%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW478+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:28 AM UTC 2026
% Result : Theorem 30.83s 12.05s
% Output : Refutation 33.93s
% 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_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i > $i > $i ).
thf(fun_decl,type,
fun: $i > $i > $i ).
thf(product_prod_decl,type,
product_prod: $i > $i > $i ).
thf(exp_decl,type,
exp: $i > $i ).
thf(list_decl,type,
list: $i > $i ).
thf(char_decl,type,
char: $i ).
thf(nat_decl,type,
nat: $i ).
thf(option_decl,type,
option: $i > $i ).
thf(val_decl,type,
val: $i ).
thf(bool_decl,type,
bool: $i ).
thf(member_decl,type,
member: $i > $i ).
thf(product_Pair_decl,type,
product_Pair: $i > $i > $i ).
thf(ea_decl,type,
ea: $i ).
thf(ha_decl,type,
ha: $i ).
thf(fun_upd_decl,type,
fun_upd: $i > $i > $i ).
thf(la_decl,type,
la: $i ).
thf(v_1_decl,type,
v_1: $i ).
thf(some_decl,type,
some: $i > $i ).
thf(v_decl,type,
v: $i ).
thf(e_a_decl,type,
e_a: $i ).
thf(h_a_decl,type,
h_a: $i ).
thf(l_a_decl,type,
l_a: $i ).
thf(ty_decl,type,
ty: $i ).
thf(red_decl,type,
red: $i ).
thf(p_decl,type,
p: $i ).
thf(ti_decl,type,
ti: $i > $i > $i ).
thf(undefined_decl,type,
undefined: $i > $i ).
thf(produc1605651328_split_decl,type,
produc1605651328_split: $i > $i > $i > $i ).
thf(product_prod_case_decl,type,
product_prod_case: $i > $i > $i > $i ).
thf(wTrt_decl,type,
wTrt: $i ).
thf(val_1_decl,type,
val_1: $i > $i ).
thf(block_decl,type,
block: $i > $i ).
thf(redp_decl,type,
redp: $i ).
thf(none_decl,type,
none: $i > $i ).
thf(assigned_decl,type,
assigned: $i ).
thf(seq_decl,type,
seq: $i > $i ).
thf(lAss_decl,type,
lAss: $i > $i ).
thf(t_1_decl,type,
t_1: $i ).
thf(combb_decl,type,
combb: $i > $i > $i > $i ).
thf(e_decl,type,
e: $i ).
thf(t_decl,type,
t: $i ).
thf(product_prod_rec_decl,type,
product_prod_rec: $i > $i > $i > $i ).
thf(lconf_decl,type,
lconf: $i > $i ).
thf(typeSa885026672_sconf_decl,type,
typeSa885026672_sconf: $i ).
thf(combs_decl,type,
combs: $i > $i > $i > $i ).
thf(fconj_decl,type,
fconj: $i ).
thf(hconf_decl,type,
hconf: $i > $i ).
thf(combc_decl,type,
combc: $i > $i > $i > $i ).
thf(combk_decl,type,
combk: $i > $i > $i ).
thf(widen_decl,type,
widen: $i > $i ).
thf(hp_decl,type,
hp: $i ).
thf(wf_J_mdecl_decl,type,
wf_J_mdecl: $i ).
thf(v_2_decl,type,
v_2: $i ).
thf(wf_prog_decl,type,
wf_prog: $i > $i ).
thf(unit_decl,type,
unit: $i ).
thf(37,axiom,
( ( v @ ( val @ ti ) )
= v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_v_____res) ).
thf(289,plain,
( ( v @ ( val @ ti ) )
= v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( F @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ( H @ ( G @ ( E @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( E @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mem__splitI2) ).
thf(645,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( F @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ( H @ ( G @ ( E @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( E @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( E @ ( C @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_widen__trans) ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( E @ ( C @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
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] :
( ( F @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( K @ ( J @ ( E @ ( D @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( E @ fun ) @ ( D @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( E @ hAPP ) ) ) @ ( I @ ( E @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) @ ( H @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( G @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
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] :
( ( F @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( K @ ( J @ ( E @ ( D @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( E @ fun ) @ ( D @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( E @ hAPP ) ) ) @ ( I @ ( E @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) @ ( H @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( G @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
!= ( D @ ( C @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_exp_Osimps_I74_J) ).
thf(379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
!= ( D @ ( C @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ product_Pair ) @ ( D @ ( B @ ( C @ ( B @ ( A @ product_prod ) @ combb ) ) @ ( C @ ( B @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ fun ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ combb ) ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ( C @ ( B @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_split__eta) ).
thf(440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ product_Pair ) @ ( D @ ( B @ ( C @ ( B @ ( A @ product_prod ) @ combb ) ) @ ( C @ ( B @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ fun ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ combb ) ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ( C @ ( B @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( B @ product_prod ) @ ti ) )
= ( F @ ( C @ ( B @ product_prod ) @ ti ) ) )
=> ( ( E @ ( D @ ( A @ ( C @ ( B @ product_prod_case ) ) @ ( A @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( D @ ( A @ ( C @ ( B @ product_prod_case ) ) @ ( A @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_split__weak__cong) ).
thf(472,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( B @ product_prod ) @ ti ) )
= ( F @ ( C @ ( B @ product_prod ) @ ti ) ) )
=> ( ( E @ ( D @ ( A @ ( C @ ( B @ product_prod_case ) ) @ ( A @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( D @ ( A @ ( C @ ( B @ product_prod_case ) ) @ ( A @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( D @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_exp_Osimps_I75_J) ).
thf(670,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( D @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(8,axiom,
( ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= wTrt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_WellTypeRT_OWTrt_res) ).
thf(174,plain,
( ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= wTrt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,axiom,
( ( la @ ( val @ option @ ( char @ list @ fun ) @ ti ) )
= la ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_la_____res) ).
thf(417,plain,
( ( la @ ( val @ option @ ( char @ list @ fun ) @ ti ) )
= la ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(436,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(389,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(121,axiom,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms) ).
thf(570,plain,
p @ ( wf_J_mdecl @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( F @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( E @ ( D @ ( C @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_WTrtSeq) ).
thf(196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( F @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( E @ ( D @ ( C @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ combk ) @ ( B @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ combk ) @ ( B @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(86,axiom,
( ( v_1 @ ( l_a @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( v_2 @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).
thf(460,plain,
( ( v_1 @ ( l_a @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( v_2 @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( B @ ti ) )
!= ( G @ ( B @ ti ) ) )
=> ( ( E @ ( G @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( D @ ( F @ ( E @ ( G @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_fun__upd__twist) ).
thf(475,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( B @ ti ) )
!= ( G @ ( B @ ti ) ) )
=> ( ( E @ ( G @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( D @ ( F @ ( E @ ( G @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combc ) ) @ ( C @ ( A @ fun ) @ ( B @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
thf(591,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combc ) ) @ ( C @ ( A @ fun ) @ ( B @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(82,axiom,
( ( wf_J_mdecl @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= wf_J_mdecl ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_JWellForm_Owf__J__mdecl_res) ).
thf(443,plain,
( ( wf_J_mdecl @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= wf_J_mdecl ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ combk ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ti ) )
= ( B @ ( A @ combk ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
thf(376,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ combk ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ti ) )
= ( B @ ( A @ combk ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(27,axiom,
t @ ( ea @ ( v @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( v_1 @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( t_1 @ ( v_1 @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( e @ ( ha @ ( p @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_InitBlockRed_I5_J) ).
thf(253,plain,
t @ ( ea @ ( v @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( v_1 @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( t_1 @ ( v_1 @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( e @ ( ha @ ( p @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ ( B @ ti ) )
!= ( E @ ( B @ ti ) ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( F @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ) )
& ( ( ( F @ ( B @ ti ) )
= ( E @ ( B @ ti ) ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_fun__upd__def) ).
thf(485,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ ( B @ ti ) )
!= ( E @ ( B @ ti ) ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( F @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ) )
& ( ( ( F @ ( B @ ti ) )
= ( E @ ( B @ ti ) ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( D @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( A @ ( B @ fun ) @ ti ) ) )
<=> ( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) )
= ( E @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_fun__upd__idem__iff) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) )
= ( E @ ( A @ ti ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( A @ ( B @ fun ) @ ti ) ) ) )
& ( ( ( E @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( A @ ( B @ fun ) @ ti ) ) )
=> ( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) )
= ( E @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ product_prod_case ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_Oprod_Oprod__case_res) ).
thf(348,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ product_prod_case ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod_Osimps_I2_J) ).
thf(480,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( E @ ( B @ ti ) )
!= ( F @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ) )
& ( ( ( E @ ( B @ ti ) )
= ( F @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_fun__upd__apply) ).
thf(602,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( E @ ( B @ ti ) )
!= ( F @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ) )
& ( ( ( E @ ( B @ ti ) )
= ( F @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( D @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
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] : ( L @ ( K @ ( E @ ( D @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( E @ fun ) @ ( D @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( E @ hAPP ) ) ) @ ( J @ ( E @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) @ ( I @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( H @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) @ ( G @ ( bool @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( G @ ( bool @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_prod__induct5) ).
thf(634,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] : ( L @ ( K @ ( E @ ( D @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( E @ fun ) @ ( D @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( E @ hAPP ) ) ) @ ( J @ ( E @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) @ ( I @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( H @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) @ ( G @ ( bool @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( G @ ( bool @ ( E @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( ( F @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ~ ( H @ ( G @ ( E @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_mem__splitE) ).
thf(396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( ( F @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ~ ( H @ ( G @ ( E @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( D @ ( C @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_redp__redsp_ORedSeq) ).
thf(265,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ ( D @ ( C @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( D @ ( C @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( D @ ( C @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( B @ ( A @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_red__reds_ORedBlock) ).
thf(233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( D @ ( C @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( D @ ( C @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( B @ ( A @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( ( E @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ~ ( F @ ( H @ ( G @ ( D @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_splitE_H) ).
thf(248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( ( E @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ~ ( F @ ( H @ ( G @ ( D @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ fun_upd ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( B @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_fun__upd__same) ).
thf(512,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ fun_upd ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( B @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(106,axiom,
( ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= typeSa885026672_sconf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TypeSafe__Mirabelle__mcolmsuaig_Osconf_res) ).
thf(529,plain,
( ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= typeSa885026672_sconf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( val @ none @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( F @ ( I @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( val @ none ) )
=> ( ~ ( C @ ( F @ ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( E @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( F @ ( I @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_redp__redsp_OBlockRedNone) ).
thf(366,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( val @ none @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( F @ ( I @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( val @ none ) )
=> ( ~ ( C @ ( F @ ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( E @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( F @ ( I @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( E @ ( D @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_splitD_H) ).
thf(534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( E @ ( D @ ( bool @ ( A @ fun ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_fun__upd__upd) ).
thf(334,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ product_prod_rec ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_prod_Orecs) ).
thf(260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ product_prod_rec ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( A @ some @ ( A @ option @ ( A @ hAPP ) ) ) @ ( D @ ( C @ ( A @ option @ ( B @ fun_upd ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ fun ) @ ( A @ option @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ hAPP ) ) ) )
= ( G @ ( A @ some @ ( A @ option @ ( A @ hAPP ) ) ) @ ( D @ ( F @ ( A @ option @ ( B @ fun_upd ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ fun ) @ ( A @ option @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ hAPP ) ) ) ) )
=> ( ( E @ ( A @ ti ) )
= ( G @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_map__upd__eqD1) ).
thf(561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ ( A @ some @ ( A @ option @ ( A @ hAPP ) ) ) @ ( D @ ( C @ ( A @ option @ ( B @ fun_upd ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ fun ) @ ( A @ option @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ hAPP ) ) ) )
= ( G @ ( A @ some @ ( A @ option @ ( A @ hAPP ) ) ) @ ( D @ ( F @ ( A @ option @ ( B @ fun_upd ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ fun ) @ ( A @ option @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ option @ ( B @ fun ) @ ( A @ option @ hAPP ) ) ) ) )
=> ( ( E @ ( A @ ti ) )
= ( G @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(64,axiom,
( ( hp @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ti ) )
= hp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_State_Ohp_res) ).
thf(392,plain,
( ( hp @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ti ) )
= hp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
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] : ( N @ ( M @ ( F @ ( E @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( F @ fun ) @ ( E @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( F @ hAPP ) ) ) @ ( L @ ( F @ ( E @ product_prod ) @ ( D @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ fun ) @ ( D @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ hAPP ) ) ) @ ( K @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ hAPP ) ) ) @ ( J @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( I @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) @ ( H @ ( bool @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( H @ ( bool @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_prod__induct6) ).
thf(297,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] : ( N @ ( M @ ( F @ ( E @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( F @ fun ) @ ( E @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( F @ hAPP ) ) ) @ ( L @ ( F @ ( E @ product_prod ) @ ( D @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ fun ) @ ( D @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ hAPP ) ) ) @ ( K @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ hAPP ) ) ) @ ( J @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( I @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) @ ( H @ ( bool @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( H @ ( bool @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ produc1605651328_split ) ) )
= ( C @ ( B @ ( A @ product_prod_case ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_internal__split__def) ).
thf(165,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ produc1605651328_split ) ) )
= ( C @ ( B @ ( A @ product_prod_case ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(69,axiom,
( ( l_a @ ( val @ option @ ( char @ list @ fun ) @ ti ) )
= l_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_l_Ha_____res) ).
thf(407,plain,
( ( l_a @ ( val @ option @ ( char @ list @ fun ) @ ti ) )
= l_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(156,axiom,
( ( v_1 @ ( char @ list @ ti ) )
= v_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_V_____res) ).
thf(693,plain,
( ( v_1 @ ( char @ list @ ti ) )
= v_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(137,axiom,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( e @ ( p @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_InitBlockRed_I4_J) ).
thf(630,plain,
la @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( e @ ( p @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combs ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(467,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combs ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( D @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_splitI) ).
thf(229,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( D @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(493,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(153,axiom,
( ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fconj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
thf(682,plain,
( ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fconj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ produc1605651328_split ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ produc1605651328_split ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_Ointernal__split_res) ).
thf(583,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ produc1605651328_split ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ produc1605651328_split ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( B @ ti ) )
!= ( F @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_fun__upd__other) ).
thf(522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( B @ ti ) )
!= ( F @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( F @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( B @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( G @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) )
<=> ( ( ( ( F @ ( C @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( G @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) )
& ( ( F @ ( A @ ti ) )
!= ( D @ ( A @ ti ) ) ) )
| ( ( ( E @ ( B @ ti ) )
= ( G @ ( B @ ti ) ) )
& ( ( F @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_map__upd__Some__unfold) ).
thf(317,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( ( ( F @ ( C @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( G @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) )
& ( ( F @ ( A @ ti ) )
!= ( D @ ( A @ ti ) ) ) )
| ( ( ( E @ ( B @ ti ) )
= ( G @ ( B @ ti ) ) )
& ( ( F @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) )
=> ( ( F @ ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( G @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( G @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) )
=> ( ( ( ( F @ ( C @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( G @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) )
& ( ( F @ ( A @ ti ) )
!= ( D @ ( A @ ti ) ) ) )
| ( ( ( E @ ( B @ ti ) )
= ( G @ ( B @ ti ) ) )
& ( ( F @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(144,axiom,
( ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Conform_Ohconf_res) ).
thf(650,plain,
( ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ none @ ( A @ option @ ti ) )
= ( A @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Option_Ooption_ONone_res) ).
thf(615,plain,
! [A: $i] :
( ( A @ none @ ( A @ option @ ti ) )
= ( A @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( E @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_redp__redsp_OLAssRed) ).
thf(356,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( E @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(610,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_redp__red__eq) ).
thf(499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( D @ ( C @ ( B @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combc ) ) @ ( B @ ( A @ fun ) @ ( C @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(519,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combc ) ) @ ( B @ ( A @ fun ) @ ( C @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( A @ fun ) @ ti ) )
= ( D @ ( B @ ( A @ fun ) @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( A @ fun ) @ ti ) )
= ( D @ ( B @ ( A @ fun ) @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ! [E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( G @ ( F @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) @ ( E @ ( C @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_prod__cases3) ).
thf(225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ! [E: $i,F: $i,G: $i] :
( ( D @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( G @ ( F @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) @ ( E @ ( C @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( B @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ hAPP ) ) ) @ ( A @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ combb ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
<=> ( ( E @ ( D @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
& ( C @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_split__part) ).
thf(686,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ ( D @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
& ( C @ hBOOL ) )
=> ( E @ ( D @ ( C @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( B @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ hAPP ) ) ) @ ( A @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ combb ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( E @ ( D @ ( C @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( B @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ hAPP ) ) ) @ ( A @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ combb ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( D @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
& ( C @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( A @ ( E @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( D @ ( A @ ( C @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_redp__redsp_OSeqRed) ).
thf(547,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( A @ ( E @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( D @ ( A @ ( C @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( E @ ( D @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_exp_Osimps_I144_J) ).
thf(515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( E @ ( D @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(146,axiom,
( ( e @ ( ty @ option @ ( char @ list @ fun ) @ ti ) )
= e ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_E_____res) ).
thf(654,plain,
( ( e @ ( ty @ option @ ( char @ list @ fun ) @ ti ) )
= e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( D @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod__caseI) ).
thf(371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( D @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( B @ product_prod_case ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ ( B @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( A @ ( B @ fun ) @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).
thf(205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ fun_upd ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( A @ ( B @ fun ) @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
= ( C @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_exp_Osimps_I3_J) ).
thf(674,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = C )
=> ( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
= ( C @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
= ( C @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ some @ ( A @ option @ ( A @ fun ) @ ti ) )
= ( A @ some ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Option_Ooption_OSome_res) ).
thf(586,plain,
! [A: $i] :
( ( A @ some @ ( A @ option @ ( A @ fun ) @ ti ) )
= ( A @ some ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ fun_upd ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ fun ) @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_fun__upd__idem) ).
thf(412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( B @ ti ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ fun_upd ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( B @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ fun ) @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( G @ ( F @ ( E @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) )
<=> ( ( D = G )
& ( C = F )
& ( ( B @ ( A @ ti ) )
= ( E @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_exp_Osimps_I10_J) ).
thf(618,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D = G )
& ( C = F )
& ( ( B @ ( A @ ti ) )
= ( E @ ( A @ ti ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( G @ ( F @ ( E @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( G @ ( F @ ( E @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) )
=> ( ( D = G )
& ( C = F )
& ( ( B @ ( A @ ti ) )
= ( E @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
<=> ? [D: $i,E: $i] : ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_split__paired__Ex) ).
thf(425,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] : ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ? [D: $i] : ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) )
& ( ? [D: $i] : ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ? [D: $i,E: $i] : ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( E @ ( D @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) )
<=> ( ( C = E )
& ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_exp_Osimps_I6_J) ).
thf(279,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( C = E )
& ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) )
=> ( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( E @ ( D @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( E @ ( D @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) )
=> ( ( C = E )
& ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( C @ ( B @ product_prod_case ) ) @ ( A @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( ( F @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ~ ( H @ ( G @ ( E @ ( A @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( C @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_splitE2) ).
thf(573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( C @ ( B @ product_prod_case ) ) @ ( A @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ ( C @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( ( F @ ( C @ ( B @ product_prod ) @ ti ) )
= ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) ) )
=> ~ ( H @ ( G @ ( E @ ( A @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( C @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ val_1 @ ( A @ exp @ ( val @ fun ) @ ti ) )
= ( A @ val_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OVal_res) ).
thf(180,plain,
! [A: $i] :
( ( A @ val_1 @ ( A @ exp @ ( val @ fun ) @ ti ) )
= ( A @ val_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
!= ( E @ ( D @ ( C @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
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] :
( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
!= ( E @ ( D @ ( C @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) ) )
=> ~ ( ( ( C @ ( B @ ti ) )
= ( E @ ( B @ ti ) ) )
=> ( ( D @ ( A @ ti ) )
!= ( F @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Pair__inject) ).
thf(291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) ) )
=> ~ ( ( ( C @ ( B @ ti ) )
= ( E @ ( B @ ti ) ) )
=> ( ( D @ ( A @ ti ) )
!= ( F @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(112,axiom,
( ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= redp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SmallStep_Oredp_res) ).
thf(545,plain,
( ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= redp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) ) )
<=> ( ( ( D @ ( A @ ti ) )
= ( F @ ( A @ ti ) ) )
& ( ( C @ ( B @ ti ) )
= ( E @ ( B @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__eq) ).
thf(445,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( D @ ( A @ ti ) )
= ( F @ ( A @ ti ) ) )
& ( ( C @ ( B @ ti ) )
= ( E @ ( B @ ti ) ) ) )
=> ( ( D @ ( C @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) ) ) )
& ( ( ( D @ ( C @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( A @ ( B @ product_Pair ) @ ( A @ ( B @ product_prod ) @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( A @ ( B @ product_prod ) @ ( A @ hAPP ) ) ) ) )
=> ( ( ( D @ ( A @ ti ) )
= ( F @ ( A @ ti ) ) )
& ( ( C @ ( B @ ti ) )
= ( E @ ( B @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i,H: $i] : ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) @ ( F @ ( C @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( E @ ( bool @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( E @ ( bool @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_prod__induct3) ).
thf(313,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i,H: $i] : ( H @ ( G @ ( C @ ( B @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( C @ fun ) @ ( B @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( C @ hAPP ) ) ) @ ( F @ ( C @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( C @ ( B @ product_prod ) @ hAPP ) ) ) @ ( E @ ( bool @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( E @ ( bool @ ( C @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
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] :
( ( G @ ( F @ ( D @ ( B @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( G @ ( F @ ( A @ ( C @ product_Pair ) @ ( A @ ( C @ product_prod ) @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( A @ ( C @ product_prod ) @ ( A @ hAPP ) ) ) @ ( E @ ( B @ ( A @ ( C @ product_prod ) @ hAPP ) ) ) ) )
=> ( ( D @ ( B @ ( A @ ( C @ product_prod_case ) ) @ ( B @ ( A @ ( C @ product_prod ) @ fun ) @ ( B @ ( A @ fun ) @ ( C @ fun ) @ hAPP ) ) ) )
= ( E @ ( B @ ( A @ ( C @ product_prod ) @ fun ) @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_cond__split__eta) ).
thf(419,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( G @ ( F @ ( D @ ( B @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( G @ ( F @ ( A @ ( C @ product_Pair ) @ ( A @ ( C @ product_prod ) @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( A @ ( C @ product_prod ) @ ( A @ hAPP ) ) ) @ ( E @ ( B @ ( A @ ( C @ product_prod ) @ hAPP ) ) ) ) )
=> ( ( D @ ( B @ ( A @ ( C @ product_prod_case ) ) @ ( B @ ( A @ ( C @ product_prod ) @ fun ) @ ( B @ ( A @ fun ) @ ( C @ fun ) @ hAPP ) ) ) )
= ( E @ ( B @ ( A @ ( C @ product_prod ) @ fun ) @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( C @ ( B @ ( A @ product_prod ) @ ti ) )
!= ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod_Oexhaust) ).
thf(362,plain,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( C @ ( B @ ( A @ product_prod ) @ ti ) )
!= ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ block ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OBlock_res) ).
thf(303,plain,
! [A: $i] :
( ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ block ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ti ) )
= ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ti ) )
= ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( H @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_red__preserves__hconf) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( H @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ combc ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ combb ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ combc ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( A @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( fconj @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( bool @ ( bool @ combb ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ combs ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod_case ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_sconf__def) ).
thf(271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ combc ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ combb ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ combc ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( A @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( fconj @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( bool @ ( bool @ combb ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ combs ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod_case ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ combc ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ combb ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ combc ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( A @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( fconj @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( bool @ ( bool @ combb ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ combb ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ combs ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod_case ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( D @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) )
<=> ( ( D @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) )
= ( C @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_pred__equals__eq2) ).
thf(208,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) )
= ( C @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) ) )
=> ! [E: $i,F: $i] :
( ( ( C @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) )
& ( ! [E: $i,F: $i] :
( ( ( C @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ member @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ fun ) @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) )
=> ( ( D @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) )
= ( C @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( J @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( I @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ none @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( F @ ( I @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( ~ ( C @ ( F @ ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ hAPP ) ) ) @ hBOOL )
=> ( J @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( F @ ( I @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_red__reds_OBlockRedSome) ).
thf(631,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( J @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( I @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ none @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( F @ ( I @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( ~ ( C @ ( F @ ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ hAPP ) ) ) @ hBOOL )
=> ( J @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( F @ ( I @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( G @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(130,axiom,
( ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ fun ) @ ti ) )
= ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_WellForm_Owf__prog_res) ).
thf(594,plain,
( ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ( bool @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ fun ) @ ti ) )
= ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ wf_prog ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(95,axiom,
( ( t @ ( ty @ ti ) )
= t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_T_H_____res) ).
thf(483,plain,
( ( t @ ( ty @ ti ) )
= t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(150,axiom,
( ( unit @ ( val @ ti ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Value_Oval_OUnit_res) ).
thf(668,plain,
( ( unit @ ( val @ ti ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(87,axiom,
( ( e_a @ ( char @ list @ exp @ ti ) )
= e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_e_Ha_____res) ).
thf(462,plain,
( ( e_a @ ( char @ list @ exp @ ti ) )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) )
=> ( ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) )
= ( C @ ( B @ option @ ( A @ fun ) @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_map__upd__triv) ).
thf(345,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) ) )
=> ( ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) )
= ( C @ ( B @ option @ ( A @ fun ) @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( B @ ( A @ product_prod ) @ ( E @ ( D @ product_prod_case ) ) @ ( B @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ ( D @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) @ ( F @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( H @ ( G @ ( F @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( E @ ( C @ ( B @ ( A @ product_prod ) @ combb ) ) @ ( C @ ( E @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ fun ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( E @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ combb ) ) @ ( C @ ( E @ fun ) @ ( D @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ ( D @ fun ) @ fun ) @ ( C @ ( E @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( E @ fun ) @ ( D @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ ( D @ fun ) @ hAPP ) ) ) @ ( C @ ( E @ ( D @ product_prod_case ) ) @ ( C @ ( E @ ( D @ product_prod ) @ fun ) @ ( C @ ( E @ fun ) @ ( D @ fun ) @ hAPP ) ) ) @ ( C @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_split__twice) ).
thf(552,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( B @ ( A @ product_prod ) @ ( E @ ( D @ product_prod_case ) ) @ ( B @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ ( D @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) @ ( F @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( H @ ( G @ ( F @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( E @ ( C @ ( B @ ( A @ product_prod ) @ combb ) ) @ ( C @ ( E @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ fun ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( E @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ combb ) ) @ ( C @ ( E @ fun ) @ ( D @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ ( D @ fun ) @ fun ) @ ( C @ ( E @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( E @ fun ) @ ( D @ fun ) @ ( B @ ( A @ product_prod ) @ ( E @ fun ) @ ( D @ fun ) @ hAPP ) ) ) @ ( C @ ( E @ ( D @ product_prod_case ) ) @ ( C @ ( E @ ( D @ product_prod ) @ fun ) @ ( C @ ( E @ fun ) @ ( D @ fun ) @ hAPP ) ) ) @ ( C @ ( E @ ( D @ product_prod ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(455,plain,
! [A: $i] :
( ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_exp_Osimps_I143_J) ).
thf(299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_exp_Osimps_I196_J) ).
thf(267,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combb ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combb ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
thf(431,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combb ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( E @ ( D @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_exp_Osimps_I145_J) ).
thf(636,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( E @ ( D @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
!= ( D @ ( C @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_exp_Osimps_I84_J) ).
thf(695,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) )
!= ( D @ ( C @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(65,axiom,
( ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ fun ) @ ti ) )
= assigned ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SmallStep_Oassigned_res) ).
thf(394,plain,
( ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ fun ) @ ti ) )
= assigned ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ product_prod_rec ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ product_prod_rec ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_Oprod_Oprod__rec_res) ).
thf(306,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ product_prod_rec ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ product_prod_rec ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i] :
( ( F @ ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( B @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_map__upd__nonempty) ).
thf(505,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i] :
( ( F @ ( E @ ( B @ some @ ( B @ option @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( B @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( D @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( hp @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( G @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( G @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( A @ ( G @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_red__preserves__sconf) ).
thf(438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( D @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( hp @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( G @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( G @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( A @ ( G @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( ty @ some @ ( ty @ option @ ( ty @ hAPP ) ) ) @ ( D @ ( C @ ( ty @ option @ ( char @ list @ fun_upd ) @ ( ty @ option @ ( char @ list @ fun ) @ ( ty @ option @ fun ) @ ( char @ list @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( ty @ option @ ( char @ list @ fun ) @ ( ty @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( ty @ option @ ( char @ list @ fun ) @ ( ty @ option @ hAPP ) ) ) @ ( B @ ( A @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( E @ ( D @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( B @ ( A @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_WTrtBlock) ).
thf(589,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( ty @ some @ ( ty @ option @ ( ty @ hAPP ) ) ) @ ( D @ ( C @ ( ty @ option @ ( char @ list @ fun_upd ) @ ( ty @ option @ ( char @ list @ fun ) @ ( ty @ option @ fun ) @ ( char @ list @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( ty @ option @ ( char @ list @ fun ) @ ( ty @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( ty @ option @ ( char @ list @ fun ) @ ( ty @ option @ hAPP ) ) ) @ ( B @ ( A @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( E @ ( D @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( B @ ( A @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( H @ ( G @ ( B @ ( C @ product_Pair ) @ ( B @ ( C @ product_prod ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( C @ product_prod ) @ ( B @ hAPP ) ) ) )
= ( F @ ( B @ ( C @ product_prod ) @ ti ) ) )
=> ( E @ ( H @ ( G @ ( D @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( E @ ( F @ ( D @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_splitI2_H) ).
thf(663,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( ( H @ ( G @ ( B @ ( C @ product_Pair ) @ ( B @ ( C @ product_prod ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( C @ product_prod ) @ ( B @ hAPP ) ) ) )
= ( F @ ( B @ ( C @ product_prod ) @ ti ) ) )
=> ( E @ ( H @ ( G @ ( D @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( E @ ( F @ ( D @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ none @ ( C @ ( B @ none @ ( A @ ( B @ option @ combk ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( B @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_empty__upd__none) ).
thf(342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ none @ ( C @ ( B @ none @ ( A @ ( B @ option @ combk ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ fun_upd ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ fun ) @ ( B @ option @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ option @ ( A @ fun ) @ ( B @ option @ hAPP ) ) ) @ ( B @ option @ ( A @ hAPP ) ) ) )
= ( B @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(85,axiom,
( ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= red ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SmallStep_Ored_res) ).
thf(458,plain,
( ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= red ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(162,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_split__conv) ).
thf(531,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ product_prod_case ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i,G: $i,H: $i,I: $i] :
( ( E @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( I @ ( H @ ( D @ ( C @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( D @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( D @ hAPP ) ) ) @ ( G @ ( D @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ hAPP ) ) ) @ ( F @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod__cases4) ).
thf(525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ! [F: $i,G: $i,H: $i,I: $i] :
( ( E @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( I @ ( H @ ( D @ ( C @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( D @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( D @ hAPP ) ) ) @ ( G @ ( D @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ hAPP ) ) ) @ ( F @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( E @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_exp_Osimps_I83_J) ).
thf(557,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( B @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( E @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ fun ) @ ti ) )
= ( B @ ( A @ product_Pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_res) ).
thf(640,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ fun ) @ ti ) )
= ( B @ ( A @ product_Pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ fun ) @ ti ) )
= ( A @ seq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OSeq_res) ).
thf(409,plain,
! [A: $i] :
( ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ fun ) @ ti ) )
= ( A @ seq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( H @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( H @ ( G @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_red__preserves__lconf) ).
thf(263,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( H @ ( G @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( F @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( H @ ( G @ ( I @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(14,axiom,
p @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( v @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( v_1 @ ( la @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).
thf(199,plain,
p @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( v @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( v_1 @ ( la @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( E @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( B @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( B @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_redp__redsp_ORedInitBlock) ).
thf(470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( E @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( B @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( B @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(142,axiom,
( ( v_2 @ ( val @ ti ) )
= v_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_v_H_____res) ).
thf(643,plain,
( ( v_2 @ ( val @ ti ) )
= v_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ lAss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Expr_Oexp_OLAss_res) ).
thf(656,plain,
! [A: $i] :
( ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ lAss ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( A @ ( D @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( unit @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( D @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_red__reds_ORedLAss) ).
thf(571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( A @ ( D @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( unit @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( D @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ti ) @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ti ) @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_red__reds_ORedSeq) ).
thf(231,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
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] :
( ( K @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( J @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( G @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( F @ ( J @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( K @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( F @ ( J @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( G @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_red__reds_OInitBlockRed) ).
thf(539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( K @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( J @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( G @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( F @ ( J @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( K @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( F @ ( J @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( C @ ( G @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( F @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( F @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(16,axiom,
( ( t_1 @ ( ty @ ti ) )
= t_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_T_____res) ).
thf(203,plain,
( ( t_1 @ ( ty @ ti ) )
= t_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(125,axiom,
( ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Conform_Olconf_res) ).
thf(581,plain,
( ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf @ ( bool @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ lconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(29,axiom,
( ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ti ) )
= p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_P_res) ).
thf(258,plain,
( ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ti ) )
= p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( E @ ( D @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) )
<=> ( ( C = E )
& ( B = D ) ) ),
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] :
( ( ( ( C = E )
& ( B = D ) )
=> ( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( E @ ( D @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
= ( E @ ( D @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) )
=> ( ( C = E )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( D @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exp_Osimps_I197_J) ).
thf(401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( D @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1,conjecture,
p @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( v @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( v_1 @ ( la @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( p @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( v @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( v_1 @ ( la @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(158,plain,
~ ( p @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( l_a @ ( h_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( e_a @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( v @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( v_1 @ ( la @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( ea @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(145,axiom,
( ( ea @ ( char @ list @ exp @ ti ) )
= ea ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_ea_____res) ).
thf(652,plain,
( ( ea @ ( char @ list @ exp @ ti ) )
= ea ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( B @ ( A @ product_prod ) @ ti ) )
= ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) )
=> ( F @ ( E @ ( C @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_splitI2) ).
thf(351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( B @ ( A @ product_prod ) @ ti ) )
= ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) )
=> ( F @ ( E @ ( C @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(120,axiom,
( ( h_a @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ti ) )
= h_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_h_Ha_____res) ).
thf(568,plain,
( ( h_a @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ti ) )
= h_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( C @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( A @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_red__reds_ORedInitBlock) ).
thf(478,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( C @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( B @ ( A @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ( bool @ ti ) @ hBOOL )
<=> ( A @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(383,plain,
! [A: $i] :
( ( ( A @ hBOOL )
=> ( A @ ( bool @ ti ) @ hBOOL ) )
& ( ( A @ ( bool @ ti ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( C @ ( B @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_widen__refl) ).
thf(684,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( C @ ( B @ ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= ( A @ widen ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TypeRel_Owiden_res) ).
thf(549,plain,
! [A: $i] :
( ( A @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( A @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ fun ) @ ti ) )
= ( A @ widen ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ fun ) @ ti ) @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ fun ) @ ti ) @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ ( C @ combb ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(235,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ ( C @ combb ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( C @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( C @ ( B @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_redp__redsp_ORedBlock) ).
thf(246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( E @ ( D @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( C @ ( B @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( D @ ( C @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_splitD) ).
thf(315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( D @ ( C @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i,I: $i,J: $i] : ( J @ ( I @ ( D @ ( C @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( D @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( D @ hAPP ) ) ) @ ( H @ ( D @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ hAPP ) ) ) @ ( G @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) @ ( F @ ( bool @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( F @ ( bool @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
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] : ( J @ ( I @ ( D @ ( C @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( D @ fun ) @ ( C @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( D @ hAPP ) ) ) @ ( H @ ( D @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( D @ ( C @ product_prod ) @ hAPP ) ) ) @ ( G @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) @ ( F @ ( bool @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( F @ ( bool @ ( D @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,axiom,
( ( ha @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ti ) )
= ha ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_ha_____res) ).
thf(405,plain,
( ( ha @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ ti ) )
= ha ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( J @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( val @ none @ ( G @ ( F @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( G @ ( J @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( ~ ( D @ ( G @ ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( G @ ( J @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( G @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
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] :
( ( J @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( val @ none @ ( G @ ( F @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( G @ ( J @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( ~ ( D @ ( G @ ( assigned @ ( bool @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( bool @ ( char @ list @ exp @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( G @ ( J @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( I @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( H @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( G @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ fun_upd ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( B @ ( A @ fun_upd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Fun_Ofun__upd_res) ).
thf(422,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ fun_upd ) @ ( B @ ( A @ fun ) @ ( B @ fun ) @ ( A @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( B @ ( A @ fun_upd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combs ) ) @ ( C @ ( A @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
thf(373,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combs ) ) @ ( C @ ( A @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
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] :
( ( G @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( M @ ( L @ ( F @ ( E @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( F @ fun ) @ ( E @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( F @ hAPP ) ) ) @ ( K @ ( F @ ( E @ product_prod ) @ ( D @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ fun ) @ ( D @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ hAPP ) ) ) @ ( J @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ hAPP ) ) ) @ ( I @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( H @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_prod__cases6) ).
thf(564,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] :
( ( G @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ti ) )
!= ( M @ ( L @ ( F @ ( E @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( F @ fun ) @ ( E @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( F @ hAPP ) ) ) @ ( K @ ( F @ ( E @ product_prod ) @ ( D @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ fun ) @ ( D @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( F @ ( E @ product_prod ) @ hAPP ) ) ) @ ( J @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ fun ) @ ( C @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ hAPP ) ) ) @ ( I @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ fun ) @ ( B @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ hAPP ) ) ) @ ( H @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_Pair ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ fun ) @ ( A @ hAPP ) ) ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ ( A @ product_prod ) @ ( F @ ( E @ product_prod ) @ ( D @ product_prod ) @ ( C @ product_prod ) @ ( B @ product_prod ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( v @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( v_1 @ ( la @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( B @ ( p @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_InitBlockRed_I2_J) ).
thf(358,plain,
! [A: $i,B: $i] :
( ( v @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( v_1 @ ( la @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( ha @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( B @ ( p @ ( typeSa885026672_sconf @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( A @ ( C @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen @ ( bool @ ( ty @ fun ) @ ( ty @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( ty @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ ( wTrt @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ fun ) @ ( ty @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( bool @ ( ty @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( ty @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( B @ ( C @ product_Pair ) @ ( B @ ( C @ product_prod ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( C @ product_prod ) @ ( B @ hAPP ) ) ) @ ( E @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_mem__splitI) ).
thf(415,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( F @ ( B @ ( C @ product_Pair ) @ ( B @ ( C @ product_prod ) @ ( B @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( C @ product_prod ) @ ( B @ hAPP ) ) ) @ ( E @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod_case ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ ( C @ product_prod ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ produc1605651328_split ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_internal__split__conv) ).
thf(464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ produc1605651328_split ) ) @ ( C @ ( B @ ( A @ product_prod ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( C @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
<=> ! [D: $i,E: $i] : ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_split__paired__All) ).
thf(596,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] : ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ! [D: $i] : ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) )
& ( ! [D: $i] : ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ! [D: $i,E: $i] : ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
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] :
( ( K @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( I @ ( H @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( G @ ( F @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( G @ ( K @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( G @ ( F @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( G @ ( K @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( I @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( G @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( H @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( G @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_redp__redsp_OInitBlockRed) ).
thf(200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( K @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( I @ ( H @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) @ ( G @ ( F @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( G @ ( K @ ( val @ option @ ( char @ list @ hAPP ) ) ) )
= ( B @ ( val @ some @ ( val @ option @ ( val @ hAPP ) ) ) ) )
=> ( G @ ( F @ ( val @ option @ ( char @ list @ hAPP ) ) ) @ ( G @ ( K @ ( val @ option @ ( char @ list @ fun_upd ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ hAPP ) ) ) @ ( J @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( I @ ( B @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( G @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( F @ ( E @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ hAPP ) ) ) @ ( D @ ( H @ ( char @ list @ val_1 @ ( char @ list @ exp @ ( val @ hAPP ) ) ) @ ( G @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( A @ ( G @ ( char @ list @ block @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( C @ ( redp @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_red__reds_OLAssRed) ).
thf(277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ ( char @ list @ lAss @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( A @ ( D @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( A @ ( B @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_red__reds_OSeqRed) ).
thf(369,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( D @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( B @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( red @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ hAPP ) ) ) @ ( E @ ( A @ ( D @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( C @ ( A @ ( B @ ( char @ list @ seq @ ( char @ list @ exp @ ( char @ list @ exp @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( char @ list @ exp @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ fun ) @ ( char @ list @ exp @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_Pair ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ hAPP ) ) ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ member @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ fun ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ ( val @ option @ ( char @ list @ fun ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) @ product_prod ) @ ( char @ list @ exp @ product_prod ) @ product_prod ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( D @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_exp_Osimps_I85_J) ).
thf(254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ seq @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ exp @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( D @ ( A @ val_1 @ ( A @ exp @ ( val @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( ( D @ ( B @ ( A @ product_prod ) @ ti ) )
= ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) )
=> ~ ( F @ ( E @ ( C @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_splitE) ).
thf(337,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( B @ ( A @ product_prod_case ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ fun ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ product_prod ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( ( D @ ( B @ ( A @ product_prod ) @ ti ) )
= ( F @ ( E @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) )
=> ~ ( F @ ( E @ ( C @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( C @ ( B @ ( A @ product_prod ) @ ti ) )
!= ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_PairE) ).
thf(309,plain,
! [A: $i,B: $i,C: $i] :
~ ! [D: $i,E: $i] :
( ( C @ ( B @ ( A @ product_prod ) @ ti ) )
!= ( E @ ( D @ ( B @ ( A @ product_Pair ) @ ( B @ ( A @ product_prod ) @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( A @ product_prod ) @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( D @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_exp_Osimps_I142_J) ).
thf(659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( B @ ( A @ lAss @ ( A @ exp @ ( A @ exp @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) )
!= ( F @ ( E @ ( D @ ( A @ block @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ fun ) @ ( ty @ hAPP ) ) ) @ ( A @ exp @ ( A @ exp @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(749,plain,
$false,
inference(e,[status(thm)],[289,645,555,170,379,440,472,670,174,417,436,389,570,196,542,460,475,591,443,376,253,485,238,348,480,602,634,396,265,233,248,512,529,366,534,334,260,561,392,297,165,407,693,630,467,229,493,682,583,522,317,650,615,356,610,499,519,578,225,686,547,515,654,371,205,674,586,412,618,425,279,573,180,176,291,545,445,313,159,419,362,303,509,434,271,208,631,594,483,668,462,345,552,455,299,267,431,636,695,394,306,505,438,589,663,342,458,162,531,525,557,640,409,263,199,470,643,656,571,612,231,539,203,581,258,186,401,158,652,351,568,478,383,684,549,536,235,246,315,168,405,183,422,373,564,358,415,464,596,200,277,369,254,337,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW478+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 16:08:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.82/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.16/1.46 % [INFO] Parsing done (459ms).
% 2.16/1.47 % [INFO] Running in sequential loop mode.
% 3.57/1.86 % [INFO] eprover registered as external prover.
% 3.57/1.87 % [INFO] Scanning for conjecture ...
% 5.42/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 155 axioms. Running axiom selection ...
% 6.28/2.65 % [INFO] Axiom selection finished. Selected 155 axioms (removed 0 axioms).
% 8.65/3.59 % [INFO] Problem is first-order (TPTP FOF).
% 8.81/3.63 % [INFO] Type checking passed.
% 8.81/3.64 % [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 ...
% 30.83/12.04 % External prover 'e' found a proof!
% 30.83/12.05 % [INFO] Killing All external provers ...
% 30.83/12.05 % Time passed: 11492ms (effective reasoning time: 10568ms)
% 30.83/12.05 % 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)>
% 30.83/12.05 % 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
% 30.83/12.05 % No. of inferences in proof: 314
% 30.83/12.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11492 ms resp. 10568 ms w/o parsing
% 33.93/13.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.93/13.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------