TSTP Solution File: SWW478+5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW478+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:23:05 EDT 2024
% Result : Theorem 23.30s 10.18s
% Output : Refutation 24.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 156
% Syntax : Number of formulae : 314 ( 192 unt; 0 typ; 0 def)
% Number of atoms : 562 ( 311 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 65201 ( 97 ~; 11 |; 47 &;64856 @)
% ( 16 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 56 usr; 28 con; 0-4 aty)
% Number of variables : 1354 ( 0 ^1343 !; 11 ?;1354 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i > $i > $i ).
thf(fun_type,type,
fun: $i > $i > $i ).
thf(product_prod_type,type,
product_prod: $i > $i > $i ).
thf(exp_type,type,
exp: $i > $i ).
thf(list_type,type,
list: $i > $i ).
thf(char_type,type,
char: $i ).
thf(nat_type,type,
nat: $i ).
thf(option_type,type,
option: $i > $i ).
thf(val_type,type,
val: $i ).
thf(bool_type,type,
bool: $i ).
thf(member_type,type,
member: $i > $i ).
thf(product_Pair_type,type,
product_Pair: $i > $i > $i ).
thf(ea_type,type,
ea: $i ).
thf(ha_type,type,
ha: $i ).
thf(fun_upd_type,type,
fun_upd: $i > $i > $i ).
thf(la_type,type,
la: $i ).
thf(v_1_type,type,
v_1: $i ).
thf(some_type,type,
some: $i > $i ).
thf(v_type,type,
v: $i ).
thf(e_a_type,type,
e_a: $i ).
thf(h_a_type,type,
h_a: $i ).
thf(l_a_type,type,
l_a: $i ).
thf(ty_type,type,
ty: $i ).
thf(red_type,type,
red: $i ).
thf(p_type,type,
p: $i ).
thf(ti_type,type,
ti: $i > $i > $i ).
thf(undefined_type,type,
undefined: $i > $i ).
thf(produc1605651328_split_type,type,
produc1605651328_split: $i > $i > $i > $i ).
thf(product_prod_case_type,type,
product_prod_case: $i > $i > $i > $i ).
thf(wTrt_type,type,
wTrt: $i ).
thf(val_1_type,type,
val_1: $i > $i ).
thf(block_type,type,
block: $i > $i ).
thf(redp_type,type,
redp: $i ).
thf(none_type,type,
none: $i > $i ).
thf(assigned_type,type,
assigned: $i ).
thf(seq_type,type,
seq: $i > $i ).
thf(lAss_type,type,
lAss: $i > $i ).
thf(t_1_type,type,
t_1: $i ).
thf(combb_type,type,
combb: $i > $i > $i > $i ).
thf(e_type,type,
e: $i ).
thf(t_type,type,
t: $i ).
thf(product_prod_rec_type,type,
product_prod_rec: $i > $i > $i > $i ).
thf(lconf_type,type,
lconf: $i > $i ).
thf(typeSa885026672_sconf_type,type,
typeSa885026672_sconf: $i ).
thf(combs_type,type,
combs: $i > $i > $i > $i ).
thf(fconj_type,type,
fconj: $i ).
thf(hconf_type,type,
hconf: $i > $i ).
thf(combc_type,type,
combc: $i > $i > $i > $i ).
thf(combk_type,type,
combk: $i > $i > $i ).
thf(widen_type,type,
widen: $i > $i ).
thf(hp_type,type,
hp: $i ).
thf(wf_J_mdecl_type,type,
wf_J_mdecl: $i ).
thf(v_2_type,type,
v_2: $i ).
thf(wf_prog_type,type,
wf_prog: $i > $i ).
thf(unit_type,type,
unit: $i ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ E )
= ( ti @ ( product_prod @ B @ C ) @ F ) )
=> ( ( hAPP @ ( product_prod @ B @ C ) @ A @ ( hAPP @ ( fun @ B @ ( fun @ C @ A ) ) @ ( fun @ ( product_prod @ B @ C ) @ A ) @ ( product_prod_case @ B @ C @ A ) @ D ) @ E )
= ( hAPP @ ( product_prod @ B @ C ) @ A @ ( hAPP @ ( fun @ B @ ( fun @ C @ A ) ) @ ( fun @ ( product_prod @ B @ C ) @ A ) @ ( product_prod_case @ B @ C @ A ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_split__weak__cong) ).
thf(457,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ E )
= ( ti @ ( product_prod @ B @ C ) @ F ) )
=> ( ( hAPP @ ( product_prod @ B @ C ) @ A @ ( hAPP @ ( fun @ B @ ( fun @ C @ A ) ) @ ( fun @ ( product_prod @ B @ C ) @ A ) @ ( product_prod_case @ B @ C @ A ) @ D ) @ E )
= ( hAPP @ ( product_prod @ B @ C ) @ A @ ( hAPP @ ( fun @ B @ ( fun @ C @ A ) ) @ ( fun @ ( product_prod @ B @ C ) @ A ) @ ( product_prod_case @ B @ C @ A ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(145,axiom,
( ( ti @ ( exp @ ( list @ char ) ) @ ea )
= ea ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_ea_____res) ).
thf(629,plain,
( ( ti @ ( exp @ ( list @ char ) ) @ ea )
= ea ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ B @ A ) ) @ ( combk @ A @ B ) )
= ( combk @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
thf(365,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ B @ A ) ) @ ( combk @ A @ B ) )
= ( combk @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(518,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(95,axiom,
( ( ti @ ty @ t )
= t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_T_H_____res) ).
thf(468,plain,
( ( ti @ ty @ t )
= t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ D @ ( hAPP @ ( product_prod @ B @ C ) @ A @ ( hAPP @ ( fun @ B @ ( fun @ C @ A ) ) @ ( fun @ ( product_prod @ B @ C ) @ A ) @ ( product_prod_case @ B @ C @ A ) @ E ) @ F ) ) )
=> ~ ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ F )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ D @ ( hAPP @ C @ A @ ( hAPP @ B @ ( fun @ C @ A ) @ E @ G ) @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_splitE2) ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ D @ ( hAPP @ ( product_prod @ B @ C ) @ A @ ( hAPP @ ( fun @ B @ ( fun @ C @ A ) ) @ ( fun @ ( product_prod @ B @ C ) @ A ) @ ( product_prod_case @ B @ C @ A ) @ E ) @ F ) ) )
=> ~ ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ F )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ D @ ( hAPP @ C @ A @ ( hAPP @ B @ ( fun @ C @ A ) @ E @ G ) @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( combk @ ( option @ B ) @ A ) @ ( none @ B ) ) ) @ C ) @ ( none @ B ) ) @ D )
= ( none @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_empty__upd__none) ).
thf(333,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( combk @ ( option @ B ) @ A ) @ ( none @ B ) ) ) @ C ) @ ( none @ B ) ) @ D )
= ( none @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(27,axiom,
hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ p ) @ ha ) @ e ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ v_1 ) @ t_1 ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ v_1 ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ v ) ) ) @ ea ) ) ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_InitBlockRed_I5_J) ).
thf(249,plain,
hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ p ) @ ha ) @ e ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ v_1 ) @ t_1 ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ v_1 ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ v ) ) ) @ ea ) ) ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ! [G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ F )
!= ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ G ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ H ) @ ( hAPP @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ E ) ) @ I ) @ ( hAPP @ E @ ( product_prod @ D @ E ) @ ( hAPP @ D @ ( fun @ E @ ( product_prod @ D @ E ) ) @ ( product_Pair @ D @ E ) @ J ) @ K ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_prod__cases5) ).
thf(170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ! [G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ F )
!= ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ G ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ H ) @ ( hAPP @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ E ) ) @ I ) @ ( hAPP @ E @ ( product_prod @ D @ E ) @ ( hAPP @ D @ ( fun @ E @ ( product_prod @ D @ E ) ) @ ( product_Pair @ D @ E ) @ J ) @ K ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ E )
= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_fun__upd__apply) ).
thf(582,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ E )
= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ C ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ A @ ( fun @ B @ bool ) @ C @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_splitD) ).
thf(308,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ C ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ A @ ( fun @ B @ bool ) @ C @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( produc1605651328_split @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_internal__split__conv) ).
thf(449,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( produc1605651328_split @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_exp_Osimps_I145_J) ).
thf(614,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(84,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(440,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(106,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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) ) @ typeSa885026672_sconf )
= typeSa885026672_sconf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TypeSafe__Mirabelle__mcolmsuaig_Osconf_res) ).
thf(511,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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) ) @ typeSa885026672_sconf )
= typeSa885026672_sconf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(16,axiom,
( ( ti @ ty @ t_1 )
= t_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_T_____res) ).
thf(202,plain,
( ( ti @ ty @ t_1 )
= t_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ E ) @ F ) @ G ) )
<=> ( ( ( ti @ A @ B )
= ( ti @ A @ E ) )
& ( C = F )
& ( D = G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_exp_Osimps_I10_J) ).
thf(597,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ E ) @ F ) @ G ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ E ) )
& ( C = F )
& ( D = G ) ) )
& ( ( ( ( ti @ A @ B )
= ( ti @ A @ E ) )
& ( C = F )
& ( D = G ) )
=> ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ E ) @ F ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ E ) @ F ) ) )
=> ~ ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ F )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ E @ G ) @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_mem__splitE) ).
thf(384,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ E ) @ F ) ) )
=> ~ ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ F )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ E @ G ) @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',tsy_v_h_Ha_____res) ).
thf(550,plain,
( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ h_a )
= h_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) ) @ ( combb @ A @ B @ C ) )
= ( combb @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
thf(417,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) ) @ ( combb @ A @ B @ C ) )
= ( combb @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(8,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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) ) @ wTrt )
= wTrt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_WellTypeRT_OWTrt_res) ).
thf(174,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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) ) @ wTrt )
= wTrt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,axiom,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ la )
= la ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_la_____res) ).
thf(404,plain,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ la )
= la ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ A ) @ B ) @ ( hAPP @ ( option @ ty ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ ty ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ ty ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ ty ) ) @ C ) @ D ) @ ( hAPP @ ty @ ( option @ ty ) @ ( some @ ty ) @ E ) ) ) @ F ) @ G ) )
=> ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ A ) @ B ) @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ D ) @ E ) @ F ) ) @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_WTrtBlock) ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ A ) @ B ) @ ( hAPP @ ( option @ ty ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( option @ ty ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( list @ char ) @ ( fun @ ( option @ ty ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ ty ) ) @ C ) @ D ) @ ( hAPP @ ty @ ( option @ ty ) @ ( some @ ty ) @ E ) ) ) @ F ) @ G ) )
=> ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ A ) @ B ) @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ D ) @ E ) @ F ) ) @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(62,axiom,
! [A: $i] :
( ( hBOOL @ ( ti @ bool @ A ) )
<=> ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(372,plain,
! [A: $i] :
( ( ( hBOOL @ ( ti @ bool @ A ) )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ ( ti @ bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_fun__upd__other) ).
thf(504,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ B @ E )
!= ( ti @ B @ F ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) @ E )
= ( hAPP @ B @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ti @ B @ F )
!= ( ti @ B @ G ) )
=> ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) ) @ G ) @ E )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ G ) @ E ) ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_fun__upd__twist) ).
thf(460,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ti @ B @ F )
!= ( ti @ B @ G ) )
=> ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ F ) @ D ) ) @ G ) @ E )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ G ) @ E ) ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $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 @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) @ C ) ) @ D ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_redp__redsp_ORedSeq) ).
thf(261,plain,
! [A: $i,B: $i,C: $i,D: $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 @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) @ C ) ) @ D ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',tsy_c_SmallStep_Ored_res) ).
thf(443,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 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ F )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ E @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mem__splitI2) ).
thf(623,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ F )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ E @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
!= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_exp_Osimps_I75_J) ).
thf(646,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
!= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(54,axiom,
! [A: $i,B: $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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ p ) @ B ) @ ( 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 ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ p ) @ ha ) @ B ) @ ea ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ p ) @ h_a ) @ B ) @ e_a ) @ C ) )
& ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ p ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_InitBlockRed_I2_J) ).
thf(348,plain,
! [A: $i,B: $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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ p ) @ B ) @ ( 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 ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ p ) @ ha ) @ B ) @ ea ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ p ) @ h_a ) @ B ) @ e_a ) @ C ) )
& ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ p ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(70,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( seq @ A ) )
= ( seq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OSeq_res) ).
thf(396,plain,
! [A: $i] :
( ( ti @ ( fun @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( seq @ A ) )
= ( seq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $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 @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ B ) @ C ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) ) @ E ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_redp__redsp_ORedBlock) ).
thf(243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $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 @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ B ) @ C ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) ) @ E ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i,G: $i,H: $i,I: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ E )
!= ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ F ) @ ( hAPP @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ D ) ) @ G ) @ ( hAPP @ D @ ( product_prod @ C @ D ) @ ( hAPP @ C @ ( fun @ D @ ( product_prod @ C @ D ) ) @ ( product_Pair @ C @ D ) @ H ) @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod__cases4) ).
thf(507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i,G: $i,H: $i,I: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ E )
!= ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ F ) @ ( hAPP @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ D ) ) @ G ) @ ( hAPP @ D @ ( product_prod @ C @ D ) @ ( hAPP @ C @ ( fun @ D @ ( product_prod @ C @ D ) ) @ ( product_Pair @ C @ D ) @ H ) @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(112,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 @ ( exp @ ( list @ char ) ) @ ( 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 )
= redp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SmallStep_Oredp_res) ).
thf(527,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 @ ( exp @ ( list @ char ) ) @ ( 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 )
= redp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_exp_Osimps_I143_J) ).
thf(292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(64,axiom,
( ( ti @ ( 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 @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ hp )
= hp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_State_Ohp_res) ).
thf(380,plain,
( ( ti @ ( 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 @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ hp )
= hp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 @ B ) @ C ) @ D ) @ E ) @ F ) )
=> ( 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 @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ C ) @ A ) ) @ D ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ E ) @ A ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_redp__redsp_OSeqRed) ).
thf(529,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 @ B ) @ C ) @ D ) @ E ) @ F ) )
=> ( 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 @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ C ) @ A ) ) @ D ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ E ) @ A ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( fun @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) ) @ ( combb @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ A ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combb @ bool @ bool @ B ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ C ) ) ) @ D ) ) @ E ) )
<=> ( ( hBOOL @ C )
& ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_split__part) ).
thf(661,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( fun @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) ) @ ( combb @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ A ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combb @ bool @ bool @ B ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ C ) ) ) @ D ) ) @ E ) )
=> ( ( hBOOL @ C )
& ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ D ) @ E ) ) ) )
& ( ( ( hBOOL @ C )
& ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( fun @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) ) @ ( combb @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ A ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combb @ bool @ bool @ B ) @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ C ) ) ) @ D ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
~ ! [H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ G )
!= ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ H ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ I ) @ ( hAPP @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ J ) @ ( hAPP @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( hAPP @ D @ ( fun @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_Pair @ D @ ( product_prod @ E @ F ) ) @ K ) @ ( hAPP @ F @ ( product_prod @ E @ F ) @ ( hAPP @ E @ ( fun @ F @ ( product_prod @ E @ F ) ) @ ( product_Pair @ E @ F ) @ L ) @ M ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_prod__cases6) ).
thf(546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
~ ! [H: $i,I: $i,J: $i,K: $i,L: $i,M: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ G )
!= ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ H ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ I ) @ ( hAPP @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ J ) @ ( hAPP @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( hAPP @ D @ ( fun @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_Pair @ D @ ( product_prod @ E @ F ) ) @ K ) @ ( hAPP @ F @ ( product_prod @ E @ F ) @ ( hAPP @ E @ ( fun @ F @ ( product_prod @ E @ F ) ) @ ( product_Pair @ E @ F ) @ L ) @ M ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ F ) @ ( hAPP @ ( product_prod @ D @ E ) @ ( product_prod @ A @ B ) @ ( hAPP @ ( fun @ D @ ( fun @ E @ ( product_prod @ A @ B ) ) ) @ ( fun @ ( product_prod @ D @ E ) @ ( product_prod @ A @ B ) ) @ ( product_prod_case @ D @ E @ ( product_prod @ A @ B ) ) @ G ) @ H ) )
= ( hAPP @ ( product_prod @ D @ E ) @ C @ ( hAPP @ ( fun @ D @ ( fun @ E @ C ) ) @ ( fun @ ( product_prod @ D @ E ) @ C ) @ ( product_prod_case @ D @ E @ C ) @ ( hAPP @ ( fun @ D @ ( fun @ E @ ( product_prod @ A @ B ) ) ) @ ( fun @ D @ ( fun @ E @ C ) ) @ ( hAPP @ ( fun @ ( fun @ E @ ( product_prod @ A @ B ) ) @ ( fun @ E @ C ) ) @ ( fun @ ( fun @ D @ ( fun @ E @ ( product_prod @ A @ B ) ) ) @ ( fun @ D @ ( fun @ E @ C ) ) ) @ ( combb @ ( fun @ E @ ( product_prod @ A @ B ) ) @ ( fun @ E @ C ) @ D ) @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( fun @ ( fun @ E @ ( product_prod @ A @ B ) ) @ ( fun @ E @ C ) ) @ ( combb @ ( product_prod @ A @ B ) @ C @ E ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ F ) ) ) @ G ) ) @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_split__twice) ).
thf(534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ F ) @ ( hAPP @ ( product_prod @ D @ E ) @ ( product_prod @ A @ B ) @ ( hAPP @ ( fun @ D @ ( fun @ E @ ( product_prod @ A @ B ) ) ) @ ( fun @ ( product_prod @ D @ E ) @ ( product_prod @ A @ B ) ) @ ( product_prod_case @ D @ E @ ( product_prod @ A @ B ) ) @ G ) @ H ) )
= ( hAPP @ ( product_prod @ D @ E ) @ C @ ( hAPP @ ( fun @ D @ ( fun @ E @ C ) ) @ ( fun @ ( product_prod @ D @ E ) @ C ) @ ( product_prod_case @ D @ E @ C ) @ ( hAPP @ ( fun @ D @ ( fun @ E @ ( product_prod @ A @ B ) ) ) @ ( fun @ D @ ( fun @ E @ C ) ) @ ( hAPP @ ( fun @ ( fun @ E @ ( product_prod @ A @ B ) ) @ ( fun @ E @ C ) ) @ ( fun @ ( fun @ D @ ( fun @ E @ ( product_prod @ A @ B ) ) ) @ ( fun @ D @ ( fun @ E @ C ) ) ) @ ( combb @ ( fun @ E @ ( product_prod @ A @ B ) ) @ ( fun @ E @ C ) @ D ) @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( fun @ ( fun @ E @ ( product_prod @ A @ B ) ) @ ( fun @ E @ C ) ) @ ( combb @ ( product_prod @ A @ B ) @ C @ E ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ F ) ) ) @ G ) ) @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combb @ C @ B @ A ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ D @ ( hAPP @ A @ C @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combb @ C @ B @ A ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ D @ ( hAPP @ A @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combs @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ ( hAPP @ A @ C @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(452,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combs @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ ( hAPP @ A @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( ti @ ( product_prod @ A @ B ) @ C )
!= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_PairE) ).
thf(302,plain,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( ti @ ( product_prod @ A @ B ) @ C )
!= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(68,axiom,
( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ha )
= ha ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_ha_____res) ).
thf(392,plain,
( ( ti @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ha )
= ha ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $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 ) ) ) ) @ C ) @ D ) ) @ ( 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 ) @ F ) ) ) @ ( 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 @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ G ) @ ( 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 @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ hp @ D ) ) @ A ) @ C ) @ B ) )
=> ( ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ G ) @ A ) @ D ) )
=> ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ G ) @ A ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_red__preserves__sconf) ).
thf(424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $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 ) ) ) ) @ C ) @ D ) ) @ ( 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 ) @ F ) ) ) @ ( 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 @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ G ) @ ( 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 @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ hp @ D ) ) @ A ) @ C ) @ B ) )
=> ( ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ G ) @ A ) @ D ) )
=> ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ G ) @ A ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(82,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 @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ) @ wf_J_mdecl )
= wf_J_mdecl ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_JWellForm_Owf__J__mdecl_res) ).
thf(429,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 @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ) @ wf_J_mdecl )
= wf_J_mdecl ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( produc1605651328_split @ A @ B @ C )
= ( product_prod_case @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_internal__split__def) ).
thf(165,plain,
! [A: $i,B: $i,C: $i] :
( ( produc1605651328_split @ A @ B @ C )
= ( product_prod_case @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ A ) ) @ B ) ) @ C ) ) @ ( 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 ) ) ) ) @ B ) @ C ) ) ) @ ( 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 @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_red__reds_ORedSeq) ).
thf(229,plain,
! [A: $i,B: $i,C: $i,D: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ A ) ) @ B ) ) @ C ) ) @ ( 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 ) ) ) ) @ B ) @ C ) ) ) @ ( 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 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ C ) @ D ) )
=> ~ ! [E: $i,F: $i] :
( ( ( ti @ ( product_prod @ A @ B ) @ D )
= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
=> ~ ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ A @ ( fun @ B @ bool ) @ C @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_splitE) ).
thf(329,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ C ) @ D ) )
=> ~ ! [E: $i,F: $i] :
( ( ( ti @ ( product_prod @ A @ B ) @ D )
= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
=> ~ ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ A @ ( fun @ B @ bool ) @ C @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ C ) @ D )
= ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ E ) @ F ) )
=> ~ ( ( ( ti @ B @ C )
= ( ti @ B @ E ) )
=> ( ( ti @ A @ D )
!= ( ti @ A @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Pair__inject) ).
thf(285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ C ) @ D )
= ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ E ) @ F ) )
=> ~ ( ( ( ti @ B @ C )
= ( ti @ B @ E ) )
=> ( ( ti @ A @ D )
!= ( ti @ A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_exp_Osimps_I3_J) ).
thf(650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ D ) @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exp_Osimps_I197_J) ).
thf(388,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ D ) @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 ) ) ) ) @ F ) @ ( 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 ) ) ) @ G ) @ H ) ) ) ) @ ( 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 @ I ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ I ) @ D ) @ A ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( 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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( 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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_red__preserves__hconf) ).
thf(420,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 ) ) ) ) @ F ) @ ( 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 ) ) ) @ G ) @ H ) ) ) ) @ ( 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 @ I ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ I ) @ D ) @ A ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( 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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( 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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_rec @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_prod_Orecs) ).
thf(256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_rec @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) ) @ ( product_prod_case @ A @ B @ C ) )
= ( product_prod_case @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_Oprod_Oprod__case_res) ).
thf(339,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) ) @ ( product_prod_case @ A @ B @ C ) )
= ( product_prod_case @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ C ) @ D ) @ E ) )
=> ( ( 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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ C ) @ E ) @ B ) )
=> ( 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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ C ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_widen__trans) ).
thf(537,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ C ) @ D ) @ E ) )
=> ( ( 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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ C ) @ E ) @ B ) )
=> ( 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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ C ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_exp_Osimps_I84_J) ).
thf(669,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(153,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
thf(657,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(147,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( lAss @ A ) )
= ( lAss @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OLAss_res) ).
thf(633,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( lAss @ A ) )
= ( lAss @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ B @ ( fun @ A @ bool ) @ C @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ B @ A ) @ bool @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ ( product_prod @ B @ A ) @ bool ) @ ( product_prod_case @ B @ A @ bool ) @ C ) @ ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod__caseI) ).
thf(360,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ B @ ( fun @ A @ bool ) @ C @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ B @ A ) @ bool @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ ( product_prod @ B @ A ) @ bool ) @ ( product_prod_case @ B @ A @ bool ) @ C ) @ ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ D ) )
<=> ? [D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_split__paired__Ex) ).
thf(412,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ D ) )
=> ? [D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) ) )
& ( ? [D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) ) @ ( product_Pair @ A @ B ) )
= ( product_Pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_res) ).
thf(618,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) ) @ ( product_Pair @ A @ B ) )
= ( product_Pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_split__conv) ).
thf(513,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(10,axiom,
! [A: $i] :
( ( ti @ ( fun @ val @ ( exp @ A ) ) @ ( val_1 @ A ) )
= ( val_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OVal_res) ).
thf(180,plain,
! [A: $i] :
( ( ti @ ( fun @ val @ ( exp @ A ) ) @ ( val_1 @ A ) )
= ( val_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) ) @ ( block @ A ) )
= ( block @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OBlock_res) ).
thf(296,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) ) @ ( block @ A ) )
= ( block @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(125,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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) )
= ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Conform_Olconf_res) ).
thf(562,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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) )
= ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ C ) @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_exp_Osimps_I82_J) ).
thf(176,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ C ) @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ B @ ( fun @ A @ bool ) @ ( hAPP @ C @ ( fun @ B @ ( fun @ A @ bool ) ) @ E @ F ) @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ C @ B @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ B @ ( product_prod @ C @ B ) @ ( hAPP @ C @ ( fun @ B @ ( product_prod @ C @ B ) ) @ ( product_Pair @ C @ B ) @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_mem__splitI) ).
thf(402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ B @ ( fun @ A @ bool ) @ ( hAPP @ C @ ( fun @ B @ ( fun @ A @ bool ) ) @ E @ F ) @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ C @ B @ ( fun @ A @ bool ) ) @ E ) @ ( hAPP @ B @ ( product_prod @ C @ B ) @ ( hAPP @ C @ ( fun @ B @ ( product_prod @ C @ B ) ) @ ( product_Pair @ C @ B ) @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_split__paired__All) ).
thf(577,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ ( hAPP @ B @ A @ C @ D ) )
= ( ti @ ( fun @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).
thf(204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ ( hAPP @ B @ A @ C @ D ) )
= ( ti @ ( fun @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 ) ) ) ) @ F ) @ ( 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 ) ) ) @ G ) @ H ) ) ) ) @ ( 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 @ I ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ I ) @ D ) @ A ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ D ) @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ G ) @ H ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_red__preserves__lconf) ).
thf(259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 ) ) ) ) @ F ) @ ( 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 ) ) ) @ G ) @ H ) ) ) ) @ ( 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 @ I ) ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ I ) @ D ) @ A ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ D ) @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ I ) @ G ) @ H ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(86,axiom,
( ( hAPP @ ( list @ char ) @ ( option @ val ) @ l_a @ v_1 )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).
thf(445,plain,
( ( hAPP @ ( list @ char ) @ ( option @ val ) @ l_a @ v_1 )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ v_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(65,axiom,
( ( ti @ ( fun @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) ) @ assigned )
= assigned ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SmallStep_Oassigned_res) ).
thf(382,plain,
( ( ti @ ( fun @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) ) @ assigned )
= assigned ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ B @ ( fun @ A @ C ) ) ) @ ( combc @ A @ B @ C ) )
= ( combc @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
thf(572,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ B @ ( fun @ A @ C ) ) ) @ ( combc @ A @ B @ C ) )
= ( combc @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ B @ A ) @ C ) )
<=> ( ( hAPP @ B @ A @ C @ D )
= ( ti @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_fun__upd__idem__iff) ).
thf(236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ B @ A ) @ C ) )
=> ( ( hAPP @ B @ A @ C @ D )
= ( ti @ A @ E ) ) )
& ( ( ( hAPP @ B @ A @ C @ D )
= ( ti @ A @ E ) )
=> ( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ D @ F ) @ G )
= ( hAPP @ ( product_prod @ C @ A ) @ B @ E @ ( hAPP @ A @ ( product_prod @ C @ A ) @ ( hAPP @ C @ ( fun @ A @ ( product_prod @ C @ A ) ) @ ( product_Pair @ C @ A ) @ F ) @ G ) ) )
=> ( ( hAPP @ ( fun @ C @ ( fun @ A @ B ) ) @ ( fun @ ( product_prod @ C @ A ) @ B ) @ ( product_prod_case @ C @ A @ B ) @ D )
= ( ti @ ( fun @ ( product_prod @ C @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_cond__split__eta) ).
thf(406,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ D @ F ) @ G )
= ( hAPP @ ( product_prod @ C @ A ) @ B @ E @ ( hAPP @ A @ ( product_prod @ C @ A ) @ ( hAPP @ C @ ( fun @ A @ ( product_prod @ C @ A ) ) @ ( product_Pair @ C @ A ) @ F ) @ G ) ) )
=> ( ( hAPP @ ( fun @ C @ ( fun @ A @ B ) ) @ ( fun @ ( product_prod @ C @ A ) @ B ) @ ( product_prod_case @ C @ A @ B ) @ D )
= ( ti @ ( fun @ ( product_prod @ C @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ D ) @ E ) )
<=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
& ( C = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_exp_Osimps_I6_J) ).
thf(274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ D ) @ E ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
& ( C = E ) ) )
& ( ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
& ( C = E ) )
=> ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(377,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ D ) @ E ) @ F ) )
=> ~ ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ E )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ D @ G ) @ H ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_splitE_H) ).
thf(245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ D ) @ E ) @ F ) )
=> ~ ! [G: $i,H: $i] :
( ( ( ti @ ( product_prod @ B @ C ) @ E )
= ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ D @ G ) @ H ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ C ) ) ) @ ( combs @ A @ B @ C ) )
= ( combs @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
thf(362,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ C ) ) ) @ ( combs @ A @ B @ C ) )
= ( combs @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(127,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( option @ A ) ) @ ( some @ A ) )
= ( some @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Option_Ooption_OSome_res) ).
thf(567,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( option @ A ) ) @ ( some @ A ) )
= ( some @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(477,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E ) @ D )
= ( ti @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_fun__upd__same) ).
thf(494,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E ) @ D )
= ( ti @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(146,axiom,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ e )
= e ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_E_____res) ).
thf(631,plain,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ e )
= e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(121,axiom,
hBOOL @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ bool @ ( hAPP @ ( 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 @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ bool ) @ ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ wf_J_mdecl ) @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms) ).
thf(552,plain,
hBOOL @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ bool @ ( hAPP @ ( 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 @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ bool ) @ ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ wf_J_mdecl ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ ( 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 ) ) @ E ) @ F ) @ ( none @ 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 ) ) ) ) @ G ) @ ( 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 ) @ I ) ) ) ) @ ( 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 @ J ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ I @ F )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( exp @ ( list @ char ) ) @ bool @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) @ assigned @ F ) @ C ) )
=> ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ C ) ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ G ) ) ) @ ( 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 ) @ ( 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 ) ) @ I ) @ F ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ E @ F ) ) ) ) ) ) @ ( 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 @ J ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_red__reds_OBlockRedSome) ).
thf(609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ ( 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 ) ) @ E ) @ F ) @ ( none @ 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 ) ) ) ) @ G ) @ ( 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 ) @ I ) ) ) ) @ ( 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 @ J ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ I @ F )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( exp @ ( list @ char ) ) @ bool @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) @ assigned @ F ) @ C ) )
=> ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ C ) ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ G ) ) ) @ ( 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 ) @ ( 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 ) ) @ I ) @ F ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ E @ F ) ) ) ) ) ) @ ( 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 @ J ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(135,axiom,
! [A: $i] :
( ( ti @ ( option @ A ) @ ( none @ A ) )
= ( none @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Option_Ooption_ONone_res) ).
thf(594,plain,
! [A: $i] :
( ( ti @ ( option @ A ) @ ( none @ A ) )
= ( none @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(142,axiom,
( ( ti @ val @ v_2 )
= v_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_v_H_____res) ).
thf(621,plain,
( ( ti @ val @ v_2 )
= v_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).
thf(198,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ ( 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 ) ) @ E ) @ F ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ G ) ) ) ) ) @ ( 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 ) ) ) ) @ H ) @ ( 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 ) ) ) @ I ) @ J ) ) ) ) @ ( 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 @ K ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ J @ F )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ G ) ) ) @ C ) ) ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ H ) ) ) @ ( 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 ) ) ) @ I ) @ ( 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 ) ) @ J ) @ F ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ E @ F ) ) ) ) ) ) @ ( 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 @ K ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_red__reds_OInitBlockRed) ).
thf(521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $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 ) ) ) ) @ C ) @ ( 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 ) ) ) @ D ) @ ( 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 ) ) @ E ) @ F ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ G ) ) ) ) ) @ ( 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 ) ) ) ) @ H ) @ ( 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 ) ) ) @ I ) @ J ) ) ) ) @ ( 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 @ K ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ J @ F )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ G ) ) ) @ C ) ) ) @ ( 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 ) ) ) @ D ) @ E ) ) ) @ ( 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 @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ H ) ) ) @ ( 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 ) ) ) @ I ) @ ( 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 ) ) @ J ) @ F ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ E @ F ) ) ) ) ) ) @ ( 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 @ K ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ B @ C @ D )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_fun__upd__idem) ).
thf(399,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ B @ C @ D )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ ( fun @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( fun @ A @ B ) ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) @ ( fun_upd @ A @ B ) @ C ) @ D ) @ E )
= ( ti @ ( fun @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ D ) @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_exp_Osimps_I142_J) ).
thf(636,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ D ) @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ B ) @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ B ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ E ) ) ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ E ) ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_redp__redsp_ORedInitBlock) ).
thf(455,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ B ) @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ B ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ E ) ) ) ) @ F ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) ) @ ( product_prod_rec @ A @ B @ C ) )
= ( product_prod_rec @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_Oprod_Oprod__rec_res) ).
thf(299,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) ) @ ( product_prod_rec @ A @ B @ C ) )
= ( product_prod_rec @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ A ) @ B ) @ C ) )
<=> ( 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 @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( 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 ) @ ( product_prod_case @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( combs @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ ( combb @ bool @ bool @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ fconj ) @ ( 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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ A ) ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( combc @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ ( combc @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( option @ 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ A ) ) ) @ B ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_sconf__def) ).
thf(267,plain,
! [A: $i,B: $i,C: $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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ A ) @ B ) @ C ) )
=> ( 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 @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( 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 ) @ ( product_prod_case @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( combs @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ ( combb @ bool @ bool @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ fconj ) @ ( 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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ A ) ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( combc @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ ( combc @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( option @ 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ A ) ) ) @ B ) ) ) @ C ) ) )
& ( ( 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 @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( 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 ) @ ( product_prod_case @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( combs @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ ( combb @ bool @ bool @ ( fun @ ( list @ char ) @ ( option @ val ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ fconj ) @ ( 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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ A ) ) ) ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( combc @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ bool ) ) @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) @ ( combc @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( list @ char ) @ ( option @ 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ bool ) ) ) @ ( lconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ A ) ) ) @ B ) ) ) @ C ) )
=> ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ C ) @ D )
= ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ E ) @ F ) )
<=> ( ( ( ti @ B @ C )
= ( ti @ B @ E ) )
& ( ( ti @ A @ D )
= ( ti @ A @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__eq) ).
thf(431,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ C ) @ D )
= ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ E ) @ F ) )
=> ( ( ( ti @ B @ C )
= ( ti @ B @ E ) )
& ( ( ti @ A @ D )
= ( ti @ A @ F ) ) ) )
& ( ( ( ( ti @ B @ C )
= ( ti @ B @ E ) )
& ( ( ti @ A @ D )
= ( ti @ A @ F ) ) )
=> ( ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ C ) @ D )
= ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ! [E: $i,F: $i,G: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ D )
!= ( hAPP @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ C ) ) @ E ) @ ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ F ) @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_prod__cases3) ).
thf(223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ! [E: $i,F: $i,G: $i] :
( ( ti @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ D )
!= ( hAPP @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ C ) ) @ E ) @ ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ F ) @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(137,axiom,
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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ p ) @ e ) @ ( 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 ) @ la ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_InitBlockRed_I4_J) ).
thf(608,plain,
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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( 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 ) ) @ typeSa885026672_sconf @ p ) @ e ) @ ( 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 ) @ la ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(69,axiom,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ l_a )
= l_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_l_Ha_____res) ).
thf(394,plain,
( ( ti @ ( fun @ ( list @ char ) @ ( option @ val ) ) @ l_a )
= l_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i,H: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ bool @ E @ ( hAPP @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ C ) ) @ F ) @ ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ bool @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_prod__induct3) ).
thf(306,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i,H: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ bool @ E @ ( hAPP @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ C ) @ ( product_prod @ A @ ( product_prod @ B @ C ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ C ) ) @ F ) @ ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ C ) ) @ bool @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) ) @ ( fun @ A @ ( fun @ B @ C ) ) @ ( hAPP @ ( fun @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) ) @ ( fun @ A @ ( fun @ B @ C ) ) ) @ ( combb @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( fun @ B @ C ) @ A ) @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( fun @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( fun @ B @ C ) ) @ ( combb @ ( product_prod @ A @ B ) @ C @ B ) @ D ) ) @ ( product_Pair @ A @ B ) ) )
= ( ti @ ( fun @ ( product_prod @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_split__eta) ).
thf(426,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ ( hAPP @ ( fun @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) ) @ ( fun @ A @ ( fun @ B @ C ) ) @ ( hAPP @ ( fun @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) ) @ ( fun @ A @ ( fun @ B @ C ) ) ) @ ( combb @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( fun @ B @ C ) @ A ) @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( fun @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( fun @ B @ C ) ) @ ( combb @ ( product_prod @ A @ B ) @ C @ B ) @ D ) ) @ ( product_Pair @ A @ B ) ) )
= ( ti @ ( fun @ ( product_prod @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(589,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( none @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_map__upd__nonempty) ).
thf(487,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i] :
( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( none @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ E ) @ F ) ) @ G ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ D @ E ) @ F ) @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_splitD_H) ).
thf(516,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ C @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ B @ C ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ B @ C @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ C @ ( product_prod @ B @ C ) @ ( hAPP @ B @ ( fun @ C @ ( product_prod @ B @ C ) ) @ ( product_Pair @ B @ C ) @ E ) @ F ) ) @ G ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ C @ ( fun @ A @ bool ) @ ( hAPP @ B @ ( fun @ C @ ( fun @ A @ bool ) ) @ D @ E ) @ F ) @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( ti @ ( product_prod @ A @ B ) @ D )
= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ A @ ( fun @ B @ bool ) @ C @ E ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_splitI2) ).
thf(342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( ti @ ( product_prod @ A @ B ) @ D )
= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ ( hAPP @ A @ ( fun @ B @ bool ) @ C @ E ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ B ) @ bool @ ( hAPP @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ ( product_prod_case @ A @ B @ bool ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $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 @ B ) @ C ) @ ( 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 ) ) ) @ D ) @ ( 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 ) ) @ E ) @ F ) @ ( none @ val ) ) ) ) @ G ) @ ( 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 ) @ I ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ I @ F )
= ( none @ val ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( exp @ ( list @ char ) ) @ bool @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) @ assigned @ F ) @ C ) )
=> ( 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 @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ C ) ) @ ( 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 ) ) ) @ D ) @ E ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ G ) ) @ ( 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 ) @ ( 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 ) ) @ I ) @ F ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_redp__redsp_OBlockRedNone) ).
thf(355,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $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 @ B ) @ C ) @ ( 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 ) ) ) @ D ) @ ( 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 ) ) @ E ) @ F ) @ ( none @ val ) ) ) ) @ G ) @ ( 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 ) @ I ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ I @ F )
= ( none @ val ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( exp @ ( list @ char ) ) @ bool @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) @ assigned @ F ) @ C ) )
=> ( 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 @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ C ) ) @ ( 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 ) ) ) @ D ) @ E ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ F ) @ A ) @ G ) ) @ ( 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 ) @ ( 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 ) ) @ I ) @ F ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ ( 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 ) ) ) @ C ) @ D ) ) ) @ ( 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 @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ unit ) ) @ ( 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 ) ) ) @ C ) @ ( 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 ) ) @ D ) @ A ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) ) ) ) ) ) @ ( 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 @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_red__reds_ORedLAss) ).
thf(553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ ( 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 ) ) ) @ C ) @ D ) ) ) @ ( 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 @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ unit ) ) @ ( 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 ) ) ) @ C ) @ ( 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 ) ) @ D ) @ A ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) ) ) ) ) ) @ ( 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 @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(4,axiom,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(162,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(114,axiom,
! [A: $i] :
( ( 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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) ) @ ( widen @ A ) )
= ( widen @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TypeRel_Owiden_res) ).
thf(531,plain,
! [A: $i] :
( ( 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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) ) @ ( widen @ A ) )
= ( widen @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( hAPP @ B @ ( product_prod @ C @ B ) @ ( hAPP @ C @ ( fun @ B @ ( product_prod @ C @ B ) ) @ ( product_Pair @ C @ B ) @ G ) @ H )
= ( ti @ ( product_prod @ C @ B ) @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ B @ ( fun @ A @ bool ) @ ( hAPP @ C @ ( fun @ B @ ( fun @ A @ bool ) ) @ D @ G ) @ H ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ C @ B @ ( fun @ A @ bool ) ) @ D ) @ F ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_splitI2_H) ).
thf(640,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( hAPP @ B @ ( product_prod @ C @ B ) @ ( hAPP @ C @ ( fun @ B @ ( product_prod @ C @ B ) ) @ ( product_Pair @ C @ B ) @ G ) @ H )
= ( ti @ ( product_prod @ C @ B ) @ F ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ B @ ( fun @ A @ bool ) @ ( hAPP @ C @ ( fun @ B @ ( fun @ A @ bool ) ) @ D @ G ) @ H ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( fun @ ( product_prod @ C @ B ) @ ( fun @ A @ bool ) ) @ ( product_prod_case @ C @ B @ ( fun @ A @ bool ) ) @ D ) @ F ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) ) @ ( fun_upd @ A @ B ) )
= ( fun_upd @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Fun_Ofun__upd_res) ).
thf(409,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ ( fun @ B @ ( fun @ A @ B ) ) ) ) @ ( fun_upd @ A @ B ) )
= ( fun_upd @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_exp_Osimps_I196_J) ).
thf(263,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) )
<=> ( ( ( ( ti @ A @ F )
= ( ti @ A @ D ) )
& ( ( ti @ B @ E )
= ( ti @ B @ G ) ) )
| ( ( ( ti @ A @ F )
!= ( ti @ A @ D ) )
& ( ( hAPP @ A @ ( option @ B ) @ C @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_map__upd__Some__unfold) ).
thf(310,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) )
=> ( ( ( ( ti @ A @ F )
= ( ti @ A @ D ) )
& ( ( ti @ B @ E )
= ( ti @ B @ G ) ) )
| ( ( ( ti @ A @ F )
!= ( ti @ A @ D ) )
& ( ( hAPP @ A @ ( option @ B ) @ C @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) ) )
& ( ( ( ( ( ti @ A @ F )
= ( ti @ A @ D ) )
& ( ( ti @ B @ E )
= ( ti @ B @ G ) ) )
| ( ( ( ti @ A @ F )
!= ( ti @ A @ D ) )
& ( ( hAPP @ A @ ( option @ B ) @ C @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) )
=> ( ( hAPP @ A @ ( option @ B ) @ ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) ) @ F )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $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 @ C ) @ D ) @ ( 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 ) ) ) @ E ) @ ( 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 ) ) @ F ) @ G ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ H ) ) ) ) @ I ) @ ( 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 ) ) ) @ J ) @ K ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ K @ G )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( 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 @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ G ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ H ) ) ) @ D ) ) ) @ ( 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 ) ) ) @ E ) @ F ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ G ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ I ) ) ) @ ( 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 ) ) ) @ J ) @ ( 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 ) ) @ K ) @ G ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ F @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_redp__redsp_OInitBlockRed) ).
thf(199,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $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 @ C ) @ D ) @ ( 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 ) ) ) @ E ) @ ( 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 ) ) @ F ) @ G ) @ ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ H ) ) ) ) @ I ) @ ( 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 ) ) ) @ J ) @ K ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ K @ G )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( 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 @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ G ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ H ) ) ) @ D ) ) ) @ ( 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 ) ) ) @ E ) @ F ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ G ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ I ) ) ) @ ( 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 ) ) ) @ J ) @ ( 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 ) ) @ K ) @ G ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ F @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ A ) @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ C ) ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) ) ) @ E ) ) @ ( 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 @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) @ E ) ) ) @ ( 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 @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_red__reds_ORedInitBlock) ).
thf(463,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ A ) @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ C ) ) ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) ) ) @ E ) ) @ ( 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 @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ D ) ) @ E ) ) ) @ ( 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 @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ F )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ F )
!= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( hAPP @ B @ A @ C @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_fun__upd__def) ).
thf(470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ti @ B @ F )
= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( ti @ A @ D ) ) )
& ( ( ( ti @ B @ F )
!= ( ti @ B @ E ) )
=> ( ( hAPP @ B @ A @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ E ) @ D ) @ F )
= ( hAPP @ B @ A @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
= ( ti @ ( fun @ A @ ( option @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_map__upd__triv) ).
thf(336,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ A @ ( option @ B ) @ C @ D )
= ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
=> ( ( hAPP @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) @ ( hAPP @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) @ ( hAPP @ ( fun @ A @ ( option @ B ) ) @ ( fun @ A @ ( fun @ ( option @ B ) @ ( fun @ A @ ( option @ B ) ) ) ) @ ( fun_upd @ A @ ( option @ B ) ) @ C ) @ D ) @ ( hAPP @ B @ ( option @ B ) @ ( some @ B ) @ E ) )
= ( ti @ ( fun @ A @ ( option @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i,I: $i,J: $i,K: $i,L: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ bool @ G @ ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ H ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ I ) @ ( hAPP @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ E ) ) @ J ) @ ( hAPP @ E @ ( product_prod @ D @ E ) @ ( hAPP @ D @ ( fun @ E @ ( product_prod @ D @ E ) ) @ ( product_Pair @ D @ E ) @ K ) @ L ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ bool @ G @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_prod__induct5) ).
thf(612,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i,I: $i,J: $i,K: $i,L: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ bool @ G @ ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ H ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ I ) @ ( hAPP @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ E ) @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ E ) ) @ J ) @ ( hAPP @ E @ ( product_prod @ D @ E ) @ ( hAPP @ D @ ( fun @ E @ ( product_prod @ D @ E ) ) @ ( product_Pair @ D @ E ) @ K ) @ L ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) @ bool @ G @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_exp_Osimps_I144_J) ).
thf(497,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ B ) @ C )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(144,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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) )
= ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Conform_Ohconf_res) ).
thf(627,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 @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ bool ) ) @ ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) )
= ( hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_exp_Osimps_I83_J) ).
thf(539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( hAPP @ A @ ( fun @ ty @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) ) @ ( block @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $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 @ A ) @ B ) @ C ) @ D ) @ E ) )
<=> ( 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 ) ) ) ) @ B ) @ C ) ) @ ( 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 ) ) ) ) @ D ) @ E ) ) ) @ ( 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 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_redp__red__eq) ).
thf(482,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $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 @ A ) @ B ) @ C ) @ D ) @ E ) )
=> ( 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 ) ) ) ) @ B ) @ C ) ) @ ( 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 ) ) ) ) @ D ) @ E ) ) ) @ ( 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 @ A ) ) ) )
& ( ( 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 ) ) ) ) @ B ) @ C ) ) @ ( 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 ) ) ) ) @ D ) @ E ) ) ) @ ( 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 @ A ) ) )
=> ( 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 @ A ) @ B ) @ C ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( combk @ B @ A ) @ C ) @ D )
= ( ti @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( hAPP @ B @ ( fun @ A @ B ) @ ( combk @ B @ A ) @ C ) @ D )
= ( ti @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_exp_Osimps_I74_J) ).
thf(368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ B )
!= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ A @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( lAss @ A ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
!= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_exp_Osimps_I85_J) ).
thf(250,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
!= ( hAPP @ val @ ( exp @ A ) @ ( val_1 @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod_Osimps_I2_J) ).
thf(465,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( product_prod @ A @ B ) @ C @ ( hAPP @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) @ ( product_prod_case @ A @ B @ C ) @ D ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) )
= ( hAPP @ B @ C @ ( hAPP @ A @ ( fun @ B @ C ) @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ A ) @ B ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ C ) ) ) @ D ) ) @ ( 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 @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ C ) ) @ D ) ) ) @ ( 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 @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_red__reds_ORedBlock) ).
thf(231,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $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 ) ) ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ A ) @ B ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ C ) ) ) @ D ) ) @ ( 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 @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ C ) ) @ D ) ) ) @ ( 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 @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ D ) @ E ) )
<=> ( ( B = D )
& ( C = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_exp_Osimps_I11_J) ).
thf(186,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ D ) @ E ) )
=> ( ( B = D )
& ( C = E ) ) )
& ( ( ( B = D )
& ( C = E ) )
=> ( ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ B ) @ C )
= ( hAPP @ ( exp @ A ) @ ( exp @ A ) @ ( hAPP @ ( exp @ A ) @ ( fun @ ( exp @ A ) @ ( exp @ A ) ) @ ( seq @ A ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,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 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( ti @ ( product_prod @ A @ B ) @ C )
!= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod_Oexhaust) ).
thf(351,plain,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( ti @ ( product_prod @ A @ B ) @ C )
!= ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ! [I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ bool @ H @ ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ I ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ J ) @ ( hAPP @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ K ) @ ( hAPP @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( hAPP @ D @ ( fun @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_Pair @ D @ ( product_prod @ E @ F ) ) @ L ) @ ( hAPP @ F @ ( product_prod @ E @ F ) @ ( hAPP @ E @ ( fun @ F @ ( product_prod @ E @ F ) ) @ ( product_Pair @ E @ F ) @ M ) @ N ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ bool @ H @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_prod__induct6) ).
thf(290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ! [I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ bool @ H @ ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ I ) @ ( hAPP @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ J ) @ ( hAPP @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( hAPP @ C @ ( fun @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ K ) @ ( hAPP @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ ( hAPP @ D @ ( fun @ ( product_prod @ E @ F ) @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ ( product_Pair @ D @ ( product_prod @ E @ F ) ) @ L ) @ ( hAPP @ F @ ( product_prod @ E @ F ) @ ( hAPP @ E @ ( fun @ F @ ( product_prod @ E @ F ) ) @ ( product_Pair @ E @ F ) @ M ) @ N ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) @ bool @ H @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ C ) ) )
<=> ( ( ti @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ D )
= ( ti @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_pred__equals__eq2) ).
thf(207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ D ) ) ) )
=> ( ( ti @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ D )
= ( ti @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ C ) ) )
& ( ( ( ti @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ D )
= ( ti @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ C ) )
=> ! [E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ A @ B ) @ ( fun @ ( fun @ ( product_prod @ A @ B ) @ bool ) @ bool ) @ ( member @ ( product_prod @ A @ B ) ) @ ( hAPP @ B @ ( product_prod @ A @ B ) @ ( hAPP @ A @ ( fun @ B @ ( product_prod @ A @ B ) ) @ ( product_Pair @ A @ B ) @ E ) @ F ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(156,axiom,
( ( ti @ ( list @ char ) @ v_1 )
= v_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_V_____res) ).
thf(667,plain,
( ( ti @ ( list @ char ) @ v_1 )
= v_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) ) @ B ) @ C ) ) @ ( 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 ) ) ) ) @ D ) @ E ) ) ) @ ( 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 @ F ) ) )
=> ( 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 ) ) @ A ) @ B ) ) @ C ) ) @ ( 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 ) ) @ A ) @ D ) ) @ E ) ) ) @ ( 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 @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_red__reds_OLAssRed) ).
thf(272,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) ) @ B ) @ C ) ) @ ( 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 ) ) ) ) @ D ) @ E ) ) ) @ ( 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 @ F ) ) )
=> ( 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 ) ) @ A ) @ B ) ) @ C ) ) @ ( 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 ) ) @ A ) @ D ) ) @ E ) ) ) @ ( 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 @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 @ B ) @ C ) @ D ) @ E ) @ F ) )
=> ( 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 @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ C ) ) @ D ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_redp__redsp_OLAssRed) ).
thf(346,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 @ B ) @ C ) @ D ) @ E ) @ F ) )
=> ( 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 @ B ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ C ) ) @ D ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ A ) @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(87,axiom,
( ( ti @ ( exp @ ( list @ char ) ) @ e_a )
= e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_e_Ha_____res) ).
thf(447,plain,
( ( ti @ ( exp @ ( list @ char ) ) @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i,I: $i,J: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ bool @ F @ ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ G ) @ ( hAPP @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ D ) ) @ H ) @ ( hAPP @ D @ ( product_prod @ C @ D ) @ ( hAPP @ C @ ( fun @ D @ ( product_prod @ C @ D ) ) @ ( product_Pair @ C @ D ) @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ bool @ F @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod__induct4) ).
thf(168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i,I: $i,J: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ bool @ F @ ( hAPP @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( hAPP @ A @ ( fun @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) ) @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ G ) @ ( hAPP @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ ( hAPP @ B @ ( fun @ ( product_prod @ C @ D ) @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ ( product_Pair @ B @ ( product_prod @ C @ D ) ) @ H ) @ ( hAPP @ D @ ( product_prod @ C @ D ) @ ( hAPP @ C @ ( fun @ D @ ( product_prod @ C @ D ) ) @ ( product_Pair @ C @ D ) @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) @ bool @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $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 @ C ) @ D ) @ ( 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 ) ) ) @ E ) @ ( 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 ) ) @ F ) @ G ) @ ( none @ val ) ) ) ) @ H ) @ ( 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 ) ) ) @ I ) @ J ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ J @ G )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( exp @ ( list @ char ) ) @ bool @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) @ assigned @ G ) @ D ) )
=> ( 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 @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ D ) ) @ ( 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 ) ) ) @ E ) @ F ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ G ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ H ) ) ) @ ( 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 ) ) ) @ I ) @ ( 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 ) ) @ J ) @ G ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_redp__redsp_OBlockRedSome) ).
thf(183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $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 @ C ) @ D ) @ ( 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 ) ) ) @ E ) @ ( 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 ) ) @ F ) @ G ) @ ( none @ val ) ) ) ) @ H ) @ ( 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 ) ) ) @ I ) @ J ) ) )
=> ( ( ( hAPP @ ( list @ char ) @ ( option @ val ) @ J @ G )
= ( hAPP @ val @ ( option @ val ) @ ( some @ val ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( exp @ ( list @ char ) ) @ bool @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ bool ) @ assigned @ G ) @ D ) )
=> ( 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 @ C ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ D ) ) @ ( 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 ) ) ) @ E ) @ F ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ty @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) @ ( block @ ( list @ char ) ) @ G ) @ A ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( list @ char ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( lAss @ ( list @ char ) ) @ G ) @ ( hAPP @ val @ ( exp @ ( list @ char ) ) @ ( val_1 @ ( list @ char ) ) @ B ) ) ) @ H ) ) ) @ ( 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 ) ) ) @ I ) @ ( 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 ) ) @ J ) @ G ) @ ( hAPP @ ( list @ char ) @ ( option @ val ) @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(422,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) ) @ ( produc1605651328_split @ A @ B @ C ) )
= ( produc1605651328_split @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_Ointernal__split_res) ).
thf(564,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( product_prod @ A @ B ) @ C ) ) @ ( produc1605651328_split @ A @ B @ C ) )
= ( produc1605651328_split @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E ) ) @ D ) @ F )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_fun__upd__upd) ).
thf(326,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ E ) ) @ D ) @ F )
= ( hAPP @ A @ ( fun @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( fun @ B @ A ) ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ ( fun @ B @ A ) ) ) @ ( fun_upd @ B @ A ) @ C ) @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) ) @ B ) @ C ) ) @ ( 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 ) ) ) ) @ D ) @ E ) ) ) @ ( 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 @ F ) ) )
=> ( 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 ) ) @ B ) @ A ) ) @ C ) ) @ ( 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 ) ) @ D ) @ A ) ) @ E ) ) ) @ ( 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 @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_red__reds_OSeqRed) ).
thf(358,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $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 ) ) ) ) @ B ) @ C ) ) @ ( 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 ) ) ) ) @ D ) @ E ) ) ) @ ( 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 @ F ) ) )
=> ( 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 ) ) @ B ) @ A ) ) @ C ) ) @ ( 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 ) ) @ D ) @ A ) ) @ E ) ) ) @ ( 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 @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ C ) @ D ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ C ) @ D ) @ E ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ C ) @ D ) @ E ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ F ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_WTrtSeq) ).
thf(195,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ C ) @ D ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ C ) @ D ) @ E ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ty @ bool @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) @ ( hAPP @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( 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 @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) @ ( fun @ ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ ( fun @ ( fun @ ( list @ char ) @ ( option @ ty ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( fun @ ty @ bool ) ) ) ) @ wTrt @ C ) @ D ) @ E ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) @ ( hAPP @ ( exp @ ( list @ char ) ) @ ( fun @ ( exp @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ ( seq @ ( list @ char ) ) @ F ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(37,axiom,
( ( ti @ val @ v )
= v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_v_____res) ).
thf(283,plain,
( ( ti @ val @ v )
= v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(130,axiom,
( ( ti @ ( fun @ ( 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 @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ bool ) ) @ ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) )
= ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_WellForm_Owf__prog_res) ).
thf(575,plain,
( ( ti @ ( fun @ ( 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 @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) @ bool ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ bool ) ) @ ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) )
= ( wf_prog @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(150,axiom,
( ( ti @ val @ unit )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Value_Oval_OUnit_res) ).
thf(644,plain,
( ( ti @ val @ unit )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ C @ ( fun @ A @ B ) ) @ ( combc @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(501,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ C @ ( fun @ A @ B ) ) @ ( combc @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ B ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_widen__refl) ).
thf(659,plain,
! [A: $i,B: $i,C: $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 @ A ) ) ) ) ) ) ) ) @ ( fun @ ty @ ( fun @ ty @ bool ) ) @ ( widen @ A ) @ B ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ C ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ E ) )
= ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ F ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ G ) ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_map__upd__eqD1) ).
thf(543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ C ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ E ) )
= ( hAPP @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) @ ( hAPP @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) @ ( hAPP @ ( fun @ B @ ( option @ A ) ) @ ( fun @ B @ ( fun @ ( option @ A ) @ ( fun @ B @ ( option @ A ) ) ) ) @ ( fun_upd @ B @ ( option @ A ) ) @ F ) @ D ) @ ( hAPP @ A @ ( option @ A ) @ ( some @ A ) @ G ) ) )
=> ( ( ti @ A @ E )
= ( ti @ A @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',tsy_v_P_res) ).
thf(254,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 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ B @ ( fun @ A @ bool ) @ C @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ B @ A ) @ bool @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ ( product_prod @ B @ A ) @ bool ) @ ( product_prod_case @ B @ A @ bool ) @ C ) @ ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_splitI) ).
thf(227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ B @ ( fun @ A @ bool ) @ C @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( product_prod @ B @ A ) @ bool @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ ( product_prod @ B @ A ) @ bool ) @ ( product_prod_case @ B @ A @ bool ) @ C ) @ ( hAPP @ A @ ( product_prod @ B @ A ) @ ( hAPP @ B @ ( fun @ A @ ( product_prod @ B @ A ) ) @ ( product_Pair @ B @ A ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(723,plain,
$false,
inference(e,[status(thm)],[457,629,365,518,468,555,333,249,170,582,308,449,614,440,511,202,597,384,550,417,174,404,570,372,504,460,559,261,591,443,623,646,348,396,243,507,527,292,380,529,661,546,534,233,452,302,392,424,429,165,229,329,285,650,388,420,256,339,537,669,657,633,360,412,618,513,180,296,562,176,402,577,204,259,445,382,572,236,159,406,274,377,245,362,567,477,494,631,552,609,594,621,198,521,399,636,455,299,267,431,223,608,394,306,426,589,487,516,342,355,553,162,531,640,409,263,310,199,463,470,336,612,497,627,539,482,524,368,250,465,231,186,158,351,290,207,667,272,346,447,168,183,422,564,326,358,195,283,575,644,501,659,543,491,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWW478+5 : TPTP v8.2.0. Released v5.3.0.
% 0.06/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Jun 19 09:31:25 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.90/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.75/1.12 % [INFO] Parsing done (283ms).
% 1.75/1.13 % [INFO] Running in sequential loop mode.
% 2.65/1.38 % [INFO] eprover registered as external prover.
% 2.65/1.38 % [INFO] Scanning for conjecture ...
% 3.65/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 155 axioms. Running axiom selection ...
% 4.22/1.86 % [INFO] Axiom selection finished. Selected 155 axioms (removed 0 axioms).
% 5.68/2.62 % [INFO] Problem is first-order (TPTP FOF).
% 5.68/2.64 % [INFO] Type checking passed.
% 5.68/2.64 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 23.30/10.18 % External prover 'e' found a proof!
% 23.30/10.18 % [INFO] Killing All external provers ...
% 23.30/10.18 % Time passed: 9679ms (effective reasoning time: 9046ms)
% 23.30/10.18 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 23.30/10.18 % Axioms used in derivation (155): fact_92_redp__redsp_OBlockRedNone, fact_31_red__preserves__sconf, tsy_c_TypeSafe__Mirabelle__mcolmsuaig_Osconf_res, fact_22_fun__upd__apply, tsy_c_Expr_Oexp_OLAss_res, fact_96_empty__upd__none, tsy_c_fconj_res, fact_51_red__reds_OInitBlockRed, fact_25_fun__upd__idem__iff, help_COMBS_1_1_U, fact_61_red__reds_ORedSeq, fact_27_red__preserves__hconf, tsy_c_SmallStep_Ored_res, fact_64_mem__splitE, fact_10_prod__induct5, fact_48_prod_Osimps_I2_J, tsy_v_V_____res, tsy_c_TypeRel_Owiden_res, fact_67_red__reds_ORedLAss, fact_78_exp_Osimps_I84_J, fact_45_internal__split__def, fact_20_fun__upd__other, tsy_c_Product__Type_OPair_res, fact_74_exp_Osimps_I6_J, tsy_c_COMBK_res, help_fconj_3_1_U, tsy_c_SmallStep_Oassigned_res, fact_62_red__reds_ORedBlock, tsy_c_Option_Ooption_ONone_res, tsy_c_member_res, fact_3_assms, fact_42_splitI, fact_91_redp__redsp_OLAssRed, fact_0_InitBlockRed_I3_J, fact_44_split__weak__cong, fact_30_prod__induct3, fact_2_fun__upd__triv, fact_97_redp__redsp_OBlockRedSome, fact_88_redp__redsp_OInitBlockRed, fact_89_red__reds_OBlockRedSome, fact_7_InitBlockRed_I2_J, fact_93_redp__redsp_ORedSeq, tsy_c_Conform_Ohconf_res, tsy_v_h_Ha_____res, fact_77_exp_Osimps_I10_J, tsy_c_hAPP_res, fact_19_fun__upd__idem, fact_18_fun__upd__def, fact_54_splitE, fact_16_Pair__eq, fact_41_prod__caseI, fact_46_split__twice, tsy_c_hAPP_arg1, fact_33_pred__equals__eq2, fact_50_split__eta, fact_12_prod__induct4, fact_36_InitBlockRed_I5_J, tsy_c_Expr_Oexp_OVal_res, tsy_c_Expr_Oexp_OBlock_res, tsy_v_v_____res, tsy_c_COMBC_res, tsy_c_JWellForm_Owf__J__mdecl_res, fact_86_exp_Osimps_I197_J, fact_70_exp_Osimps_I143_J, fact_95_redp__redsp_ORedBlock, tsy_v_E_____res, fact_17_split__paired__All, tsy_c_COMBS_res, tsy_c_Product__Type_Ointernal__split_res, tsy_c_WellTypeRT_OWTrt_res, tsy_c_hBOOL_arg1, tsy_v_T_H_____res, fact_23_fun__upd__same, fact_9_prod__cases6, tsy_v_v_H_____res, fact_47_split__part, tsy_c_WellForm_Owf__prog_res, help_COMBB_1_1_U, fact_81_exp_Osimps_I75_J, tsy_c_Expr_Oexp_OSeq_res, tsy_v_e_Ha_____res, tsy_c_hAPP_arg2, fact_60_red__reds_OLAssRed, tsy_c_COMBB_res, fact_94_map__upd__nonempty, help_fconj_2_1_U, tsy_c_Fun_Ofun__upd_res, fact_58_splitD_H, fact_13_prod__cases4, tsy_c_Product__Type_Oprod_Oprod__rec_res, fact_26_widen__refl, fact_8_prod__induct6, fact_4_map__upd__Some__unfold, tsy_c_Value_Oval_OUnit_res, fact_83_exp_Osimps_I83_J, tsy_c_HOL_Oundefined_res, fact_43_splitD, tsy_c_SmallStep_Oredp_res, fact_57_WTrtSeq, help_ti_idem, fact_56_mem__splitI, tsy_v_la_____res, fact_80_exp_Osimps_I85_J, fact_40_sconf__def, fact_49_split__conv, fact_76_mem__def, tsy_v_P_res, tsy_v_ea_____res, fact_6_map__upd__eqD1, fact_15_Pair__inject, fact_65_splitI2_H, fact_98_redp__red__eq, help_COMBK_1_1_U, fact_11_prod__cases5, fact_68_cond__split__eta, fact_34_prod_Oexhaust, fact_5_map__upd__triv, help_COMBC_1_1_U, fact_71_exp_Osimps_I196_J, fact_24_fun__upd__upd, fact_87_exp_Osimps_I142_J, fact_59_red__reds_OSeqRed, fact_53_splitI2, help_fconj_1_1_U, fact_28_red__preserves__lconf, fact_38_PairE, fact_21_fun__upd__twist, fact_90_redp__redsp_OSeqRed, fact_69_splitE2, fact_32_prod_Orecs, fact_29_prod__cases3, fact_1_InitBlockRed_I1_J, fact_82_exp_Osimps_I82_J, fact_39_internal__split__conv, fact_79_exp_Osimps_I74_J, fact_99_redp__redsp_ORedInitBlock, fact_63_splitE_H, fact_72_exp_Osimps_I3_J, fact_55_WTrtBlock, fact_73_exp_Osimps_I11_J, tsy_c_State_Ohp_res, fact_84_exp_Osimps_I145_J, tsy_v_ha_____res, fact_75_ext, tsy_c_Option_Ooption_OSome_res, fact_37_split__paired__Ex, fact_35_widen__trans, tsy_c_Product__Type_Oprod_Oprod__case_res, tsy_v_T_____res, fact_52_red__reds_ORedInitBlock, tsy_c_Conform_Olconf_res, fact_85_exp_Osimps_I144_J, fact_14_InitBlockRed_I4_J, tsy_v_l_Ha_____res, fact_66_mem__splitI2
% 23.30/10.18 % No. of inferences in proof: 314
% 23.30/10.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9679 ms resp. 9046 ms w/o parsing
% 24.82/10.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.82/10.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------