @ SY1031 ) @ SY1032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(529,plain,
! [SV180: $i,SV129: $i,SV74: $i,SV16: $i] :
( ( ! [SY1033: $i] :
~ ! [SY1034: $i] :
( ( hAPP @ SV16 @ ( option @ SV74 ) @ ( hAPP @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( hAPP @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) @ ( hAPP @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( fun @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) ) @ ( fun_upd @ SV16 @ ( option @ SV74 ) ) @ SV129 ) @ SV180 ) @ ( hAPP @ SV74 @ ( option @ SV74 ) @ ( some @ SV74 ) @ SY1033 ) ) @ SY1034 )
= ( none @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(530,plain,
! [SV181: $i,SV130: $i,SV75: $i,SV17: $i] :
( ( ! [SY1035: $i,SY1036: $i] :
( ( hAPP @ SV17 @ SV75 @ ( hAPP @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) @ ( hAPP @ ( fun @ SV130 @ SV75 ) @ ( fun @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) ) @ ( combb @ SV130 @ SV75 @ SV17 ) @ SV181 ) @ SY1035 ) @ SY1036 )
= ( hAPP @ SV130 @ SV75 @ SV181 @ ( hAPP @ SV17 @ SV130 @ SY1035 @ SY1036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(531,plain,
! [SV182: $i,SV131: $i,SV76: $i,SV18: $i] :
( ( ! [SY1037: $i,SY1038: $i] :
( ( hAPP @ SV18 @ SV76 @ ( hAPP @ SV131 @ ( fun @ SV18 @ SV76 ) @ ( hAPP @ ( fun @ SV18 @ ( fun @ SV131 @ SV76 ) ) @ ( fun @ SV131 @ ( fun @ SV18 @ SV76 ) ) @ ( combc @ SV18 @ SV131 @ SV76 ) @ SV182 ) @ SY1037 ) @ SY1038 )
= ( hAPP @ SV131 @ SV76 @ ( hAPP @ SV18 @ ( fun @ SV131 @ SV76 ) @ SV182 @ SY1038 ) @ SY1037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(532,plain,
! [SV183: $i,SV132: $i,SV77: $i,SV19: $i] :
( ( ! [SY1039: $i,SY1040: $i] :
( ( hAPP @ SV19 @ SV77 @ ( hAPP @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) @ ( hAPP @ ( fun @ SV19 @ ( fun @ SV132 @ SV77 ) ) @ ( fun @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) ) @ ( combs @ SV19 @ SV132 @ SV77 ) @ SV183 ) @ SY1039 ) @ SY1040 )
= ( hAPP @ SV132 @ SV77 @ ( hAPP @ SV19 @ ( fun @ SV132 @ SV77 ) @ SV183 @ SY1040 ) @ ( hAPP @ SV19 @ SV132 @ SY1039 @ SY1040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(533,plain,
! [SV20: $i,SV78: $i] :
( ( ( ~ ( hBOOL @ SV78 ) )
= $true )
| ( ( ~ ( hBOOL @ SV20 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV78 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(534,plain,
! [SV79: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV21 ) @ SV79 ) )
= $false )
| ( ( hBOOL @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(535,plain,
! [SV80: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV22 ) @ SV80 ) )
= $false )
| ( ( hBOOL @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(536,plain,
! [SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ! [SY1041: $i,SY1042: $i] :
~ ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY1041 ) @ SY1042 ) )
| ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SY1041 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SY1042 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SY1041 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SY1042 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SY1041 ) @ SY1042 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(537,plain,
! [SV24: $i,SV185: $i,SV134: $i,SV82: $i] :
( ( ! [SY1043: $i,SY1044: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV82 ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV185 ) @ SY1043 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1044 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV82 ) @ SV24 ) ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV185 ) @ SV24 ) ) @ SY1043 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1044 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(538,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV83: $i] :
( ( ! [SY1045: $i,SY1046: $i] :
~ ( ~ ( ( ( ti @ SV83 @ SY1046 )
!= ( ti @ SV83 @ SY1045 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SY1045 ) @ SV186 ) @ SY1046 )
= ( ti @ SV25 @ SV186 ) ) )
| ~ ( ~ ( ( ( ti @ SV83 @ SY1046 )
!= ( ti @ SV83 @ SY1045 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SY1045 ) @ SV186 ) @ SY1046 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SY1046 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(539,plain,
! [SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ! [SY1047: $i,SY1048: $i] :
( ~ ! [SY1049: $i,SY1050: $i,SY1051: $i,SY1052: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SY1048 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ SY1049 ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ SY1050 ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ SY1051 ) @ SY1052 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SY1048 @ SY1047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(540,plain,
! [SV188: $i,SV137: $i,SV27: $i,SV85: $i] :
( ( ! [SY1053: $i,SY1054: $i] :
( ~ ( ( ( ti @ SV85 @ SY1053 )
!= ( ti @ SV85 @ SY1054 ) ) )
| ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SV137 ) @ SY1054 ) @ SV188 ) @ SY1053 )
= ( hAPP @ SV85 @ SV27 @ SV137 @ SY1053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(541,plain,
! [SV189: $i,SV138: $i,SV86: $i,SV28: $i] :
( ( ! [SY1055: $i,SY1056: $i,SY1057: $i] :
( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV138 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY1055 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SY1056 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY1057 ) ) )
| ( ( ti @ SV28 @ SY1055 )
= ( ti @ SV28 @ SY1057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(542,plain,
! [SV139: $i,SV87: $i,SV29: $i] :
( ( ! [SY903: $i,SY904: $i] :
( ( ti @ ( product_prod @ SV29 @ SV87 ) @ SV139 )
!= ( hAPP @ SV87 @ ( product_prod @ SV29 @ SV87 ) @ ( hAPP @ SV29 @ ( fun @ SV87 @ ( product_prod @ SV29 @ SV87 ) ) @ ( product_Pair @ SV29 @ SV87 ) @ SY903 ) @ SY904 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(543,plain,
! [SV190: $i,SV140: $i,SV30: $i,SV88: $i] :
( ( ! [SY1058: $i,SY1059: $i,SY1060: $i] :
( ~ ( ( ( ti @ SV88 @ SY1059 )
!= ( ti @ SV88 @ SY1060 ) ) )
| ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SY1059 ) @ SV190 ) ) @ SY1060 ) @ SY1058 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SY1060 ) @ SY1058 ) ) @ SY1059 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(544,plain,
! [SV141: $i,SV89: $i,SV191: $i,SV31: $i] :
( ( ! [SY1061: $i,SY1062: $i,SY1063: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SY1061 @ SY1062 ) @ SY1063 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SV141 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SY1061 ) @ ( hAPP @ SV89 @ ( product_prod @ SV141 @ SV89 ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( product_prod @ SV141 @ SV89 ) ) @ ( product_Pair @ SV141 @ SV89 ) @ SY1062 ) @ SY1063 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(545,plain,
! [SV192: $i,SV142: $i,SV90: $i,SV32: $i] :
( ( ! [SY1064: $i] :
( ( ( hAPP @ SV32 @ SV90 @ SV142 @ SV192 )
!= ( ti @ SV90 @ SY1064 ) )
| ( ( hAPP @ SV90 @ ( fun @ SV32 @ SV90 ) @ ( hAPP @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) @ ( hAPP @ ( fun @ SV32 @ SV90 ) @ ( fun @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) ) @ ( fun_upd @ SV32 @ SV90 ) @ SV142 ) @ SV192 ) @ SY1064 )
= ( ti @ ( fun @ SV32 @ SV90 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(546,plain,
! [SV193: $i,SV143: $i,SV91: $i,SV33: $i] :
( ( ! [SY1065: $i] :
( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV91 @ ( fun @ SV33 @ bool ) @ SV143 @ SV193 ) @ SY1065 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV91 @ SV33 ) @ bool @ ( hAPP @ ( fun @ SV91 @ ( fun @ SV33 @ bool ) ) @ ( fun @ ( product_prod @ SV91 @ SV33 ) @ bool ) @ ( product_prod_case @ SV91 @ SV33 @ bool ) @ SV143 ) @ ( hAPP @ SV33 @ ( product_prod @ SV91 @ SV33 ) @ ( hAPP @ SV91 @ ( fun @ SV33 @ ( product_prod @ SV91 @ SV33 ) ) @ ( product_Pair @ SV91 @ SV33 ) @ SV193 ) @ SY1065 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(547,plain,
! [SV194: $i,SV144: $i,SV92: $i,SV34: $i] :
( ( ! [SY1066: $i] :
( ( ( hAPP @ SV34 @ ( option @ SV92 ) @ SV144 @ SV194 )
!= ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SY1066 ) )
| ( ( hAPP @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( hAPP @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) @ ( hAPP @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( fun @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) ) @ ( fun_upd @ SV34 @ ( option @ SV92 ) ) @ SV144 ) @ SV194 ) @ ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SY1066 ) )
= ( ti @ ( fun @ SV34 @ ( option @ SV92 ) ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(548,plain,
! [SV35: $i] :
( ( ~ ( hBOOL @ ( ti @ bool @ SV35 ) )
| ( hBOOL @ SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(549,plain,
! [SV35: $i] :
( ( ~ ( hBOOL @ SV35 )
| ( hBOOL @ ( ti @ bool @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(550,plain,
! [SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ! [SY1067: $i] :
~ ! [SY1068: $i,SY1069: $i,SY1070: $i,SY1071: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SY1067 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SY1068 ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ SY1069 ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ SY1070 ) @ SY1071 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(551,plain,
! [SV146: $i,SV94: $i,SV37: $i] :
( ( ! [SY925: $i,SY926: $i] :
( ( ti @ ( product_prod @ SV37 @ SV94 ) @ SV146 )
!= ( hAPP @ SV94 @ ( product_prod @ SV37 @ SV94 ) @ ( hAPP @ SV37 @ ( fun @ SV94 @ ( product_prod @ SV37 @ SV94 ) ) @ ( product_Pair @ SV37 @ SV94 ) @ SY925 ) @ SY926 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(552,plain,
! [SV196: $i,SV147: $i,SV95: $i,SV38: $i] :
( ( ~ ! [SY1072: $i,SY1073: $i,SY1074: $i] :
( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SV196 )
!= ( hAPP @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SY1072 ) @ ( hAPP @ SV147 @ ( product_prod @ SV95 @ SV147 ) @ ( hAPP @ SV95 @ ( fun @ SV147 @ ( product_prod @ SV95 @ SV147 ) ) @ ( product_Pair @ SV95 @ SV147 ) @ SY1073 ) @ SY1074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(553,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV96: $i] :
( ( ! [SY1075: $i,SY1076: $i] :
~ ( ~ ( ( ( ti @ SV96 @ SY1075 )
!= ( ti @ SV96 @ SY1076 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SY1076 ) @ SV197 ) @ SY1075 )
= ( ti @ SV39 @ SV197 ) ) )
| ~ ( ~ ( ( ( ti @ SV96 @ SY1075 )
!= ( ti @ SV96 @ SY1076 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SY1076 ) @ SV197 ) @ SY1075 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SY1075 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(554,plain,
! [SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY1077: $i,SY1078: $i] :
~ ! [SY1079: $i,SY1080: $i,SY1081: $i,SY1082: $i,SY1083: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) ) @ SY1078 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) ) @ SY1079 ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) @ SY1080 ) @ ( hAPP @ ( product_prod @ SV198 @ SY1077 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SY1077 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SY1077 ) ) @ SY1081 ) @ ( hAPP @ SY1077 @ ( product_prod @ SV198 @ SY1077 ) @ ( hAPP @ SV198 @ ( fun @ SY1077 @ ( product_prod @ SV198 @ SY1077 ) ) @ ( product_Pair @ SV198 @ SY1077 ) @ SY1082 ) @ SY1083 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(555,plain,
! [SV199: $i,SV150: $i,SV98: $i,SV41: $i] :
( ( ! [SY1084: $i] :
( ~ ! [SY944: $i,SY945: $i,SY946: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SY1084 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ SY944 ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ SY945 ) @ SY946 ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SY1084 @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(556,plain,
! [SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ! [SY1088: $i,SY1089: $i,SY1090: $i] :
( ~ ! [SY1091: $i,SY1092: $i,SY1093: $i,SY1094: $i,SY1095: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) ) @ bool @ SY1090 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) ) @ SY1091 ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) @ SY1092 ) @ ( hAPP @ ( product_prod @ SV200 @ SY1088 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SY1088 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) @ SY1093 ) @ ( hAPP @ SY1088 @ ( product_prod @ SV200 @ SY1088 ) @ ( hAPP @ SV200 @ ( fun @ SY1088 @ ( product_prod @ SV200 @ SY1088 ) ) @ ( product_Pair @ SV200 @ SY1088 ) @ SY1094 ) @ SY1095 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SY1088 ) ) ) ) @ bool @ SY1090 @ SY1089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(557,plain,
! [SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ! [SY1096: $i,SY1097: $i,SY1098: $i] :
~ ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1096 ) ) @ SY1097 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1098 ) )
| ~ ( ( ( ti @ SV43 @ SY1097 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SY1096 )
!= ( ti @ SV100 @ SY1098 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY1097 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SY1097 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1098 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SY1097 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SY1096 )
!= ( ti @ SV100 @ SY1098 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY1097 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SY1097 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1098 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1096 ) ) @ SY1097 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1098 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(558,plain,
! [SV202: $i,SV153: $i,SV101: $i,SV44: $i] :
( ( ! [SY1099: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV101 @ ( fun @ SV44 @ bool ) @ SV153 @ SV202 ) @ SY1099 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV44 ) @ bool @ ( hAPP @ ( fun @ SV101 @ ( fun @ SV44 @ bool ) ) @ ( fun @ ( product_prod @ SV101 @ SV44 ) @ bool ) @ ( product_prod_case @ SV101 @ SV44 @ bool ) @ SV153 ) @ ( hAPP @ SV44 @ ( product_prod @ SV101 @ SV44 ) @ ( hAPP @ SV101 @ ( fun @ SV44 @ ( product_prod @ SV101 @ SV44 ) ) @ ( product_Pair @ SV101 @ SV44 ) @ SV202 ) @ SY1099 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(559,plain,
! [SV203: $i,SV154: $i,SV102: $i,SV45: $i] :
( ( ! [SY1100: $i] :
~ ( ~ ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SY1100 ) )
| ~ ( ( SV102 != SV203 )
| ( SV154 != SY1100 ) ) )
| ~ ( ~ ~ ( ( SV102 != SV203 )
| ( SV154 != SY1100 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SY1100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(560,plain,
! [SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ! [SY1101: $i,SY1102: $i,SY1103: $i,SY1104: $i] :
( ~ ! [SY1105: $i,SY1106: $i,SY1107: $i,SY1108: $i,SY1109: $i,SY1110: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) ) @ bool @ SY1104 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) ) @ SY1105 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) @ SY1106 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) @ SY1107 ) @ ( hAPP @ ( product_prod @ SY1101 @ SY1102 ) @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SY1101 @ SY1102 ) @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) @ SY1108 ) @ ( hAPP @ SY1102 @ ( product_prod @ SY1101 @ SY1102 ) @ ( hAPP @ SY1101 @ ( fun @ SY1102 @ ( product_prod @ SY1101 @ SY1102 ) ) @ ( product_Pair @ SY1101 @ SY1102 ) @ SY1109 ) @ SY1110 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SY1101 @ SY1102 ) ) ) ) ) @ bool @ SY1104 @ SY1103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(561,plain,
! [SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1111: $i,SY1112: $i,SY1113: $i] :
~ ! [SY1114: $i,SY1115: $i,SY1116: $i,SY1117: $i,SY1118: $i,SY1119: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) ) @ SY1113 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) ) @ SY1114 ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) @ SY1115 ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) @ SY1116 ) @ ( hAPP @ ( product_prod @ SY1111 @ SY1112 ) @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SY1111 @ SY1112 ) @ ( product_prod @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SY1111 @ SY1112 ) ) @ SY1117 ) @ ( hAPP @ SY1112 @ ( product_prod @ SY1111 @ SY1112 ) @ ( hAPP @ SY1111 @ ( fun @ SY1112 @ ( product_prod @ SY1111 @ SY1112 ) ) @ ( product_Pair @ SY1111 @ SY1112 ) @ SY1118 ) @ SY1119 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(562,plain,
! [SV206: $i,SV157: $i,SV105: $i,SV48: $i] :
( ( ! [SY1120: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV48 @ SV105 ) @ bool @ ( hAPP @ ( fun @ SV48 @ ( fun @ SV105 @ bool ) ) @ ( fun @ ( product_prod @ SV48 @ SV105 ) @ bool ) @ ( product_prod_case @ SV48 @ SV105 @ bool ) @ SV157 ) @ ( hAPP @ SV105 @ ( product_prod @ SV48 @ SV105 ) @ ( hAPP @ SV48 @ ( fun @ SV105 @ ( product_prod @ SV48 @ SV105 ) ) @ ( product_Pair @ SV48 @ SV105 ) @ SV206 ) @ SY1120 ) ) )
| ( hBOOL @ ( hAPP @ SV105 @ bool @ ( hAPP @ SV48 @ ( fun @ SV105 @ bool ) @ SV157 @ SV206 ) @ SY1120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(563,plain,
! [SV49: $i,SV207: $i,SV158: $i,SV106: $i] :
( ( ! [SY1121: $i,SY1122: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV106 ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV207 ) @ SY1121 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1122 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV106 ) ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV207 ) ) @ SY1121 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(564,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ~ ( ~ ( ~ ! [SY1123: $i,SY1124: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) ) )
| ~ ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
| ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(565,plain,
! [SV209: $i,SV160: $i,SV108: $i,SV51: $i] :
( ( ~ ! [SY1127: $i] :
( ( hAPP @ SV51 @ SV108 @ SV160 @ SY1127 )
= ( hAPP @ SV51 @ SV108 @ SV209 @ SY1127 ) )
| ( ( ti @ ( fun @ SV51 @ SV108 ) @ SV160 )
= ( ti @ ( fun @ SV51 @ SV108 ) @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(566,plain,
! [SV161: $i,SV109: $i,SV52: $i] :
( ( ~ ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
!= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
| ( SV109 = SV161 ) )
| ~ ( ( SV109 != SV161 )
| ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(567,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ~ ( ~ ~ ! [SY997: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY997 ) )
| ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
| ~ ( ~ ~ ! [SY1000: $i] :
~ ~ ! [SY1001: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY1000 ) @ SY1001 ) ) )
| ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(568,plain,
! [SV210: $i,SV163: $i,SV111: $i,SV54: $i] :
( ( ! [SY1128: $i,SY1129: $i,SY1130: $i] :
( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 ) @ ( hAPP @ SV163 @ ( product_prod @ SV111 @ SV163 ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( product_prod @ SV111 @ SV163 ) ) @ ( product_Pair @ SV111 @ SV163 ) @ SY1128 ) @ SY1129 ) ) @ SY1130 ) )
| ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SV163 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 @ SY1128 ) @ SY1129 ) @ SY1130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(569,plain,
! [SV211: $i,SV164: $i,SV112: $i,SV55: $i] :
( ( ! [SY1131: $i,SY1132: $i] :
( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
!= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SY1131 ) @ SY1132 ) )
| ~ ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SY1131 ) )
| ( ( ti @ SV55 @ SV211 )
!= ( ti @ SV55 @ SY1132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(570,plain,
! [SV165: $i,SV113: $i,SV56: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) )
| ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(571,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ~ ( ~ ! [SY1010: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1010 ) )
| ! [SY1011: $i,SY1012: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1011 ) @ SY1012 ) ) ) )
| ~ ( ~ ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1013 ) @ SY1014 ) ) )
| ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(572,plain,
! [SV212: $i,SV167: $i,SV115: $i,SV58: $i] :
( ( ! [SY1133: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SY1133 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SY1133 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SY1133 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SY1133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(573,plain,
! [SV116: $i,SV213: $i,SV168: $i,SV59: $i] :
( ( ! [SY1134: $i] :
( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SY1134 ) )
| ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SY1134 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(574,plain,
! [SV214: $i,SV169: $i,SV117: $i,SV60: $i] :
( ( ! [SY1135: $i] :
~ ( ~ ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SY1135 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
| ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SY1135 ) ) )
| ~ ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
!= ( ti @ SV60 @ SY1135 ) )
| ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SY1135 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(575,plain,
! [SV215: $i,SV174: $i,SV122: $i,SV67: $i,SV9: $i] :
( ( ( hAPP @ SV9 @ SV67 @ ( hAPP @ SV67 @ ( fun @ SV9 @ SV67 ) @ ( hAPP @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) @ ( hAPP @ ( fun @ SV9 @ SV67 ) @ ( fun @ SV9 @ ( fun @ SV67 @ ( fun @ SV9 @ SV67 ) ) ) @ ( fun_upd @ SV9 @ SV67 ) @ SV122 ) @ SV174 ) @ SV215 ) @ SV174 )
= ( ti @ SV67 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(576,plain,
! [SV216: $i,SV175: $i,SV123: $i,SV68: $i,SV10: $i] :
( ( ! [SY1136: $i] :
( ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SV175 ) @ SV216 ) ) @ SV175 ) @ SY1136 )
= ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SV175 ) @ SY1136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(577,plain,
! [SV217: $i,SV176: $i,SV125: $i,SV70: $i,SV12: $i] :
( ( ! [SY1137: $i] :
( ( hAPP @ ( product_prod @ SV12 @ SV70 ) @ SV125 @ ( hAPP @ ( fun @ SV12 @ ( fun @ SV70 @ SV125 ) ) @ ( fun @ ( product_prod @ SV12 @ SV70 ) @ SV125 ) @ ( product_prod_rec @ SV12 @ SV70 @ SV125 ) @ SV176 ) @ ( hAPP @ SV70 @ ( product_prod @ SV12 @ SV70 ) @ ( hAPP @ SV12 @ ( fun @ SV70 @ ( product_prod @ SV12 @ SV70 ) ) @ ( product_Pair @ SV12 @ SV70 ) @ SV217 ) @ SY1137 ) )
= ( hAPP @ SV70 @ SV125 @ ( hAPP @ SV12 @ ( fun @ SV70 @ SV125 ) @ SV176 @ SV217 ) @ SY1137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(578,plain,
! [SV218: $i,SV177: $i,SV126: $i,SV71: $i,SV13: $i] :
( ( ! [SY1138: $i] :
( ( hAPP @ ( product_prod @ SV13 @ SV71 ) @ SV126 @ ( hAPP @ ( fun @ SV13 @ ( fun @ SV71 @ SV126 ) ) @ ( fun @ ( product_prod @ SV13 @ SV71 ) @ SV126 ) @ ( produc1605651328_split @ SV13 @ SV71 @ SV126 ) @ SV177 ) @ ( hAPP @ SV71 @ ( product_prod @ SV13 @ SV71 ) @ ( hAPP @ SV13 @ ( fun @ SV71 @ ( product_prod @ SV13 @ SV71 ) ) @ ( product_Pair @ SV13 @ SV71 ) @ SV218 ) @ SY1138 ) )
= ( hAPP @ SV71 @ SV126 @ ( hAPP @ SV13 @ ( fun @ SV71 @ SV126 ) @ SV177 @ SV218 ) @ SY1138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(579,plain,
! [SV219: $i,SV178: $i,SV127: $i,SV72: $i,SV14: $i] :
( ( ! [SY1139: $i] :
( ( hAPP @ ( product_prod @ SV14 @ SV72 ) @ SV127 @ ( hAPP @ ( fun @ SV14 @ ( fun @ SV72 @ SV127 ) ) @ ( fun @ ( product_prod @ SV14 @ SV72 ) @ SV127 ) @ ( product_prod_case @ SV14 @ SV72 @ SV127 ) @ SV178 ) @ ( hAPP @ SV72 @ ( product_prod @ SV14 @ SV72 ) @ ( hAPP @ SV14 @ ( fun @ SV72 @ ( product_prod @ SV14 @ SV72 ) ) @ ( product_Pair @ SV14 @ SV72 ) @ SV219 ) @ SY1139 ) )
= ( hAPP @ SV72 @ SV127 @ ( hAPP @ SV14 @ ( fun @ SV72 @ SV127 ) @ SV178 @ SV219 ) @ SY1139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(580,plain,
! [SV220: $i,SV179: $i,SV128: $i,SV73: $i,SV15: $i] :
( ( ! [SY1140: $i] :
( ( hAPP @ ( product_prod @ SV15 @ SV73 ) @ SV128 @ ( hAPP @ ( fun @ SV15 @ ( fun @ SV73 @ SV128 ) ) @ ( fun @ ( product_prod @ SV15 @ SV73 ) @ SV128 ) @ ( product_prod_case @ SV15 @ SV73 @ SV128 ) @ SV179 ) @ ( hAPP @ SV73 @ ( product_prod @ SV15 @ SV73 ) @ ( hAPP @ SV15 @ ( fun @ SV73 @ ( product_prod @ SV15 @ SV73 ) ) @ ( product_Pair @ SV15 @ SV73 ) @ SV220 ) @ SY1140 ) )
= ( hAPP @ SV73 @ SV128 @ ( hAPP @ SV15 @ ( fun @ SV73 @ SV128 ) @ SV179 @ SV220 ) @ SY1140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(581,plain,
! [SV221: $i,SV180: $i,SV129: $i,SV74: $i,SV16: $i] :
( ( ~ ! [SY1141: $i] :
( ( hAPP @ SV16 @ ( option @ SV74 ) @ ( hAPP @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( hAPP @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) @ ( hAPP @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( fun @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) ) @ ( fun_upd @ SV16 @ ( option @ SV74 ) ) @ SV129 ) @ SV180 ) @ ( hAPP @ SV74 @ ( option @ SV74 ) @ ( some @ SV74 ) @ SV221 ) ) @ SY1141 )
= ( none @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(582,plain,
! [SV222: $i,SV181: $i,SV130: $i,SV75: $i,SV17: $i] :
( ( ! [SY1142: $i] :
( ( hAPP @ SV17 @ SV75 @ ( hAPP @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) @ ( hAPP @ ( fun @ SV130 @ SV75 ) @ ( fun @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) ) @ ( combb @ SV130 @ SV75 @ SV17 ) @ SV181 ) @ SV222 ) @ SY1142 )
= ( hAPP @ SV130 @ SV75 @ SV181 @ ( hAPP @ SV17 @ SV130 @ SV222 @ SY1142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(583,plain,
! [SV223: $i,SV182: $i,SV131: $i,SV76: $i,SV18: $i] :
( ( ! [SY1143: $i] :
( ( hAPP @ SV18 @ SV76 @ ( hAPP @ SV131 @ ( fun @ SV18 @ SV76 ) @ ( hAPP @ ( fun @ SV18 @ ( fun @ SV131 @ SV76 ) ) @ ( fun @ SV131 @ ( fun @ SV18 @ SV76 ) ) @ ( combc @ SV18 @ SV131 @ SV76 ) @ SV182 ) @ SV223 ) @ SY1143 )
= ( hAPP @ SV131 @ SV76 @ ( hAPP @ SV18 @ ( fun @ SV131 @ SV76 ) @ SV182 @ SY1143 ) @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(584,plain,
! [SV224: $i,SV183: $i,SV132: $i,SV77: $i,SV19: $i] :
( ( ! [SY1144: $i] :
( ( hAPP @ SV19 @ SV77 @ ( hAPP @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) @ ( hAPP @ ( fun @ SV19 @ ( fun @ SV132 @ SV77 ) ) @ ( fun @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) ) @ ( combs @ SV19 @ SV132 @ SV77 ) @ SV183 ) @ SV224 ) @ SY1144 )
= ( hAPP @ SV132 @ SV77 @ ( hAPP @ SV19 @ ( fun @ SV132 @ SV77 ) @ SV183 @ SY1144 ) @ ( hAPP @ SV19 @ SV132 @ SV224 @ SY1144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(585,plain,
! [SV20: $i,SV78: $i] :
( ( ( hBOOL @ SV78 )
= $false )
| ( ( ~ ( hBOOL @ SV20 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV78 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(586,plain,
! [SV225: $i,SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ! [SY1145: $i] :
~ ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SY1145 ) )
| ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SY1145 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SY1145 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SY1145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(587,plain,
! [SV24: $i,SV226: $i,SV185: $i,SV134: $i,SV82: $i] :
( ( ! [SY1146: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV82 ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV185 ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1146 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV82 ) @ SV24 ) ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV185 ) @ SV24 ) ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(588,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV83: $i] :
( ( ! [SY1147: $i] :
~ ( ~ ( ( ( ti @ SV83 @ SY1147 )
!= ( ti @ SV83 @ SV227 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SY1147 )
= ( ti @ SV25 @ SV186 ) ) )
| ~ ( ~ ( ( ( ti @ SV83 @ SY1147 )
!= ( ti @ SV83 @ SV227 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SY1147 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SY1147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(589,plain,
! [SV228: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ! [SY1148: $i] :
( ~ ! [SY1049: $i,SY1050: $i,SY1051: $i,SY1052: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SY1148 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ SY1049 ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ SY1050 ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ SY1051 ) @ SY1052 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SY1148 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(590,plain,
! [SV188: $i,SV137: $i,SV27: $i,SV229: $i,SV85: $i] :
( ( ! [SY1153: $i] :
( ~ ( ( ( ti @ SV85 @ SV229 )
!= ( ti @ SV85 @ SY1153 ) ) )
| ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SV137 ) @ SY1153 ) @ SV188 ) @ SV229 )
= ( hAPP @ SV85 @ SV27 @ SV137 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(591,plain,
! [SV230: $i,SV189: $i,SV138: $i,SV86: $i,SV28: $i] :
( ( ! [SY1154: $i,SY1155: $i] :
( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV138 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV230 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SY1154 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY1155 ) ) )
| ( ( ti @ SV28 @ SV230 )
= ( ti @ SV28 @ SY1155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(592,plain,
! [SV139: $i,SV87: $i,SV29: $i] :
( ( ! [SY1156: $i] :
( ( ti @ ( product_prod @ SV29 @ SV87 ) @ SV139 )
!= ( hAPP @ SV87 @ ( product_prod @ SV29 @ SV87 ) @ ( hAPP @ SV29 @ ( fun @ SV87 @ ( product_prod @ SV29 @ SV87 ) ) @ ( product_Pair @ SV29 @ SV87 ) @ ( sK1_SY903 @ SV139 @ SV87 @ SV29 ) ) @ SY1156 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[542]) ).
thf(593,plain,
! [SV231: $i,SV190: $i,SV140: $i,SV30: $i,SV88: $i] :
( ( ! [SY1157: $i,SY1158: $i] :
( ~ ( ( ( ti @ SV88 @ SY1157 )
!= ( ti @ SV88 @ SY1158 ) ) )
| ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SY1157 ) @ SV190 ) ) @ SY1158 ) @ SV231 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SY1158 ) @ SV231 ) ) @ SY1157 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(594,plain,
! [SV232: $i,SV141: $i,SV89: $i,SV191: $i,SV31: $i] :
( ( ! [SY1159: $i,SY1160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 @ SY1159 ) @ SY1160 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SV141 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 ) @ ( hAPP @ SV89 @ ( product_prod @ SV141 @ SV89 ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( product_prod @ SV141 @ SV89 ) ) @ ( product_Pair @ SV141 @ SV89 ) @ SY1159 ) @ SY1160 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(595,plain,
! [SV233: $i,SV192: $i,SV142: $i,SV90: $i,SV32: $i] :
( ( ( ( hAPP @ SV32 @ SV90 @ SV142 @ SV192 )
!= ( ti @ SV90 @ SV233 ) )
| ( ( hAPP @ SV90 @ ( fun @ SV32 @ SV90 ) @ ( hAPP @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) @ ( hAPP @ ( fun @ SV32 @ SV90 ) @ ( fun @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) ) @ ( fun_upd @ SV32 @ SV90 ) @ SV142 ) @ SV192 ) @ SV233 )
= ( ti @ ( fun @ SV32 @ SV90 ) @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(596,plain,
! [SV234: $i,SV193: $i,SV143: $i,SV91: $i,SV33: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV91 @ ( fun @ SV33 @ bool ) @ SV143 @ SV193 ) @ SV234 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV91 @ SV33 ) @ bool @ ( hAPP @ ( fun @ SV91 @ ( fun @ SV33 @ bool ) ) @ ( fun @ ( product_prod @ SV91 @ SV33 ) @ bool ) @ ( product_prod_case @ SV91 @ SV33 @ bool ) @ SV143 ) @ ( hAPP @ SV33 @ ( product_prod @ SV91 @ SV33 ) @ ( hAPP @ SV91 @ ( fun @ SV33 @ ( product_prod @ SV91 @ SV33 ) ) @ ( product_Pair @ SV91 @ SV33 ) @ SV193 ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(597,plain,
! [SV235: $i,SV194: $i,SV144: $i,SV92: $i,SV34: $i] :
( ( ( ( hAPP @ SV34 @ ( option @ SV92 ) @ SV144 @ SV194 )
!= ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SV235 ) )
| ( ( hAPP @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( hAPP @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) @ ( hAPP @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( fun @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) ) @ ( fun_upd @ SV34 @ ( option @ SV92 ) ) @ SV144 ) @ SV194 ) @ ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SV235 ) )
= ( ti @ ( fun @ SV34 @ ( option @ SV92 ) ) @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(598,plain,
! [SV35: $i] :
( ( ( ~ ( hBOOL @ ( ti @ bool @ SV35 ) ) )
= $true )
| ( ( hBOOL @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(599,plain,
! [SV35: $i] :
( ( ( ~ ( hBOOL @ SV35 ) )
= $true )
| ( ( hBOOL @ ( ti @ bool @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(600,plain,
! [SV236: $i,SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ~ ! [SY1161: $i,SY1162: $i,SY1163: $i,SY1164: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SV236 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SY1161 ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ SY1162 ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ SY1163 ) @ SY1164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(601,plain,
! [SV146: $i,SV94: $i,SV37: $i] :
( ( ! [SY1165: $i] :
( ( ti @ ( product_prod @ SV37 @ SV94 ) @ SV146 )
!= ( hAPP @ SV94 @ ( product_prod @ SV37 @ SV94 ) @ ( hAPP @ SV37 @ ( fun @ SV94 @ ( product_prod @ SV37 @ SV94 ) ) @ ( product_Pair @ SV37 @ SV94 ) @ ( sK2_SY925 @ SV146 @ SV94 @ SV37 ) ) @ SY1165 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[551]) ).
thf(602,plain,
! [SV196: $i,SV147: $i,SV95: $i,SV38: $i] :
( ( ! [SY1072: $i,SY1073: $i,SY1074: $i] :
( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SV196 )
!= ( hAPP @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SY1072 ) @ ( hAPP @ SV147 @ ( product_prod @ SV95 @ SV147 ) @ ( hAPP @ SV95 @ ( fun @ SV147 @ ( product_prod @ SV95 @ SV147 ) ) @ ( product_Pair @ SV95 @ SV147 ) @ SY1073 ) @ SY1074 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(603,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV237: $i,SV96: $i] :
( ( ! [SY1166: $i] :
~ ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SY1166 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SY1166 ) @ SV197 ) @ SV237 )
= ( ti @ SV39 @ SV197 ) ) )
| ~ ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SY1166 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SY1166 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(604,plain,
! [SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY1167: $i] :
~ ! [SY1168: $i,SY1169: $i,SY1170: $i,SY1171: $i,SY1172: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SY1167 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SY1168 ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ SY1169 ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ SY1170 ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ SY1171 ) @ SY1172 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(605,plain,
! [SV199: $i,SV239: $i,SV150: $i,SV98: $i,SV41: $i] :
( ( ~ ! [SY1173: $i,SY1174: $i,SY1175: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ SY1173 ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ SY1174 ) @ SY1175 ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(606,plain,
! [SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ! [SY1176: $i,SY1177: $i] :
( ~ ! [SY1178: $i,SY1179: $i,SY1180: $i,SY1181: $i,SY1182: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SY1177 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ SY1178 ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ SY1179 ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ SY1180 ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1181 ) @ SY1182 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SY1177 @ SY1176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(607,plain,
! [SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ! [SY1183: $i,SY1184: $i] :
~ ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SY1183 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1184 ) )
| ~ ( ( ( ti @ SV43 @ SY1183 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SY1184 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY1183 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SY1183 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1184 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SY1183 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SY1184 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SY1183 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SY1183 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1184 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SY1183 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(608,plain,
! [SV242: $i,SV202: $i,SV153: $i,SV101: $i,SV44: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV101 @ ( fun @ SV44 @ bool ) @ SV153 @ SV202 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV44 ) @ bool @ ( hAPP @ ( fun @ SV101 @ ( fun @ SV44 @ bool ) ) @ ( fun @ ( product_prod @ SV101 @ SV44 ) @ bool ) @ ( product_prod_case @ SV101 @ SV44 @ bool ) @ SV153 ) @ ( hAPP @ SV44 @ ( product_prod @ SV101 @ SV44 ) @ ( hAPP @ SV101 @ ( fun @ SV44 @ ( product_prod @ SV101 @ SV44 ) ) @ ( product_Pair @ SV101 @ SV44 ) @ SV202 ) @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(609,plain,
! [SV243: $i,SV203: $i,SV154: $i,SV102: $i,SV45: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
| ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) )
| ~ ( ~ ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(610,plain,
! [SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ! [SY1185: $i,SY1186: $i,SY1187: $i] :
( ~ ! [SY1188: $i,SY1189: $i,SY1190: $i,SY1191: $i,SY1192: $i,SY1193: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) ) @ bool @ SY1187 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) ) @ SY1188 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) @ SY1189 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) @ SY1190 ) @ ( hAPP @ ( product_prod @ SV244 @ SY1185 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SY1185 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) @ SY1191 ) @ ( hAPP @ SY1185 @ ( product_prod @ SV244 @ SY1185 ) @ ( hAPP @ SV244 @ ( fun @ SY1185 @ ( product_prod @ SV244 @ SY1185 ) ) @ ( product_Pair @ SV244 @ SY1185 ) @ SY1192 ) @ SY1193 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SY1185 ) ) ) ) ) @ bool @ SY1187 @ SY1186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(611,plain,
! [SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1194: $i,SY1195: $i] :
~ ! [SY1196: $i,SY1197: $i,SY1198: $i,SY1199: $i,SY1200: $i,SY1201: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) ) @ SY1195 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) ) @ SY1196 ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) @ SY1197 ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) @ SY1198 ) @ ( hAPP @ ( product_prod @ SV245 @ SY1194 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SY1194 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SY1194 ) ) @ SY1199 ) @ ( hAPP @ SY1194 @ ( product_prod @ SV245 @ SY1194 ) @ ( hAPP @ SV245 @ ( fun @ SY1194 @ ( product_prod @ SV245 @ SY1194 ) ) @ ( product_Pair @ SV245 @ SY1194 ) @ SY1200 ) @ SY1201 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(612,plain,
! [SV246: $i,SV206: $i,SV157: $i,SV105: $i,SV48: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV48 @ SV105 ) @ bool @ ( hAPP @ ( fun @ SV48 @ ( fun @ SV105 @ bool ) ) @ ( fun @ ( product_prod @ SV48 @ SV105 ) @ bool ) @ ( product_prod_case @ SV48 @ SV105 @ bool ) @ SV157 ) @ ( hAPP @ SV105 @ ( product_prod @ SV48 @ SV105 ) @ ( hAPP @ SV48 @ ( fun @ SV105 @ ( product_prod @ SV48 @ SV105 ) ) @ ( product_Pair @ SV48 @ SV105 ) @ SV206 ) @ SV246 ) ) )
| ( hBOOL @ ( hAPP @ SV105 @ bool @ ( hAPP @ SV48 @ ( fun @ SV105 @ bool ) @ SV157 @ SV206 ) @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(613,plain,
! [SV49: $i,SV247: $i,SV207: $i,SV158: $i,SV106: $i] :
( ( ! [SY1202: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV106 ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV207 ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1202 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV106 ) ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV207 ) ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SY1202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(614,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ~ ( ~ ! [SY1123: $i,SY1124: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) ) )
| ~ ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
| ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(615,plain,
! [SV209: $i,SV160: $i,SV108: $i,SV51: $i] :
( ( ( ~ ! [SY1127: $i] :
( ( hAPP @ SV51 @ SV108 @ SV160 @ SY1127 )
= ( hAPP @ SV51 @ SV108 @ SV209 @ SY1127 ) ) )
= $true )
| ( ( ( ti @ ( fun @ SV51 @ SV108 ) @ SV160 )
= ( ti @ ( fun @ SV51 @ SV108 ) @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(616,plain,
! [SV161: $i,SV109: $i,SV52: $i] :
( ( ~ ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
!= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
| ( SV109 = SV161 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(617,plain,
! [SV52: $i,SV161: $i,SV109: $i] :
( ( ~ ( ( SV109 != SV161 )
| ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(618,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ~ ( ~ ~ ! [SY997: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY997 ) )
| ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[567]) ).
thf(619,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ~ ( ~ ~ ! [SY1000: $i] :
~ ~ ! [SY1001: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY1000 ) @ SY1001 ) ) )
| ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[567]) ).
thf(620,plain,
! [SV248: $i,SV210: $i,SV163: $i,SV111: $i,SV54: $i] :
( ( ! [SY1203: $i,SY1204: $i] :
( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 ) @ ( hAPP @ SV163 @ ( product_prod @ SV111 @ SV163 ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( product_prod @ SV111 @ SV163 ) ) @ ( product_Pair @ SV111 @ SV163 ) @ SV248 ) @ SY1203 ) ) @ SY1204 ) )
| ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SV163 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 @ SV248 ) @ SY1203 ) @ SY1204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(621,plain,
! [SV249: $i,SV211: $i,SV164: $i,SV112: $i,SV55: $i] :
( ( ! [SY1205: $i] :
( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
!= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SY1205 ) )
| ~ ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SV249 ) )
| ( ( ti @ SV55 @ SV211 )
!= ( ti @ SV55 @ SY1205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(622,plain,
! [SV165: $i,SV113: $i,SV56: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) )
| ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(623,plain,
! [SV113: $i,SV165: $i,SV56: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(624,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ~ ( ~ ! [SY1010: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1010 ) )
| ! [SY1011: $i,SY1012: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1011 ) @ SY1012 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(625,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ~ ( ~ ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1013 ) @ SY1014 ) ) )
| ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(626,plain,
! [SV250: $i,SV212: $i,SV167: $i,SV115: $i,SV58: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(627,plain,
! [SV116: $i,SV251: $i,SV213: $i,SV168: $i,SV59: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV251 ) )
| ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV251 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(628,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV117: $i,SV60: $i] :
( ( ~ ( ~ ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
| ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SV252 ) ) )
| ~ ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
!= ( ti @ SV60 @ SV252 ) )
| ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(629,plain,
! [SV253: $i,SV216: $i,SV175: $i,SV123: $i,SV68: $i,SV10: $i] :
( ( ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SV175 ) @ SV216 ) ) @ SV175 ) @ SV253 )
= ( hAPP @ SV10 @ ( fun @ SV68 @ SV10 ) @ ( hAPP @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) @ ( hAPP @ ( fun @ SV68 @ SV10 ) @ ( fun @ SV68 @ ( fun @ SV10 @ ( fun @ SV68 @ SV10 ) ) ) @ ( fun_upd @ SV68 @ SV10 ) @ SV123 ) @ SV175 ) @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(630,plain,
! [SV254: $i,SV217: $i,SV176: $i,SV125: $i,SV70: $i,SV12: $i] :
( ( ( hAPP @ ( product_prod @ SV12 @ SV70 ) @ SV125 @ ( hAPP @ ( fun @ SV12 @ ( fun @ SV70 @ SV125 ) ) @ ( fun @ ( product_prod @ SV12 @ SV70 ) @ SV125 ) @ ( product_prod_rec @ SV12 @ SV70 @ SV125 ) @ SV176 ) @ ( hAPP @ SV70 @ ( product_prod @ SV12 @ SV70 ) @ ( hAPP @ SV12 @ ( fun @ SV70 @ ( product_prod @ SV12 @ SV70 ) ) @ ( product_Pair @ SV12 @ SV70 ) @ SV217 ) @ SV254 ) )
= ( hAPP @ SV70 @ SV125 @ ( hAPP @ SV12 @ ( fun @ SV70 @ SV125 ) @ SV176 @ SV217 ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(631,plain,
! [SV255: $i,SV218: $i,SV177: $i,SV126: $i,SV71: $i,SV13: $i] :
( ( ( hAPP @ ( product_prod @ SV13 @ SV71 ) @ SV126 @ ( hAPP @ ( fun @ SV13 @ ( fun @ SV71 @ SV126 ) ) @ ( fun @ ( product_prod @ SV13 @ SV71 ) @ SV126 ) @ ( produc1605651328_split @ SV13 @ SV71 @ SV126 ) @ SV177 ) @ ( hAPP @ SV71 @ ( product_prod @ SV13 @ SV71 ) @ ( hAPP @ SV13 @ ( fun @ SV71 @ ( product_prod @ SV13 @ SV71 ) ) @ ( product_Pair @ SV13 @ SV71 ) @ SV218 ) @ SV255 ) )
= ( hAPP @ SV71 @ SV126 @ ( hAPP @ SV13 @ ( fun @ SV71 @ SV126 ) @ SV177 @ SV218 ) @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(632,plain,
! [SV256: $i,SV219: $i,SV178: $i,SV127: $i,SV72: $i,SV14: $i] :
( ( ( hAPP @ ( product_prod @ SV14 @ SV72 ) @ SV127 @ ( hAPP @ ( fun @ SV14 @ ( fun @ SV72 @ SV127 ) ) @ ( fun @ ( product_prod @ SV14 @ SV72 ) @ SV127 ) @ ( product_prod_case @ SV14 @ SV72 @ SV127 ) @ SV178 ) @ ( hAPP @ SV72 @ ( product_prod @ SV14 @ SV72 ) @ ( hAPP @ SV14 @ ( fun @ SV72 @ ( product_prod @ SV14 @ SV72 ) ) @ ( product_Pair @ SV14 @ SV72 ) @ SV219 ) @ SV256 ) )
= ( hAPP @ SV72 @ SV127 @ ( hAPP @ SV14 @ ( fun @ SV72 @ SV127 ) @ SV178 @ SV219 ) @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(633,plain,
! [SV257: $i,SV220: $i,SV179: $i,SV128: $i,SV73: $i,SV15: $i] :
( ( ( hAPP @ ( product_prod @ SV15 @ SV73 ) @ SV128 @ ( hAPP @ ( fun @ SV15 @ ( fun @ SV73 @ SV128 ) ) @ ( fun @ ( product_prod @ SV15 @ SV73 ) @ SV128 ) @ ( product_prod_case @ SV15 @ SV73 @ SV128 ) @ SV179 ) @ ( hAPP @ SV73 @ ( product_prod @ SV15 @ SV73 ) @ ( hAPP @ SV15 @ ( fun @ SV73 @ ( product_prod @ SV15 @ SV73 ) ) @ ( product_Pair @ SV15 @ SV73 ) @ SV220 ) @ SV257 ) )
= ( hAPP @ SV73 @ SV128 @ ( hAPP @ SV15 @ ( fun @ SV73 @ SV128 ) @ SV179 @ SV220 ) @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(634,plain,
! [SV221: $i,SV180: $i,SV129: $i,SV74: $i,SV16: $i] :
( ( ! [SY1141: $i] :
( ( hAPP @ SV16 @ ( option @ SV74 ) @ ( hAPP @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( hAPP @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) @ ( hAPP @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( fun @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) ) @ ( fun_upd @ SV16 @ ( option @ SV74 ) ) @ SV129 ) @ SV180 ) @ ( hAPP @ SV74 @ ( option @ SV74 ) @ ( some @ SV74 ) @ SV221 ) ) @ SY1141 )
= ( none @ SV74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(635,plain,
! [SV258: $i,SV222: $i,SV181: $i,SV130: $i,SV75: $i,SV17: $i] :
( ( ( hAPP @ SV17 @ SV75 @ ( hAPP @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) @ ( hAPP @ ( fun @ SV130 @ SV75 ) @ ( fun @ ( fun @ SV17 @ SV130 ) @ ( fun @ SV17 @ SV75 ) ) @ ( combb @ SV130 @ SV75 @ SV17 ) @ SV181 ) @ SV222 ) @ SV258 )
= ( hAPP @ SV130 @ SV75 @ SV181 @ ( hAPP @ SV17 @ SV130 @ SV222 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(636,plain,
! [SV259: $i,SV223: $i,SV182: $i,SV131: $i,SV76: $i,SV18: $i] :
( ( ( hAPP @ SV18 @ SV76 @ ( hAPP @ SV131 @ ( fun @ SV18 @ SV76 ) @ ( hAPP @ ( fun @ SV18 @ ( fun @ SV131 @ SV76 ) ) @ ( fun @ SV131 @ ( fun @ SV18 @ SV76 ) ) @ ( combc @ SV18 @ SV131 @ SV76 ) @ SV182 ) @ SV223 ) @ SV259 )
= ( hAPP @ SV131 @ SV76 @ ( hAPP @ SV18 @ ( fun @ SV131 @ SV76 ) @ SV182 @ SV259 ) @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(637,plain,
! [SV260: $i,SV224: $i,SV183: $i,SV132: $i,SV77: $i,SV19: $i] :
( ( ( hAPP @ SV19 @ SV77 @ ( hAPP @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) @ ( hAPP @ ( fun @ SV19 @ ( fun @ SV132 @ SV77 ) ) @ ( fun @ ( fun @ SV19 @ SV132 ) @ ( fun @ SV19 @ SV77 ) ) @ ( combs @ SV19 @ SV132 @ SV77 ) @ SV183 ) @ SV224 ) @ SV260 )
= ( hAPP @ SV132 @ SV77 @ ( hAPP @ SV19 @ ( fun @ SV132 @ SV77 ) @ SV183 @ SV260 ) @ ( hAPP @ SV19 @ SV132 @ SV224 @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(638,plain,
! [SV78: $i,SV20: $i] :
( ( ( hBOOL @ SV20 )
= $false )
| ( ( hBOOL @ SV78 )
= $false )
| ( ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ SV78 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(639,plain,
! [SV261: $i,SV225: $i,SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ~ ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
| ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(640,plain,
! [SV24: $i,SV262: $i,SV226: $i,SV185: $i,SV134: $i,SV82: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV82 ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV185 ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV262 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV82 ) @ SV24 ) ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV185 ) @ SV24 ) ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(641,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ~ ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( ti @ SV25 @ SV186 ) ) )
| ~ ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SV263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(642,plain,
! [SV228: $i,SV264: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ~ ! [SY1206: $i,SY1207: $i,SY1208: $i,SY1209: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ SY1206 ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ SY1207 ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ SY1208 ) @ SY1209 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(643,plain,
! [SV188: $i,SV137: $i,SV27: $i,SV265: $i,SV229: $i,SV85: $i] :
( ( ~ ( ( ( ti @ SV85 @ SV229 )
!= ( ti @ SV85 @ SV265 ) ) )
| ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SV137 ) @ SV265 ) @ SV188 ) @ SV229 )
= ( hAPP @ SV85 @ SV27 @ SV137 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(644,plain,
! [SV266: $i,SV230: $i,SV189: $i,SV138: $i,SV86: $i,SV28: $i] :
( ( ! [SY1210: $i] :
( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV138 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV230 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV266 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SY1210 ) ) )
| ( ( ti @ SV28 @ SV230 )
= ( ti @ SV28 @ SY1210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(645,plain,
! [SV139: $i,SV87: $i,SV29: $i] :
( ( ( ti @ ( product_prod @ SV29 @ SV87 ) @ SV139 )
!= ( hAPP @ SV87 @ ( product_prod @ SV29 @ SV87 ) @ ( hAPP @ SV29 @ ( fun @ SV87 @ ( product_prod @ SV29 @ SV87 ) ) @ ( product_Pair @ SV29 @ SV87 ) @ ( sK1_SY903 @ SV139 @ SV87 @ SV29 ) ) @ ( sK3_SY1156 @ SV139 @ SV87 @ SV29 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[592]) ).
thf(646,plain,
! [SV231: $i,SV190: $i,SV140: $i,SV30: $i,SV267: $i,SV88: $i] :
( ( ! [SY1211: $i] :
( ~ ( ( ( ti @ SV88 @ SV267 )
!= ( ti @ SV88 @ SY1211 ) ) )
| ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV267 ) @ SV190 ) ) @ SY1211 ) @ SV231 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SY1211 ) @ SV231 ) ) @ SV267 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(647,plain,
! [SV268: $i,SV232: $i,SV141: $i,SV89: $i,SV191: $i,SV31: $i] :
( ( ! [SY1212: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 @ SV268 ) @ SY1212 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SV141 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 ) @ ( hAPP @ SV89 @ ( product_prod @ SV141 @ SV89 ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( product_prod @ SV141 @ SV89 ) ) @ ( product_Pair @ SV141 @ SV89 ) @ SV268 ) @ SY1212 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(648,plain,
! [SV233: $i,SV192: $i,SV142: $i,SV90: $i,SV32: $i] :
( ( ( ( hAPP @ SV32 @ SV90 @ SV142 @ SV192 )
!= ( ti @ SV90 @ SV233 ) )
= $true )
| ( ( ( hAPP @ SV90 @ ( fun @ SV32 @ SV90 ) @ ( hAPP @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) @ ( hAPP @ ( fun @ SV32 @ SV90 ) @ ( fun @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) ) @ ( fun_upd @ SV32 @ SV90 ) @ SV142 ) @ SV192 ) @ SV233 )
= ( ti @ ( fun @ SV32 @ SV90 ) @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(649,plain,
! [SV234: $i,SV193: $i,SV143: $i,SV91: $i,SV33: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV91 @ ( fun @ SV33 @ bool ) @ SV143 @ SV193 ) @ SV234 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV91 @ SV33 ) @ bool @ ( hAPP @ ( fun @ SV91 @ ( fun @ SV33 @ bool ) ) @ ( fun @ ( product_prod @ SV91 @ SV33 ) @ bool ) @ ( product_prod_case @ SV91 @ SV33 @ bool ) @ SV143 ) @ ( hAPP @ SV33 @ ( product_prod @ SV91 @ SV33 ) @ ( hAPP @ SV91 @ ( fun @ SV33 @ ( product_prod @ SV91 @ SV33 ) ) @ ( product_Pair @ SV91 @ SV33 ) @ SV193 ) @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(650,plain,
! [SV235: $i,SV194: $i,SV144: $i,SV92: $i,SV34: $i] :
( ( ( ( hAPP @ SV34 @ ( option @ SV92 ) @ SV144 @ SV194 )
!= ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SV235 ) )
= $true )
| ( ( ( hAPP @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( hAPP @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) @ ( hAPP @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( fun @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) ) @ ( fun_upd @ SV34 @ ( option @ SV92 ) ) @ SV144 ) @ SV194 ) @ ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SV235 ) )
= ( ti @ ( fun @ SV34 @ ( option @ SV92 ) ) @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(651,plain,
! [SV35: $i] :
( ( ( hBOOL @ ( ti @ bool @ SV35 ) )
= $false )
| ( ( hBOOL @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(652,plain,
! [SV35: $i] :
( ( ( hBOOL @ SV35 )
= $false )
| ( ( hBOOL @ ( ti @ bool @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(653,plain,
! [SV236: $i,SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ! [SY1161: $i,SY1162: $i,SY1163: $i,SY1164: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SV236 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SY1161 ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ SY1162 ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ SY1163 ) @ SY1164 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(654,plain,
! [SV146: $i,SV94: $i,SV37: $i] :
( ( ( ti @ ( product_prod @ SV37 @ SV94 ) @ SV146 )
!= ( hAPP @ SV94 @ ( product_prod @ SV37 @ SV94 ) @ ( hAPP @ SV37 @ ( fun @ SV94 @ ( product_prod @ SV37 @ SV94 ) ) @ ( product_Pair @ SV37 @ SV94 ) @ ( sK2_SY925 @ SV146 @ SV94 @ SV37 ) ) @ ( sK4_SY1165 @ SV146 @ SV94 @ SV37 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[601]) ).
thf(655,plain,
! [SV196: $i,SV147: $i,SV95: $i,SV38: $i] :
( ( ! [SY1213: $i,SY1214: $i] :
( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SV196 )
!= ( hAPP @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( sK5_SY1072 @ SV196 @ SV147 @ SV95 @ SV38 ) ) @ ( hAPP @ SV147 @ ( product_prod @ SV95 @ SV147 ) @ ( hAPP @ SV95 @ ( fun @ SV147 @ ( product_prod @ SV95 @ SV147 ) ) @ ( product_Pair @ SV95 @ SV147 ) @ SY1213 ) @ SY1214 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[602]) ).
thf(656,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ~ ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( ti @ SV39 @ SV197 ) ) )
| ~ ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(657,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ~ ! [SY1215: $i,SY1216: $i,SY1217: $i,SY1218: $i,SY1219: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SY1215 ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ SY1216 ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ SY1217 ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ SY1218 ) @ SY1219 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(658,plain,
! [SV199: $i,SV239: $i,SV150: $i,SV98: $i,SV41: $i] :
( ( ( ~ ! [SY1173: $i,SY1174: $i,SY1175: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ SY1173 ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ SY1174 ) @ SY1175 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(659,plain,
! [SV271: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ! [SY1220: $i] :
( ~ ! [SY1178: $i,SY1179: $i,SY1180: $i,SY1181: $i,SY1182: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SY1220 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ SY1178 ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ SY1179 ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ SY1180 ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1181 ) @ SY1182 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SY1220 @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(660,plain,
! [SV272: $i,SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ! [SY1226: $i] :
~ ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1226 ) )
| ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SY1226 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1226 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SY1226 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1226 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SY1226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(661,plain,
! [SV242: $i,SV202: $i,SV153: $i,SV101: $i,SV44: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV101 @ ( fun @ SV44 @ bool ) @ SV153 @ SV202 ) @ SV242 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV44 ) @ bool @ ( hAPP @ ( fun @ SV101 @ ( fun @ SV44 @ bool ) ) @ ( fun @ ( product_prod @ SV101 @ SV44 ) @ bool ) @ ( product_prod_case @ SV101 @ SV44 @ bool ) @ SV153 ) @ ( hAPP @ SV44 @ ( product_prod @ SV101 @ SV44 ) @ ( hAPP @ SV101 @ ( fun @ SV44 @ ( product_prod @ SV101 @ SV44 ) ) @ ( product_Pair @ SV101 @ SV44 ) @ SV202 ) @ SV242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(662,plain,
! [SV243: $i,SV203: $i,SV154: $i,SV102: $i,SV45: $i] :
( ( ~ ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
| ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) )
| ~ ( ~ ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(663,plain,
! [SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ! [SY1227: $i,SY1228: $i] :
( ~ ! [SY1229: $i,SY1230: $i,SY1231: $i,SY1232: $i,SY1233: $i,SY1234: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SY1228 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ SY1229 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ SY1230 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ SY1231 ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1232 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1233 ) @ SY1234 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SY1228 @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(664,plain,
! [SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1235: $i] :
~ ! [SY1236: $i,SY1237: $i,SY1238: $i,SY1239: $i,SY1240: $i,SY1241: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SY1235 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SY1236 ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ SY1237 ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ SY1238 ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ SY1239 ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ SY1240 ) @ SY1241 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(665,plain,
! [SV246: $i,SV206: $i,SV157: $i,SV105: $i,SV48: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV48 @ SV105 ) @ bool @ ( hAPP @ ( fun @ SV48 @ ( fun @ SV105 @ bool ) ) @ ( fun @ ( product_prod @ SV48 @ SV105 ) @ bool ) @ ( product_prod_case @ SV48 @ SV105 @ bool ) @ SV157 ) @ ( hAPP @ SV105 @ ( product_prod @ SV48 @ SV105 ) @ ( hAPP @ SV48 @ ( fun @ SV105 @ ( product_prod @ SV48 @ SV105 ) ) @ ( product_Pair @ SV48 @ SV105 ) @ SV206 ) @ SV246 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV105 @ bool @ ( hAPP @ SV48 @ ( fun @ SV105 @ bool ) @ SV157 @ SV206 ) @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(666,plain,
! [SV49: $i,SV275: $i,SV247: $i,SV207: $i,SV158: $i,SV106: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV106 ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV207 ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV275 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV106 ) ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV207 ) ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(667,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ~ ( ~ ! [SY1123: $i,SY1124: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(668,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ~ ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
| ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(669,plain,
! [SV209: $i,SV160: $i,SV108: $i,SV51: $i] :
( ( ( ! [SY1127: $i] :
( ( hAPP @ SV51 @ SV108 @ SV160 @ SY1127 )
= ( hAPP @ SV51 @ SV108 @ SV209 @ SY1127 ) ) )
= $false )
| ( ( ( ti @ ( fun @ SV51 @ SV108 ) @ SV160 )
= ( ti @ ( fun @ SV51 @ SV108 ) @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(670,plain,
! [SV161: $i,SV109: $i,SV52: $i] :
( ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
!= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
| ( SV109 = SV161 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(671,plain,
! [SV52: $i,SV161: $i,SV109: $i] :
( ( ( SV109 != SV161 )
| ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(672,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ~ ~ ! [SY997: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY997 ) )
| ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(673,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ~ ~ ! [SY1000: $i] :
~ ~ ! [SY1001: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY1000 ) @ SY1001 ) ) )
| ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(674,plain,
! [SV276: $i,SV248: $i,SV210: $i,SV163: $i,SV111: $i,SV54: $i] :
( ( ! [SY1242: $i] :
( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 ) @ ( hAPP @ SV163 @ ( product_prod @ SV111 @ SV163 ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( product_prod @ SV111 @ SV163 ) ) @ ( product_Pair @ SV111 @ SV163 ) @ SV248 ) @ SV276 ) ) @ SY1242 ) )
| ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SV163 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 @ SV248 ) @ SV276 ) @ SY1242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(675,plain,
! [SV277: $i,SV249: $i,SV211: $i,SV164: $i,SV112: $i,SV55: $i] :
( ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
!= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
| ~ ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SV249 ) )
| ( ( ti @ SV55 @ SV211 )
!= ( ti @ SV55 @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(676,plain,
! [SV165: $i,SV113: $i,SV56: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) )
| ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(677,plain,
! [SV113: $i,SV165: $i,SV56: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(678,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ~ ! [SY1010: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1010 ) )
| ! [SY1011: $i,SY1012: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1011 ) @ SY1012 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(679,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ~ ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1013 ) @ SY1014 ) ) )
| ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(680,plain,
! [SV250: $i,SV212: $i,SV167: $i,SV115: $i,SV58: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(681,plain,
! [SV116: $i,SV251: $i,SV213: $i,SV168: $i,SV59: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV251 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV251 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(682,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV117: $i,SV60: $i] :
( ( ~ ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
| ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SV252 ) ) )
| ~ ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
!= ( ti @ SV60 @ SV252 ) )
| ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(683,plain,
! [SV221: $i,SV180: $i,SV129: $i,SV74: $i,SV16: $i] :
( ( ( hAPP @ SV16 @ ( option @ SV74 ) @ ( hAPP @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( hAPP @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) @ ( hAPP @ ( fun @ SV16 @ ( option @ SV74 ) ) @ ( fun @ SV16 @ ( fun @ ( option @ SV74 ) @ ( fun @ SV16 @ ( option @ SV74 ) ) ) ) @ ( fun_upd @ SV16 @ ( option @ SV74 ) ) @ SV129 ) @ SV180 ) @ ( hAPP @ SV74 @ ( option @ SV74 ) @ ( some @ SV74 ) @ SV221 ) ) @ ( sK6_SY1141 @ SV221 @ SV180 @ SV129 @ SV74 @ SV16 ) )
= ( none @ SV74 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[634]) ).
thf(684,plain,
! [SV261: $i,SV225: $i,SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
| ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) )
| ~ ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(685,plain,
! [SV24: $i,SV262: $i,SV226: $i,SV185: $i,SV134: $i,SV82: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV82 ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV185 ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV262 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV82 ) @ SV24 ) ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV185 ) @ SV24 ) ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(686,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( ti @ SV25 @ SV186 ) ) )
| ~ ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SV263 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(687,plain,
! [SV228: $i,SV264: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ( ~ ! [SY1206: $i,SY1207: $i,SY1208: $i,SY1209: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ SY1206 ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ SY1207 ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ SY1208 ) @ SY1209 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(688,plain,
! [SV188: $i,SV137: $i,SV27: $i,SV265: $i,SV229: $i,SV85: $i] :
( ( ( ~ ( ( ( ti @ SV85 @ SV229 )
!= ( ti @ SV85 @ SV265 ) ) ) )
= $true )
| ( ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SV137 ) @ SV265 ) @ SV188 ) @ SV229 )
= ( hAPP @ SV85 @ SV27 @ SV137 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(689,plain,
! [SV278: $i,SV266: $i,SV230: $i,SV189: $i,SV138: $i,SV86: $i,SV28: $i] :
( ( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV138 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV230 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV266 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV278 ) ) )
| ( ( ti @ SV28 @ SV230 )
= ( ti @ SV28 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(690,plain,
! [SV139: $i,SV87: $i,SV29: $i] :
( ( ( ti @ ( product_prod @ SV29 @ SV87 ) @ SV139 )
= ( hAPP @ SV87 @ ( product_prod @ SV29 @ SV87 ) @ ( hAPP @ SV29 @ ( fun @ SV87 @ ( product_prod @ SV29 @ SV87 ) ) @ ( product_Pair @ SV29 @ SV87 ) @ ( sK1_SY903 @ SV139 @ SV87 @ SV29 ) ) @ ( sK3_SY1156 @ SV139 @ SV87 @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(691,plain,
! [SV231: $i,SV190: $i,SV140: $i,SV30: $i,SV279: $i,SV267: $i,SV88: $i] :
( ( ~ ( ( ( ti @ SV88 @ SV267 )
!= ( ti @ SV88 @ SV279 ) ) )
| ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV267 ) @ SV190 ) ) @ SV279 ) @ SV231 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV279 ) @ SV231 ) ) @ SV267 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(692,plain,
! [SV280: $i,SV268: $i,SV232: $i,SV141: $i,SV89: $i,SV191: $i,SV31: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 @ SV268 ) @ SV280 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SV141 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 ) @ ( hAPP @ SV89 @ ( product_prod @ SV141 @ SV89 ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( product_prod @ SV141 @ SV89 ) ) @ ( product_Pair @ SV141 @ SV89 ) @ SV268 ) @ SV280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(693,plain,
! [SV233: $i,SV192: $i,SV142: $i,SV90: $i,SV32: $i] :
( ( ( ( hAPP @ SV32 @ SV90 @ SV142 @ SV192 )
= ( ti @ SV90 @ SV233 ) )
= $false )
| ( ( ( hAPP @ SV90 @ ( fun @ SV32 @ SV90 ) @ ( hAPP @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) @ ( hAPP @ ( fun @ SV32 @ SV90 ) @ ( fun @ SV32 @ ( fun @ SV90 @ ( fun @ SV32 @ SV90 ) ) ) @ ( fun_upd @ SV32 @ SV90 ) @ SV142 ) @ SV192 ) @ SV233 )
= ( ti @ ( fun @ SV32 @ SV90 ) @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(694,plain,
! [SV234: $i,SV193: $i,SV143: $i,SV91: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV91 @ ( fun @ SV33 @ bool ) @ SV143 @ SV193 ) @ SV234 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV91 @ SV33 ) @ bool @ ( hAPP @ ( fun @ SV91 @ ( fun @ SV33 @ bool ) ) @ ( fun @ ( product_prod @ SV91 @ SV33 ) @ bool ) @ ( product_prod_case @ SV91 @ SV33 @ bool ) @ SV143 ) @ ( hAPP @ SV33 @ ( product_prod @ SV91 @ SV33 ) @ ( hAPP @ SV91 @ ( fun @ SV33 @ ( product_prod @ SV91 @ SV33 ) ) @ ( product_Pair @ SV91 @ SV33 ) @ SV193 ) @ SV234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(695,plain,
! [SV235: $i,SV194: $i,SV144: $i,SV92: $i,SV34: $i] :
( ( ( ( hAPP @ SV34 @ ( option @ SV92 ) @ SV144 @ SV194 )
= ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SV235 ) )
= $false )
| ( ( ( hAPP @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( hAPP @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) @ ( hAPP @ ( fun @ SV34 @ ( option @ SV92 ) ) @ ( fun @ SV34 @ ( fun @ ( option @ SV92 ) @ ( fun @ SV34 @ ( option @ SV92 ) ) ) ) @ ( fun_upd @ SV34 @ ( option @ SV92 ) ) @ SV144 ) @ SV194 ) @ ( hAPP @ SV92 @ ( option @ SV92 ) @ ( some @ SV92 ) @ SV235 ) )
= ( ti @ ( fun @ SV34 @ ( option @ SV92 ) ) @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(696,plain,
! [SV236: $i,SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ! [SY1243: $i,SY1244: $i,SY1245: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SV236 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( sK7_SY1161 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ SY1243 ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ SY1244 ) @ SY1245 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[653]) ).
thf(697,plain,
! [SV146: $i,SV94: $i,SV37: $i] :
( ( ( ti @ ( product_prod @ SV37 @ SV94 ) @ SV146 )
= ( hAPP @ SV94 @ ( product_prod @ SV37 @ SV94 ) @ ( hAPP @ SV37 @ ( fun @ SV94 @ ( product_prod @ SV37 @ SV94 ) ) @ ( product_Pair @ SV37 @ SV94 ) @ ( sK2_SY925 @ SV146 @ SV94 @ SV37 ) ) @ ( sK4_SY1165 @ SV146 @ SV94 @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(698,plain,
! [SV196: $i,SV147: $i,SV95: $i,SV38: $i] :
( ( ! [SY1246: $i] :
( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SV196 )
!= ( hAPP @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( sK5_SY1072 @ SV196 @ SV147 @ SV95 @ SV38 ) ) @ ( hAPP @ SV147 @ ( product_prod @ SV95 @ SV147 ) @ ( hAPP @ SV95 @ ( fun @ SV147 @ ( product_prod @ SV95 @ SV147 ) ) @ ( product_Pair @ SV95 @ SV147 ) @ ( sK8_SY1213 @ SV196 @ SV147 @ SV95 @ SV38 ) ) @ SY1246 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[655]) ).
thf(699,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( ti @ SV39 @ SV197 ) ) )
| ~ ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(700,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY1215: $i,SY1216: $i,SY1217: $i,SY1218: $i,SY1219: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SY1215 ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ SY1216 ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ SY1217 ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ SY1218 ) @ SY1219 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(701,plain,
! [SV199: $i,SV239: $i,SV150: $i,SV98: $i,SV41: $i] :
( ( ( ! [SY1173: $i,SY1174: $i,SY1175: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ SY1173 ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ SY1174 ) @ SY1175 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(702,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ~ ! [SY1247: $i,SY1248: $i,SY1249: $i,SY1250: $i,SY1251: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ SY1247 ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ SY1248 ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ SY1249 ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1250 ) @ SY1251 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(703,plain,
! [SV282: $i,SV272: $i,SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ~ ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
| ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(704,plain,
! [SV242: $i,SV202: $i,SV153: $i,SV101: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV101 @ ( fun @ SV44 @ bool ) @ SV153 @ SV202 ) @ SV242 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV44 ) @ bool @ ( hAPP @ ( fun @ SV101 @ ( fun @ SV44 @ bool ) ) @ ( fun @ ( product_prod @ SV101 @ SV44 ) @ bool ) @ ( product_prod_case @ SV101 @ SV44 @ bool ) @ SV153 ) @ ( hAPP @ SV44 @ ( product_prod @ SV101 @ SV44 ) @ ( hAPP @ SV101 @ ( fun @ SV44 @ ( product_prod @ SV101 @ SV44 ) ) @ ( product_Pair @ SV101 @ SV44 ) @ SV202 ) @ SV242 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(705,plain,
! [SV243: $i,SV203: $i,SV154: $i,SV102: $i,SV45: $i] :
( ( ~ ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
| ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(706,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ~ ( ~ ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(707,plain,
! [SV283: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ! [SY1252: $i] :
( ~ ! [SY1229: $i,SY1230: $i,SY1231: $i,SY1232: $i,SY1233: $i,SY1234: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SY1252 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ SY1229 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ SY1230 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ SY1231 ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1232 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1233 ) @ SY1234 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SY1252 @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(708,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ~ ! [SY1259: $i,SY1260: $i,SY1261: $i,SY1262: $i,SY1263: $i,SY1264: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SY1259 ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ SY1260 ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ SY1261 ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ SY1262 ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ SY1263 ) @ SY1264 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(709,plain,
! [SV246: $i,SV206: $i,SV157: $i,SV105: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV48 @ SV105 ) @ bool @ ( hAPP @ ( fun @ SV48 @ ( fun @ SV105 @ bool ) ) @ ( fun @ ( product_prod @ SV48 @ SV105 ) @ bool ) @ ( product_prod_case @ SV48 @ SV105 @ bool ) @ SV157 ) @ ( hAPP @ SV105 @ ( product_prod @ SV48 @ SV105 ) @ ( hAPP @ SV48 @ ( fun @ SV105 @ ( product_prod @ SV48 @ SV105 ) ) @ ( product_Pair @ SV48 @ SV105 ) @ SV206 ) @ SV246 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV105 @ bool @ ( hAPP @ SV48 @ ( fun @ SV105 @ bool ) @ SV157 @ SV206 ) @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(710,plain,
! [SV49: $i,SV275: $i,SV247: $i,SV207: $i,SV158: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV106 ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV207 ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV275 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV106 ) ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV207 ) ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV275 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(711,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ~ ! [SY1123: $i,SY1124: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(712,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
| ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(713,plain,
! [SV209: $i,SV160: $i,SV108: $i,SV51: $i] :
( ( ( ( hAPP @ SV51 @ SV108 @ SV160 @ ( sK9_SY1127 @ SV209 @ SV160 @ SV108 @ SV51 ) )
= ( hAPP @ SV51 @ SV108 @ SV209 @ ( sK9_SY1127 @ SV209 @ SV160 @ SV108 @ SV51 ) ) )
= $false )
| ( ( ( ti @ ( fun @ SV51 @ SV108 ) @ SV160 )
= ( ti @ ( fun @ SV51 @ SV108 ) @ SV209 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[669]) ).
thf(714,plain,
! [SV161: $i,SV109: $i,SV52: $i] :
( ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
!= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
= $true )
| ( ( SV109 = SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(715,plain,
! [SV52: $i,SV161: $i,SV109: $i] :
( ( ( SV109 != SV161 )
= $true )
| ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(716,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ~ ! [SY997: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY997 ) ) )
= $true )
| ( ( ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(717,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ~ ! [SY1000: $i] :
~ ~ ! [SY1001: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY1000 ) @ SY1001 ) ) ) )
= $true )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(718,plain,
! [SV285: $i,SV276: $i,SV248: $i,SV210: $i,SV163: $i,SV111: $i,SV54: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 ) @ ( hAPP @ SV163 @ ( product_prod @ SV111 @ SV163 ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( product_prod @ SV111 @ SV163 ) ) @ ( product_Pair @ SV111 @ SV163 ) @ SV248 ) @ SV276 ) ) @ SV285 ) )
| ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SV163 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 @ SV248 ) @ SV276 ) @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(719,plain,
! [SV277: $i,SV249: $i,SV211: $i,SV164: $i,SV112: $i,SV55: $i] :
( ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
!= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SV249 ) )
| ( ( ti @ SV55 @ SV211 )
!= ( ti @ SV55 @ SV277 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(720,plain,
! [SV165: $i,SV113: $i,SV56: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(721,plain,
! [SV113: $i,SV165: $i,SV56: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(722,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ( ~ ! [SY1010: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1010 ) ) )
= $true )
| ( ( ! [SY1011: $i,SY1012: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1011 ) @ SY1012 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(723,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ( ~ ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1013 ) @ SY1014 ) ) ) )
= $true )
| ( ( ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(724,plain,
! [SV250: $i,SV212: $i,SV167: $i,SV115: $i,SV58: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(725,plain,
! [SV58: $i,SV250: $i,SV212: $i,SV167: $i,SV115: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(726,plain,
! [SV116: $i,SV251: $i,SV213: $i,SV168: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV251 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV251 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(727,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV117: $i,SV60: $i] :
( ( ~ ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
| ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SV252 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(728,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV60: $i,SV117: $i] :
( ( ~ ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
!= ( ti @ SV60 @ SV252 ) )
| ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(729,plain,
! [SV261: $i,SV225: $i,SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ~ ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
| ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(730,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ~ ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(731,plain,
! [SV24: $i,SV262: $i,SV226: $i,SV185: $i,SV134: $i,SV82: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV82 ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV185 ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV262 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV82 ) @ SV24 ) ) @ SV134 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ SV185 ) @ SV24 ) ) @ SV226 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(732,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( ti @ SV25 @ SV186 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(733,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ~ ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SV263 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(734,plain,
! [SV228: $i,SV264: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ( ! [SY1206: $i,SY1207: $i,SY1208: $i,SY1209: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ SY1206 ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ SY1207 ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ SY1208 ) @ SY1209 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(735,plain,
! [SV188: $i,SV137: $i,SV27: $i,SV265: $i,SV229: $i,SV85: $i] :
( ( ( ( ti @ SV85 @ SV229 )
!= ( ti @ SV85 @ SV265 ) )
= $false )
| ( ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SV137 ) @ SV265 ) @ SV188 ) @ SV229 )
= ( hAPP @ SV85 @ SV27 @ SV137 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(736,plain,
! [SV278: $i,SV266: $i,SV230: $i,SV189: $i,SV138: $i,SV86: $i,SV28: $i] :
( ( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV138 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV230 ) )
!= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV266 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV278 ) ) )
= $true )
| ( ( ( ti @ SV28 @ SV230 )
= ( ti @ SV28 @ SV278 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(737,plain,
! [SV231: $i,SV190: $i,SV140: $i,SV30: $i,SV279: $i,SV267: $i,SV88: $i] :
( ( ( ~ ( ( ( ti @ SV88 @ SV267 )
!= ( ti @ SV88 @ SV279 ) ) ) )
= $true )
| ( ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV267 ) @ SV190 ) ) @ SV279 ) @ SV231 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV279 ) @ SV231 ) ) @ SV267 ) @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(738,plain,
! [SV280: $i,SV268: $i,SV232: $i,SV141: $i,SV89: $i,SV191: $i,SV31: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 @ SV268 ) @ SV280 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SV141 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 ) @ ( hAPP @ SV89 @ ( product_prod @ SV141 @ SV89 ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( product_prod @ SV141 @ SV89 ) ) @ ( product_Pair @ SV141 @ SV89 ) @ SV268 ) @ SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(739,plain,
! [SV236: $i,SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ! [SY1265: $i,SY1266: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SV236 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( sK7_SY1161 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( sK10_SY1243 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ SY1265 ) @ SY1266 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[696]) ).
thf(740,plain,
! [SV196: $i,SV147: $i,SV95: $i,SV38: $i] :
( ( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SV196 )
!= ( hAPP @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( sK5_SY1072 @ SV196 @ SV147 @ SV95 @ SV38 ) ) @ ( hAPP @ SV147 @ ( product_prod @ SV95 @ SV147 ) @ ( hAPP @ SV95 @ ( fun @ SV147 @ ( product_prod @ SV95 @ SV147 ) ) @ ( product_Pair @ SV95 @ SV147 ) @ ( sK8_SY1213 @ SV196 @ SV147 @ SV95 @ SV38 ) ) @ ( sK11_SY1246 @ SV196 @ SV147 @ SV95 @ SV38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[698]) ).
thf(741,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( ti @ SV39 @ SV197 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(742,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ~ ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(743,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY1267: $i,SY1268: $i,SY1269: $i,SY1270: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( sK12_SY1215 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ SY1267 ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ SY1268 ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ SY1269 ) @ SY1270 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[700]) ).
thf(744,plain,
! [SV199: $i,SV239: $i,SV150: $i,SV98: $i,SV41: $i] :
( ( ( ! [SY1271: $i,SY1272: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( sK13_SY1173 @ SV199 @ SV239 @ SV150 @ SV98 @ SV41 ) ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ SY1271 ) @ SY1272 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ SV199 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[701]) ).
thf(745,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ( ~ ! [SY1247: $i,SY1248: $i,SY1249: $i,SY1250: $i,SY1251: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ SY1247 ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ SY1248 ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ SY1249 ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1250 ) @ SY1251 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(746,plain,
! [SV282: $i,SV272: $i,SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
| ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
| ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(747,plain,
! [SV243: $i,SV203: $i,SV154: $i,SV102: $i,SV45: $i] :
( ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
| ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(748,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ~ ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) )
| ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(749,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ~ ! [SY1273: $i,SY1274: $i,SY1275: $i,SY1276: $i,SY1277: $i,SY1278: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ SY1273 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ SY1274 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ SY1275 ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1276 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1277 ) @ SY1278 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(750,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1259: $i,SY1260: $i,SY1261: $i,SY1262: $i,SY1263: $i,SY1264: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SY1259 ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ SY1260 ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ SY1261 ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ SY1262 ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ SY1263 ) @ SY1264 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(751,plain,
! [SV49: $i,SV275: $i,SV247: $i,SV207: $i,SV158: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV106 ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV207 ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV275 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV106 ) ) @ SV158 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ SV49 ) @ SV207 ) ) @ SV247 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV275 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(752,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ( ~ ! [SY1123: $i,SY1124: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(753,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
!= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true )
| ( ( ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(754,plain,
! [SV161: $i,SV109: $i,SV52: $i] :
( ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
= $false )
| ( ( SV109 = SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(755,plain,
! [SV52: $i,SV161: $i,SV109: $i] :
( ( ( SV109 = SV161 )
= $false )
| ( ( ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV109 )
= ( hAPP @ val @ ( exp @ SV52 ) @ ( val_1 @ SV52 ) @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(756,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ! [SY997: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY997 ) ) )
= $false )
| ( ( ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(757,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ! [SY1000: $i] :
~ ~ ! [SY1001: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY1000 ) @ SY1001 ) ) ) )
= $false )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(758,plain,
! [SV285: $i,SV276: $i,SV248: $i,SV210: $i,SV163: $i,SV111: $i,SV54: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 ) @ ( hAPP @ SV163 @ ( product_prod @ SV111 @ SV163 ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( product_prod @ SV111 @ SV163 ) ) @ ( product_Pair @ SV111 @ SV163 ) @ SV248 ) @ SV276 ) ) @ SV285 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SV163 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 @ SV248 ) @ SV276 ) @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(759,plain,
! [SV277: $i,SV249: $i,SV211: $i,SV164: $i,SV112: $i,SV55: $i] :
( ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SV249 ) )
| ( ( ti @ SV55 @ SV211 )
!= ( ti @ SV55 @ SV277 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(760,plain,
! [SV165: $i,SV113: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(761,plain,
! [SV113: $i,SV165: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ SV56 @ bool @ SV165 @ SV113 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ SV56 @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( member @ SV56 ) @ SV113 ) @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(762,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ( ! [SY1010: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1010 ) ) )
= $false )
| ( ( ! [SY1011: $i,SY1012: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1011 ) @ SY1012 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(763,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ( ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1013 ) @ SY1014 ) ) ) )
= $false )
| ( ( ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(764,plain,
! [SV250: $i,SV212: $i,SV167: $i,SV115: $i,SV58: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(765,plain,
! [SV58: $i,SV250: $i,SV212: $i,SV167: $i,SV115: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
| ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(766,plain,
! [SV213: $i,SV116: $i,SV251: $i,SV168: $i,SV59: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV251 ) @ SV116 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV116 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(767,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV117: $i,SV60: $i] :
( ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
| ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SV252 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(768,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV60: $i,SV117: $i] :
( ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
!= ( ti @ SV60 @ SV252 ) )
| ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(769,plain,
! [SV261: $i,SV225: $i,SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
| ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(770,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) )
| ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(771,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( ti @ SV25 @ SV186 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(772,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) ) )
| ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SV263 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(773,plain,
! [SV228: $i,SV264: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ( ! [SY1279: $i,SY1280: $i,SY1281: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( sK14_SY1206 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ SY1279 ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ SY1280 ) @ SY1281 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[734]) ).
thf(774,plain,
! [SV188: $i,SV137: $i,SV27: $i,SV265: $i,SV229: $i,SV85: $i] :
( ( ( ( ti @ SV85 @ SV229 )
= ( ti @ SV85 @ SV265 ) )
= $true )
| ( ( ( hAPP @ SV85 @ SV27 @ ( hAPP @ SV27 @ ( fun @ SV85 @ SV27 ) @ ( hAPP @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) @ ( hAPP @ ( fun @ SV85 @ SV27 ) @ ( fun @ SV85 @ ( fun @ SV27 @ ( fun @ SV85 @ SV27 ) ) ) @ ( fun_upd @ SV85 @ SV27 ) @ SV137 ) @ SV265 ) @ SV188 ) @ SV229 )
= ( hAPP @ SV85 @ SV27 @ SV137 @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(775,plain,
! [SV278: $i,SV266: $i,SV230: $i,SV189: $i,SV138: $i,SV86: $i,SV28: $i] :
( ( ( ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV138 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV230 ) )
= ( hAPP @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( hAPP @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) @ ( hAPP @ ( fun @ SV86 @ ( option @ SV28 ) ) @ ( fun @ SV86 @ ( fun @ ( option @ SV28 ) @ ( fun @ SV86 @ ( option @ SV28 ) ) ) ) @ ( fun_upd @ SV86 @ ( option @ SV28 ) ) @ SV266 ) @ SV189 ) @ ( hAPP @ SV28 @ ( option @ SV28 ) @ ( some @ SV28 ) @ SV278 ) ) )
= $false )
| ( ( ( ti @ SV28 @ SV230 )
= ( ti @ SV28 @ SV278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(776,plain,
! [SV231: $i,SV190: $i,SV140: $i,SV30: $i,SV279: $i,SV267: $i,SV88: $i] :
( ( ( ( ti @ SV88 @ SV267 )
!= ( ti @ SV88 @ SV279 ) )
= $false )
| ( ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV267 ) @ SV190 ) ) @ SV279 ) @ SV231 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV279 ) @ SV231 ) ) @ SV267 ) @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(777,plain,
! [SV280: $i,SV268: $i,SV232: $i,SV141: $i,SV89: $i,SV191: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ SV89 @ ( fun @ SV31 @ bool ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 @ SV268 ) @ SV280 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV31 @ bool ) @ bool @ ( hAPP @ SV31 @ ( fun @ ( fun @ SV31 @ bool ) @ bool ) @ ( member @ SV31 ) @ SV191 ) @ ( hAPP @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) @ ( hAPP @ ( fun @ SV141 @ ( fun @ SV89 @ ( fun @ SV31 @ bool ) ) ) @ ( fun @ ( product_prod @ SV141 @ SV89 ) @ ( fun @ SV31 @ bool ) ) @ ( product_prod_case @ SV141 @ SV89 @ ( fun @ SV31 @ bool ) ) @ SV232 ) @ ( hAPP @ SV89 @ ( product_prod @ SV141 @ SV89 ) @ ( hAPP @ SV141 @ ( fun @ SV89 @ ( product_prod @ SV141 @ SV89 ) ) @ ( product_Pair @ SV141 @ SV89 ) @ SV268 ) @ SV280 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(778,plain,
! [SV236: $i,SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ! [SY1282: $i] :
( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SV236 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( sK7_SY1161 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( sK10_SY1243 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ ( sK15_SY1265 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ SY1282 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[739]) ).
thf(779,plain,
! [SV196: $i,SV147: $i,SV95: $i,SV38: $i] :
( ( ( ti @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ SV196 )
= ( hAPP @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( hAPP @ SV38 @ ( fun @ ( product_prod @ SV95 @ SV147 ) @ ( product_prod @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) ) @ ( product_Pair @ SV38 @ ( product_prod @ SV95 @ SV147 ) ) @ ( sK5_SY1072 @ SV196 @ SV147 @ SV95 @ SV38 ) ) @ ( hAPP @ SV147 @ ( product_prod @ SV95 @ SV147 ) @ ( hAPP @ SV95 @ ( fun @ SV147 @ ( product_prod @ SV95 @ SV147 ) ) @ ( product_Pair @ SV95 @ SV147 ) @ ( sK8_SY1213 @ SV196 @ SV147 @ SV95 @ SV38 ) ) @ ( sK11_SY1246 @ SV196 @ SV147 @ SV95 @ SV38 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(780,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( ti @ SV39 @ SV197 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(781,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) ) )
| ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(782,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY1283: $i,SY1284: $i,SY1285: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( sK12_SY1215 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( sK16_SY1267 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ SY1283 ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ SY1284 ) @ SY1285 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[743]) ).
thf(783,plain,
! [SV199: $i,SV239: $i,SV150: $i,SV98: $i,SV41: $i] :
( ( ( ! [SY1286: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( sK13_SY1173 @ SV199 @ SV239 @ SV150 @ SV98 @ SV41 ) ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ ( sK17_SY1271 @ SV199 @ SV239 @ SV150 @ SV98 @ SV41 ) ) @ SY1286 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ SV199 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[744]) ).
thf(784,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ( ! [SY1247: $i,SY1248: $i,SY1249: $i,SY1250: $i,SY1251: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ SY1247 ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ SY1248 ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ SY1249 ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1250 ) @ SY1251 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(785,plain,
! [SV282: $i,SV272: $i,SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ~ ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
| ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(786,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ~ ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(787,plain,
! [SV243: $i,SV203: $i,SV154: $i,SV102: $i,SV45: $i] :
( ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
!= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $true )
| ( ( ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(788,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ( ~ ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) )
= $true )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(789,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( ~ ! [SY1273: $i,SY1274: $i,SY1275: $i,SY1276: $i,SY1277: $i,SY1278: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ SY1273 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ SY1274 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ SY1275 ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1276 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1277 ) @ SY1278 ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(790,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1287: $i,SY1288: $i,SY1289: $i,SY1290: $i,SY1291: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( sK18_SY1259 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ SY1287 ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ SY1288 ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ SY1289 ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ SY1290 ) @ SY1291 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[750]) ).
thf(791,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ( ! [SY1123: $i,SY1124: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1123 ) @ SY1124 ) ) @ SV208 ) ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(792,plain,
! [SV159: $i,SV208: $i,SV107: $i,SV50: $i] :
( ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false )
| ( ( ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SY1125 ) @ SY1126 ) ) @ SV208 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(793,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ( ! [SY997: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY997 ) ) )
= $true )
| ( ( ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(794,plain,
! [SV162: $i,SV110: $i,SV53: $i] :
( ( ( ! [SY1000: $i] :
~ ~ ! [SY1001: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY1000 ) @ SY1001 ) ) ) )
= $true )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(795,plain,
! [SV285: $i,SV276: $i,SV248: $i,SV210: $i,SV163: $i,SV111: $i,SV54: $i] :
( ( ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) @ ( hAPP @ ( fun @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) ) @ ( fun @ ( product_prod @ SV111 @ SV163 ) @ ( fun @ SV54 @ bool ) ) @ ( product_prod_case @ SV111 @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 ) @ ( hAPP @ SV163 @ ( product_prod @ SV111 @ SV163 ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( product_prod @ SV111 @ SV163 ) ) @ ( product_Pair @ SV111 @ SV163 ) @ SV248 ) @ SV276 ) ) @ SV285 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV54 @ bool @ ( hAPP @ SV163 @ ( fun @ SV54 @ bool ) @ ( hAPP @ SV111 @ ( fun @ SV163 @ ( fun @ SV54 @ bool ) ) @ SV210 @ SV248 ) @ SV276 ) @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(796,plain,
! [SV277: $i,SV211: $i,SV55: $i,SV249: $i,SV164: $i,SV112: $i] :
( ( ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SV249 ) )
| ( ( ti @ SV55 @ SV211 )
!= ( ti @ SV55 @ SV277 ) ) )
= $false )
| ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(797,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( sK19_SY1010 @ SV166 @ SV114 @ SV57 ) ) )
= $false )
| ( ( ! [SY1011: $i,SY1012: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SY1011 ) @ SY1012 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[762]) ).
thf(798,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ( ! [SY1292: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ ( sK20_SY1013 @ SV166 @ SV114 @ SV57 ) ) @ SY1292 ) ) ) )
= $false )
| ( ( ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[763]) ).
thf(799,plain,
! [SV250: $i,SV212: $i,SV167: $i,SV115: $i,SV58: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(800,plain,
! [SV58: $i,SV250: $i,SV212: $i,SV167: $i,SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(801,plain,
! [SV213: $i,SV116: $i,SV251: $i,SV168: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV251 ) @ SV116 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV116 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ty @ ( fun @ ty @ bool ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ SV59 ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ SV59 ) @ SV168 ) @ SV213 ) @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(802,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV117: $i,SV60: $i] :
( ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
!= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
= $true )
| ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(803,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV60: $i,SV117: $i] :
( ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
!= ( ti @ SV60 @ SV252 ) )
= $true )
| ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(804,plain,
! [SV261: $i,SV225: $i,SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
!= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(805,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ~ ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) )
= $true )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(806,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) )
= $true )
| ( ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( ti @ SV25 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(807,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ( ~ ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) ) ) )
= $true )
| ( ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(808,plain,
! [SV228: $i,SV264: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ( ! [SY1293: $i,SY1294: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( sK14_SY1206 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( sK21_SY1279 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ SY1293 ) @ SY1294 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[773]) ).
thf(809,plain,
! [SV231: $i,SV190: $i,SV140: $i,SV30: $i,SV279: $i,SV267: $i,SV88: $i] :
( ( ( ( ti @ SV88 @ SV267 )
= ( ti @ SV88 @ SV279 ) )
= $true )
| ( ( ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV267 ) @ SV190 ) ) @ SV279 ) @ SV231 )
= ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ ( hAPP @ SV30 @ ( fun @ SV88 @ SV30 ) @ ( hAPP @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) @ ( hAPP @ ( fun @ SV88 @ SV30 ) @ ( fun @ SV88 @ ( fun @ SV30 @ ( fun @ SV88 @ SV30 ) ) ) @ ( fun_upd @ SV88 @ SV30 ) @ SV140 ) @ SV279 ) @ SV231 ) ) @ SV267 ) @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(810,plain,
! [SV236: $i,SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SV236 )
!= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( sK7_SY1161 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( sK10_SY1243 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ ( sK15_SY1265 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( sK22_SY1282 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[778]) ).
thf(811,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) )
= $true )
| ( ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( ti @ SV39 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(812,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ( ~ ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) ) ) )
= $true )
| ( ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(813,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY1295: $i,SY1296: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( sK12_SY1215 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( sK16_SY1267 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( sK23_SY1283 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ SY1295 ) @ SY1296 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[782]) ).
thf(814,plain,
! [SV199: $i,SV239: $i,SV150: $i,SV98: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ ( hAPP @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( hAPP @ SV41 @ ( fun @ ( product_prod @ SV98 @ SV150 ) @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) ) @ ( product_Pair @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ ( sK13_SY1173 @ SV199 @ SV239 @ SV150 @ SV98 @ SV41 ) ) @ ( hAPP @ SV150 @ ( product_prod @ SV98 @ SV150 ) @ ( hAPP @ SV98 @ ( fun @ SV150 @ ( product_prod @ SV98 @ SV150 ) ) @ ( product_Pair @ SV98 @ SV150 ) @ ( sK17_SY1271 @ SV199 @ SV239 @ SV150 @ SV98 @ SV41 ) ) @ ( sK24_SY1286 @ SV199 @ SV239 @ SV150 @ SV98 @ SV41 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV41 @ ( product_prod @ SV98 @ SV150 ) ) @ bool @ SV239 @ SV199 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[783]) ).
thf(815,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ( ! [SY1297: $i,SY1298: $i,SY1299: $i,SY1300: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( sK25_SY1247 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ SY1297 ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ SY1298 ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1299 ) @ SY1300 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[784]) ).
thf(816,plain,
! [SV282: $i,SV272: $i,SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
| ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(817,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(818,plain,
! [SV243: $i,SV203: $i,SV154: $i,SV102: $i,SV45: $i] :
( ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $false )
| ( ( ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(819,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ( ~ ( ( SV102 != SV203 )
| ( SV154 != SV243 ) ) )
= $false )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(820,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( ! [SY1273: $i,SY1274: $i,SY1275: $i,SY1276: $i,SY1277: $i,SY1278: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ SY1273 ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ SY1274 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ SY1275 ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1276 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1277 ) @ SY1278 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(821,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1301: $i,SY1302: $i,SY1303: $i,SY1304: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( sK18_SY1259 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( sK26_SY1287 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ SY1301 ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ SY1302 ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ SY1303 ) @ SY1304 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[790]) ).
thf(822,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ! [SY1305: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ SY1305 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ SY1305 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ SY1305 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ SY1305 ) ) @ SV208 ) ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[791]) ).
thf(823,plain,
! [SV159: $i,SV208: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ! [SY1306: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SY1306 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SY1306 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SY1306 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SY1306 ) ) @ SV208 ) ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(824,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) ) )
= $true )
| ( ( ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(825,plain,
! [SV289: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ~ ! [SY1307: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SY1307 ) ) ) )
= $true )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(826,plain,
! [SV277: $i,SV211: $i,SV55: $i,SV249: $i,SV164: $i,SV112: $i] :
( ( ( ( ti @ SV112 @ SV164 )
!= ( ti @ SV112 @ SV249 ) )
= $false )
| ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(827,plain,
! [SV249: $i,SV164: $i,SV112: $i,SV277: $i,SV211: $i,SV55: $i] :
( ( ( ( ti @ SV55 @ SV211 )
!= ( ti @ SV55 @ SV277 ) )
= $false )
| ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(828,plain,
! [SV290: $i,SV166: $i,SV114: $i,SV57: $i] :
( ( ( ! [SY1308: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SV290 ) @ SY1308 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( sK19_SY1010 @ SV166 @ SV114 @ SV57 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(829,plain,
! [SV166: $i,SV114: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ ( sK20_SY1013 @ SV166 @ SV114 @ SV57 ) ) @ ( sK28_SY1292 @ SV166 @ SV114 @ SV57 ) ) ) )
= $false )
| ( ( ! [SY1015: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SY1015 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[798]) ).
thf(830,plain,
! [SV250: $i,SV212: $i,SV167: $i,SV115: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(831,plain,
! [SV58: $i,SV250: $i,SV212: $i,SV167: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( fun @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) ) @ ( product_Pair @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV115 ) @ SV167 ) ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ ( product_Pair @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ SV212 ) @ SV250 ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( product_prod @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( product_prod @ ( exp @ ( list @ char ) ) @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) ) @ bool ) @ red @ SV58 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) @ ( hAPP @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) @ ( hAPP @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ( product_prod @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) @ bool ) ) ) ) @ redp @ SV58 ) @ SV115 ) @ SV167 ) @ SV212 ) @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(832,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV117: $i,SV60: $i] :
( ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
= $false )
| ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(833,plain,
! [SV252: $i,SV214: $i,SV169: $i,SV60: $i,SV117: $i] :
( ( ( ( hAPP @ SV117 @ SV60 @ SV169 @ SV214 )
= ( ti @ SV60 @ SV252 ) )
= $false )
| ( ( ( hAPP @ SV60 @ ( fun @ SV117 @ SV60 ) @ ( hAPP @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) @ ( hAPP @ ( fun @ SV117 @ SV60 ) @ ( fun @ SV117 @ ( fun @ SV60 @ ( fun @ SV117 @ SV60 ) ) ) @ ( fun_upd @ SV117 @ SV60 ) @ SV169 ) @ SV214 ) @ SV252 )
= ( ti @ ( fun @ SV117 @ SV60 ) @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(834,plain,
! [SV261: $i,SV225: $i,SV184: $i,SV133: $i,SV81: $i,SV23: $i] :
( ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(835,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ~ ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) ) )
= $false )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(836,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ( ( ti @ SV83 @ SV263 )
= ( ti @ SV83 @ SV227 ) )
= $false )
| ( ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( ti @ SV25 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(837,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ( ( ti @ SV83 @ SV263 )
!= ( ti @ SV83 @ SV227 ) )
= $false )
| ( ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(838,plain,
! [SV228: $i,SV264: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ( ! [SY1309: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( sK14_SY1206 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( sK21_SY1279 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ ( sK29_SY1293 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ SY1309 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[808]) ).
thf(839,plain,
! [SV236: $i,SV195: $i,SV145: $i,SV93: $i,SV36: $i] :
( ( ( ti @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ SV236 )
= ( hAPP @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( hAPP @ SV36 @ ( fun @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_prod @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) ) @ ( product_Pair @ SV36 @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( sK7_SY1161 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( hAPP @ SV93 @ ( fun @ ( product_prod @ SV145 @ SV195 ) @ ( product_prod @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) ) @ ( product_Pair @ SV93 @ ( product_prod @ SV145 @ SV195 ) ) @ ( sK10_SY1243 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( hAPP @ SV195 @ ( product_prod @ SV145 @ SV195 ) @ ( hAPP @ SV145 @ ( fun @ SV195 @ ( product_prod @ SV145 @ SV195 ) ) @ ( product_Pair @ SV145 @ SV195 ) @ ( sK15_SY1265 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) @ ( sK22_SY1282 @ SV236 @ SV195 @ SV145 @ SV93 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(840,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ( ( ti @ SV96 @ SV237 )
= ( ti @ SV96 @ SV269 ) )
= $false )
| ( ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( ti @ SV39 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(841,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ( ( ti @ SV96 @ SV237 )
!= ( ti @ SV96 @ SV269 ) )
= $false )
| ( ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(842,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ! [SY1310: $i] :
( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( sK12_SY1215 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( sK16_SY1267 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( sK23_SY1283 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ ( sK30_SY1295 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ SY1310 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[813]) ).
thf(843,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ( ! [SY1311: $i,SY1312: $i,SY1313: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( sK25_SY1247 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( sK31_SY1297 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ SY1311 ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1312 ) @ SY1313 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[815]) ).
thf(844,plain,
! [SV282: $i,SV272: $i,SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true )
| ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(845,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(846,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ( ( SV102 != SV203 )
| ( SV154 != SV243 ) )
= $false )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(847,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ( ( SV102 != SV203 )
| ( SV154 != SV243 ) )
= $true )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(848,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( ! [SY1314: $i,SY1315: $i,SY1316: $i,SY1317: $i,SY1318: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( sK32_SY1273 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ SY1314 ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ SY1315 ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1316 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1317 ) @ SY1318 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[820]) ).
thf(849,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1319: $i,SY1320: $i,SY1321: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( sK18_SY1259 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( sK26_SY1287 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( sK33_SY1301 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ SY1319 ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ SY1320 ) @ SY1321 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[821]) ).
thf(850,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[822]) ).
thf(851,plain,
! [SV159: $i,SV208: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(852,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) )
= $false )
| ( ( ~ ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(853,plain,
! [SV289: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ! [SY1307: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SY1307 ) ) ) )
= $false )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(854,plain,
! [SV277: $i,SV211: $i,SV55: $i,SV249: $i,SV164: $i,SV112: $i] :
( ( ( ( ti @ SV112 @ SV164 )
= ( ti @ SV112 @ SV249 ) )
= $true )
| ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(855,plain,
! [SV249: $i,SV164: $i,SV112: $i,SV277: $i,SV211: $i,SV55: $i] :
( ( ( ( ti @ SV55 @ SV211 )
= ( ti @ SV55 @ SV277 ) )
= $true )
| ( ( ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV164 ) @ SV211 )
= ( hAPP @ SV55 @ ( product_prod @ SV112 @ SV55 ) @ ( hAPP @ SV112 @ ( fun @ SV55 @ ( product_prod @ SV112 @ SV55 ) ) @ ( product_Pair @ SV112 @ SV55 ) @ SV249 ) @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(856,plain,
! [SV292: $i,SV290: $i,SV166: $i,SV114: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ SV290 ) @ SV292 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( sK19_SY1010 @ SV166 @ SV114 @ SV57 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(857,plain,
! [SV293: $i,SV166: $i,SV114: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ SV293 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV57 @ SV114 ) @ bool @ SV166 @ ( hAPP @ SV114 @ ( product_prod @ SV57 @ SV114 ) @ ( hAPP @ SV57 @ ( fun @ SV114 @ ( product_prod @ SV57 @ SV114 ) ) @ ( product_Pair @ SV57 @ SV114 ) @ ( sK20_SY1013 @ SV166 @ SV114 @ SV57 ) ) @ ( sK28_SY1292 @ SV166 @ SV114 @ SV57 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(858,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) )
= $false )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(859,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
| ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) ) )
= $true )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(860,plain,
! [SV186: $i,SV135: $i,SV25: $i,SV227: $i,SV263: $i,SV83: $i] :
( ( ( ( ti @ SV83 @ SV263 )
= ( ti @ SV83 @ SV227 ) )
= $true )
| ( ( ( hAPP @ SV83 @ SV25 @ ( hAPP @ SV25 @ ( fun @ SV83 @ SV25 ) @ ( hAPP @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) @ ( hAPP @ ( fun @ SV83 @ SV25 ) @ ( fun @ SV83 @ ( fun @ SV25 @ ( fun @ SV83 @ SV25 ) ) ) @ ( fun_upd @ SV83 @ SV25 ) @ SV135 ) @ SV227 ) @ SV186 ) @ SV263 )
= ( hAPP @ SV83 @ SV25 @ SV135 @ SV263 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(861,plain,
! [SV228: $i,SV264: $i,SV187: $i,SV136: $i,SV84: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ ( hAPP @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( hAPP @ SV26 @ ( fun @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) ) @ ( product_Pair @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( sK14_SY1206 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( hAPP @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( hAPP @ SV84 @ ( fun @ ( product_prod @ SV136 @ SV187 ) @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ ( product_Pair @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) @ ( sK21_SY1279 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( hAPP @ SV187 @ ( product_prod @ SV136 @ SV187 ) @ ( hAPP @ SV136 @ ( fun @ SV187 @ ( product_prod @ SV136 @ SV187 ) ) @ ( product_Pair @ SV136 @ SV187 ) @ ( sK29_SY1293 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) @ ( sK35_SY1309 @ SV228 @ SV264 @ SV187 @ SV136 @ SV84 @ SV26 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV26 @ ( product_prod @ SV84 @ ( product_prod @ SV136 @ SV187 ) ) ) @ bool @ SV264 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[838]) ).
thf(862,plain,
! [SV197: $i,SV148: $i,SV39: $i,SV269: $i,SV237: $i,SV96: $i] :
( ( ( ( ti @ SV96 @ SV237 )
= ( ti @ SV96 @ SV269 ) )
= $true )
| ( ( ( hAPP @ SV96 @ SV39 @ ( hAPP @ SV39 @ ( fun @ SV96 @ SV39 ) @ ( hAPP @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) @ ( hAPP @ ( fun @ SV96 @ SV39 ) @ ( fun @ SV96 @ ( fun @ SV39 @ ( fun @ SV96 @ SV39 ) ) ) @ ( fun_upd @ SV96 @ SV39 ) @ SV148 ) @ SV269 ) @ SV197 ) @ SV237 )
= ( hAPP @ SV96 @ SV39 @ SV148 @ SV237 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(863,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
!= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( sK12_SY1215 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( sK16_SY1267 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( sK23_SY1283 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ ( sK30_SY1295 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( sK36_SY1310 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[842]) ).
thf(864,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ( ! [SY1322: $i,SY1323: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( sK25_SY1247 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( sK31_SY1297 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( sK37_SY1311 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ SY1322 ) @ SY1323 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[843]) ).
thf(865,plain,
! [SV282: $i,SV272: $i,SV241: $i,SV201: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(866,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
| ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $false )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(867,plain,
! [SV243: $i,SV154: $i,SV45: $i,SV203: $i,SV102: $i] :
( ( ( SV102 != SV203 )
= $false )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(868,plain,
! [SV203: $i,SV102: $i,SV45: $i,SV243: $i,SV154: $i] :
( ( ( SV154 != SV243 )
= $false )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(869,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ( SV102 != SV203 )
= $true )
| ( ( SV154 != SV243 )
= $true )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(870,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( ! [SY1324: $i,SY1325: $i,SY1326: $i,SY1327: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( sK32_SY1273 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( sK38_SY1314 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ SY1324 ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1325 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1326 ) @ SY1327 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[848]) ).
thf(871,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1328: $i,SY1329: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( sK18_SY1259 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( sK26_SY1287 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( sK33_SY1301 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( sK39_SY1319 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ SY1328 ) @ SY1329 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[849]) ).
thf(872,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(873,plain,
! [SV159: $i,SV208: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(874,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ! [SY998: $i] :
~ ~ ! [SY999: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SY998 ) @ SY999 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(875,plain,
! [SV289: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ! [SY1307: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SY1307 ) ) ) )
= $true )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(876,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
= $false )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(877,plain,
! [SV225: $i,SV133: $i,SV81: $i,SV261: $i,SV184: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) )
= $false )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(878,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ( ti @ SV81 @ SV133 )
!= ( ti @ SV81 @ SV225 ) )
= $true )
| ( ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) )
= $true )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(879,plain,
! [SV270: $i,SV238: $i,SV198: $i,SV149: $i,SV97: $i,SV40: $i] :
( ( ( ti @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ SV270 )
= ( hAPP @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( hAPP @ SV40 @ ( fun @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_prod @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) ) @ ( product_Pair @ SV40 @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( sK12_SY1215 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( hAPP @ SV97 @ ( fun @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_prod @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) ) @ ( product_Pair @ SV97 @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( sK16_SY1267 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( hAPP @ SV149 @ ( fun @ ( product_prod @ SV198 @ SV238 ) @ ( product_prod @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) ) @ ( product_Pair @ SV149 @ ( product_prod @ SV198 @ SV238 ) ) @ ( sK23_SY1283 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( hAPP @ SV238 @ ( product_prod @ SV198 @ SV238 ) @ ( hAPP @ SV198 @ ( fun @ SV238 @ ( product_prod @ SV198 @ SV238 ) ) @ ( product_Pair @ SV198 @ SV238 ) @ ( sK30_SY1295 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) @ ( sK36_SY1310 @ SV270 @ SV238 @ SV198 @ SV149 @ SV97 @ SV40 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(880,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ( ! [SY1330: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( sK25_SY1247 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( sK31_SY1297 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( sK37_SY1311 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ ( sK40_SY1322 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ SY1330 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[864]) ).
thf(881,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(882,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) ) )
= $false )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(883,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $false )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(884,plain,
! [SV243: $i,SV154: $i,SV45: $i,SV203: $i,SV102: $i] :
( ( ( SV102 = SV203 )
= $true )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(885,plain,
! [SV203: $i,SV102: $i,SV45: $i,SV243: $i,SV154: $i] :
( ( ( SV154 = SV243 )
= $true )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(886,plain,
! [SV45: $i,SV243: $i,SV154: $i,SV203: $i,SV102: $i] :
( ( ( SV102 = SV203 )
= $false )
| ( ( SV154 != SV243 )
= $true )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(887,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( ! [SY1331: $i,SY1332: $i,SY1333: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( sK32_SY1273 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( sK38_SY1314 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( sK41_SY1324 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ SY1331 ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1332 ) @ SY1333 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[870]) ).
thf(888,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ! [SY1334: $i] :
( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( sK18_SY1259 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( sK26_SY1287 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( sK33_SY1301 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( sK39_SY1319 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ ( sK42_SY1328 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ SY1334 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[871]) ).
thf(889,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(890,plain,
! [SV159: $i,SV208: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(891,plain,
! [SV208: $i,SV159: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(892,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ~ ! [SY1335: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ ( sK43_SY998 @ SV288 @ SV162 @ SV110 @ SV53 ) ) @ SY1335 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[874]) ).
thf(893,plain,
! [SV294: $i,SV289: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SV294 ) ) ) )
= $true )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(894,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ( ti @ SV81 @ SV133 )
= ( ti @ SV81 @ SV225 ) )
= $true )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(895,plain,
! [SV225: $i,SV133: $i,SV81: $i,SV261: $i,SV184: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV184 )
= ( ti @ SV23 @ SV261 ) )
= $true )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(896,plain,
! [SV261: $i,SV184: $i,SV23: $i,SV225: $i,SV133: $i,SV81: $i] :
( ( ( ( ti @ SV81 @ SV133 )
= ( ti @ SV81 @ SV225 ) )
= $false )
| ( ( ( ti @ SV23 @ SV184 )
!= ( ti @ SV23 @ SV261 ) )
= $true )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(897,plain,
! [SV271: $i,SV281: $i,SV240: $i,SV200: $i,SV151: $i,SV99: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ ( hAPP @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( hAPP @ SV42 @ ( fun @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) ) @ ( product_Pair @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( sK25_SY1247 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( hAPP @ SV99 @ ( fun @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ ( product_Pair @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( sK31_SY1297 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( hAPP @ SV151 @ ( fun @ ( product_prod @ SV200 @ SV240 ) @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) @ ( product_Pair @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) @ ( sK37_SY1311 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( hAPP @ SV240 @ ( product_prod @ SV200 @ SV240 ) @ ( hAPP @ SV200 @ ( fun @ SV240 @ ( product_prod @ SV200 @ SV240 ) ) @ ( product_Pair @ SV200 @ SV240 ) @ ( sK40_SY1322 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) @ ( sK44_SY1330 @ SV271 @ SV281 @ SV240 @ SV200 @ SV151 @ SV99 @ SV42 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV42 @ ( product_prod @ SV99 @ ( product_prod @ SV151 @ ( product_prod @ SV200 @ SV240 ) ) ) ) @ bool @ SV281 @ SV271 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[880]) ).
thf(898,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
= $false )
| ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(899,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
| ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(900,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(901,plain,
! [SV45: $i,SV203: $i,SV102: $i,SV243: $i,SV154: $i] :
( ( ( SV154 = SV243 )
= $false )
| ( ( SV102 = SV203 )
= $false )
| ( ( ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV102 ) @ SV154 )
= ( hAPP @ ( exp @ SV45 ) @ ( exp @ SV45 ) @ ( hAPP @ ( exp @ SV45 ) @ ( fun @ ( exp @ SV45 ) @ ( exp @ SV45 ) ) @ ( seq @ SV45 ) @ SV203 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(902,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( ! [SY1336: $i,SY1337: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( sK32_SY1273 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( sK38_SY1314 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( sK41_SY1324 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( sK45_SY1331 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ SY1336 ) @ SY1337 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[887]) ).
thf(903,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
!= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( sK18_SY1259 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( sK26_SY1287 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( sK33_SY1301 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( sK39_SY1319 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ ( sK42_SY1328 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( sK46_SY1334 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[888]) ).
thf(904,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(905,plain,
! [SV159: $i,SV208: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(906,plain,
! [SV208: $i,SV159: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(907,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ! [SY1335: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ ( sK43_SY998 @ SV288 @ SV162 @ SV110 @ SV53 ) ) @ SY1335 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(908,plain,
! [SV294: $i,SV289: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SV294 ) ) )
= $false )
| ( ( ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(909,plain,
! [SV225: $i,SV133: $i,SV81: $i,SV261: $i,SV184: $i,SV23: $i] :
( ( ( ( ti @ SV23 @ SV184 )
= ( ti @ SV23 @ SV261 ) )
= $false )
| ( ( ( ti @ SV81 @ SV133 )
= ( ti @ SV81 @ SV225 ) )
= $false )
| ( ( ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV133 ) @ SV184 )
= ( hAPP @ SV23 @ ( product_prod @ SV81 @ SV23 ) @ ( hAPP @ SV81 @ ( fun @ SV23 @ ( product_prod @ SV81 @ SV23 ) ) @ ( product_Pair @ SV81 @ SV23 ) @ SV225 ) @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(910,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
= $false )
| ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(911,plain,
! [SV152: $i,SV201: $i,SV272: $i,SV43: $i,SV282: $i,SV241: $i,SV100: $i] :
( ( ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) )
= $false )
| ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(912,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(913,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(914,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( ! [SY1338: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( sK32_SY1273 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( sK38_SY1314 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( sK41_SY1324 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( sK45_SY1331 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ ( sK47_SY1336 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ SY1338 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[902]) ).
thf(915,plain,
! [SV284: $i,SV274: $i,SV245: $i,SV205: $i,SV156: $i,SV104: $i,SV47: $i] :
( ( ( ti @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ SV284 )
= ( hAPP @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( hAPP @ SV47 @ ( fun @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_prod @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) ) @ ( product_Pair @ SV47 @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( sK18_SY1259 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( hAPP @ SV104 @ ( fun @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_prod @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) ) @ ( product_Pair @ SV104 @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( sK26_SY1287 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( hAPP @ SV156 @ ( fun @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_prod @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) ) @ ( product_Pair @ SV156 @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( sK33_SY1301 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( hAPP @ SV205 @ ( fun @ ( product_prod @ SV245 @ SV274 ) @ ( product_prod @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) ) @ ( product_Pair @ SV205 @ ( product_prod @ SV245 @ SV274 ) ) @ ( sK39_SY1319 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( hAPP @ SV274 @ ( product_prod @ SV245 @ SV274 ) @ ( hAPP @ SV245 @ ( fun @ SV274 @ ( product_prod @ SV245 @ SV274 ) ) @ ( product_Pair @ SV245 @ SV274 ) @ ( sK42_SY1328 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) @ ( sK46_SY1334 @ SV284 @ SV274 @ SV245 @ SV205 @ SV156 @ SV104 @ SV47 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(916,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(917,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(918,plain,
! [SV159: $i,SV208: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(919,plain,
! [SV208: $i,SV159: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(920,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ! [SY1335: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ ( sK43_SY998 @ SV288 @ SV162 @ SV110 @ SV53 ) ) @ SY1335 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(921,plain,
! [SV294: $i,SV289: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SY1002 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SV294 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(922,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(923,plain,
! [SV152: $i,SV201: $i,SV272: $i,SV43: $i,SV282: $i,SV241: $i,SV100: $i] :
( ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ~ ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(924,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $false )
| ( ( ( ti @ SV100 @ SV241 )
!= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(925,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
= $false )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(926,plain,
! [SV283: $i,SV286: $i,SV273: $i,SV244: $i,SV204: $i,SV155: $i,SV103: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ ( hAPP @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( hAPP @ SV46 @ ( fun @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) ) @ ( product_Pair @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( sK32_SY1273 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( hAPP @ SV103 @ ( fun @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ ( product_Pair @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( sK38_SY1314 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( hAPP @ SV155 @ ( fun @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) @ ( product_Pair @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( sK41_SY1324 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( hAPP @ SV204 @ ( fun @ ( product_prod @ SV244 @ SV273 ) @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) @ ( product_Pair @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) @ ( sK45_SY1331 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( hAPP @ SV273 @ ( product_prod @ SV244 @ SV273 ) @ ( hAPP @ SV244 @ ( fun @ SV273 @ ( product_prod @ SV244 @ SV273 ) ) @ ( product_Pair @ SV244 @ SV273 ) @ ( sK47_SY1336 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) @ ( sK48_SY1338 @ SV283 @ SV286 @ SV273 @ SV244 @ SV204 @ SV155 @ SV103 @ SV46 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV46 @ ( product_prod @ SV103 @ ( product_prod @ SV155 @ ( product_prod @ SV204 @ ( product_prod @ SV244 @ SV273 ) ) ) ) ) @ bool @ SV286 @ SV283 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[914]) ).
thf(927,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(928,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(929,plain,
! [SV159: $i,SV208: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(930,plain,
! [SV208: $i,SV159: $i,SV291: $i,SV287: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV159 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ SV287 ) @ SV291 ) ) @ SV208 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(931,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ ( sK43_SY998 @ SV288 @ SV162 @ SV110 @ SV53 ) ) @ ( sK49_SY1335 @ SV288 @ SV162 @ SV110 @ SV53 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[920]) ).
thf(932,plain,
! [SV289: $i,SV294: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( sK50_SY1002 @ SV294 @ SV289 @ SV162 @ SV110 @ SV53 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SV294 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[921]) ).
thf(933,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) )
= $false )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(934,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) )
| ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) ) )
= $false )
| ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(935,plain,
! [SV152: $i,SV201: $i,SV272: $i,SV43: $i,SV282: $i,SV241: $i,SV100: $i] :
( ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $false )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $false )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(936,plain,
! [SV241: $i,SV282: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(937,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(938,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(939,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(940,plain,
! [SV288: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ ( sK43_SY998 @ SV288 @ SV162 @ SV110 @ SV53 ) ) @ ( sK49_SY1335 @ SV288 @ SV162 @ SV110 @ SV53 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(941,plain,
! [SV289: $i,SV294: $i,SV162: $i,SV110: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( sK50_SY1002 @ SV294 @ SV289 @ SV162 @ SV110 @ SV53 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV53 @ SV110 ) @ bool @ SV162 @ ( hAPP @ SV110 @ ( product_prod @ SV53 @ SV110 ) @ ( hAPP @ SV53 @ ( fun @ SV110 @ ( product_prod @ SV53 @ SV110 ) ) @ ( product_Pair @ SV53 @ SV110 ) @ SV289 ) @ SV294 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(942,plain,
! [SV282: $i,SV241: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) ) )
= $false )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(943,plain,
! [SV241: $i,SV201: $i,SV282: $i,SV272: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(944,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ~ ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) ) ) )
= $false )
| ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(945,plain,
! [SV201: $i,SV241: $i,SV282: $i,SV272: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
!= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false )
| ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(946,plain,
! [SV241: $i,SV201: $i,SV282: $i,SV272: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(947,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(948,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(949,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(950,plain,
! [SV282: $i,SV241: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(951,plain,
! [SV241: $i,SV201: $i,SV282: $i,SV272: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(952,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
!= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(953,plain,
! [SV201: $i,SV241: $i,SV282: $i,SV272: $i,SV152: $i,SV100: $i,SV43: $i] :
( ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ SV152 @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $true )
| ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(954,plain,
! [SV208: $i,SV159: $i,SV107: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV159 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV50 @ SV107 ) @ ( fun @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV50 @ SV107 ) ) @ ( hAPP @ SV107 @ ( product_prod @ SV50 @ SV107 ) @ ( hAPP @ SV50 @ ( fun @ SV107 @ ( product_prod @ SV50 @ SV107 ) ) @ ( product_Pair @ SV50 @ SV107 ) @ ( sK27_SY1123 @ SV159 @ SV208 @ SV107 @ SV50 ) ) @ ( sK34_SY1305 @ SV208 @ SV159 @ SV107 @ SV50 ) ) ) @ SV208 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV208 )
= ( ti @ ( fun @ ( product_prod @ SV50 @ SV107 ) @ bool ) @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(955,plain,
! [SV282: $i,SV241: $i,SV152: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $false )
| ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(956,plain,
! [SV152: $i,SV282: $i,SV241: $i,SV100: $i,SV201: $i,SV272: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV272 )
= ( ti @ SV43 @ SV201 ) )
= $false )
| ( ( ( ti @ SV100 @ SV241 )
= ( ti @ SV100 @ SV282 ) )
= $true )
| ( ( ( hAPP @ SV43 @ ( option @ SV100 ) @ ( hAPP @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( hAPP @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) @ ( hAPP @ ( fun @ SV43 @ ( option @ SV100 ) ) @ ( fun @ SV43 @ ( fun @ ( option @ SV100 ) @ ( fun @ SV43 @ ( option @ SV100 ) ) ) ) @ ( fun_upd @ SV43 @ ( option @ SV100 ) ) @ SV152 ) @ SV201 ) @ ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV241 ) ) @ SV272 )
= ( hAPP @ SV100 @ ( option @ SV100 ) @ ( some @ SV100 ) @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(957,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[232,956,955,954,953,951,949,948,946,941,940,939,935,930,929,926,915,909,901,897,895,894,885,884,879,862,861,860,857,856,855,854,840,839,836,833,832,831,830,814,809,801,795,779,777,775,774,761,760,755,754,751,731,713,709,704,697,695,694,693,690,683,652,651,638,637,636,635,633,632,631,630,629,575,535,534,522,521,520,519,468,405,404,365,349,344,251,250,242,241,240,239,238,237,236,235,234]) ).
thf(958,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[957]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW478+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n001.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 17:06:09 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.52/13.63 .
% 80.52/13.63
% 80.52/13.63 No.of.Axioms: 72
% 80.52/13.63
% 80.52/13.63 Length.of.Defs: 0
% 80.52/13.63
% 80.52/13.63 Contains.Choice.Funs: false
% 80.52/13.63 ..............................................................................................................................................................................................................................................................................
% 80.52/13.63
% 80.52/13.63 ********************************
% 80.52/13.63 * All subproblems solved! *
% 80.52/13.63 ********************************
% 80.52/13.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:72,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:957,loop_count:0,foatp_calls:1,translation:fof_full)
% 80.52/13.63
% 80.52/13.63 %**** Beginning of derivation protocol ****
% 80.52/13.63 % SZS output start CNFRefutation
% See solution above
% 80.52/13.64
% 80.52/13.64 %**** End of derivation protocol ****
% 80.52/13.64 %**** no. of clauses in derivation: 875 ****
% 80.52/13.64 %**** clause counter: 957 ****
% 80.52/13.64
% 80.52/13.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:72,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:957,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------