TSTP Solution File: SWW553_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW553_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:25:02 EDT 2023
% Result : Theorem 20.65s 9.80s
% Output : Refutation 20.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 152
% Syntax : Number of formulae : 258 ( 61 unt; 48 typ; 0 def)
% Number of atoms : 2062 ( 255 equ; 0 cnn)
% Maximal formula atoms : 47 ( 9 avg)
% Number of connectives : 9180 ( 69 ~; 3 |; 52 &;8829 @)
% ( 20 <=>; 207 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 20 con; 0-6 aty)
% Number of variables : 1056 ( 0 ^;1001 !; 25 ?;1056 :)
% ( 30 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char_type,type,
char: $tType ).
thf(ty_type,type,
ty: $tType ).
thf(val_type,type,
val: $tType ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(conf_type,type,
conf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > val > ty > $o ) ).
thf(hconf_type,type,
hconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ) ).
thf(lconf_type,type,
lconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ val ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > $o ) ).
thf(oconf_type,type,
oconf:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) > $o ) ).
thf(is_type_type,type,
is_type:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ty > $o ) ).
thf(preallocated_type,type,
preallocated: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ).
thf(start_heap_type,type,
start_heap:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) ) ).
thf(fAss_type,type,
fAss:
!>[TA: $tType] : ( ( exp @ TA ) > ( list @ char ) > ( list @ char ) > ( exp @ TA ) > ( exp @ TA ) ) ).
thf(val1_type,type,
val1:
!>[TA: $tType] : ( val > ( exp @ TA ) ) ).
thf(fun_upd_type,type,
fun_upd:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA > ( fun @ TB @ TA ) ) ).
thf(map_comp_type,type,
map_comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( option @ TB ) ) > ( fun @ TA @ ( option @ TC ) ) > TA > ( option @ TB ) ) ).
thf(hext_type,type,
hext: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > $o ).
thf(typeof_h_type,type,
typeof_h: ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > val > ( option @ ty ) ).
thf(none_type,type,
none:
!>[TA: $tType] : ( option @ TA ) ).
thf(some_type,type,
some:
!>[TA: $tType] : ( TA > ( option @ TA ) ) ).
thf(option_rec_type,type,
option_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) > ( option @ TA ) > TB ) ).
thf(set_type,type,
set:
!>[TA: $tType] : ( ( option @ TA ) > ( fun @ TA @ bool ) ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(has_field_type,type,
has_field:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ( list @ char ) > ( list @ char ) > ty > ( list @ char ) > $o ) ).
thf(widen_type,type,
widen:
!>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ty > ty > $o ) ).
thf(default_val_type,type,
default_val: ty > val ).
thf(the_Addr_type,type,
the_Addr: val > nat ).
thf(addr_type,type,
addr: nat > val ).
thf(wTrt_type,type,
wTrt: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > ( exp @ ( list @ char ) ) > ty > $o ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(c_type,type,
c: list @ char ).
thf(d_type,type,
d: list @ char ).
thf(e_type,type,
e: fun @ ( list @ char ) @ ( option @ ty ) ).
thf(f_type,type,
f: list @ char ).
thf(p_type,type,
p: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ).
thf(tf_type,type,
tf: ty ).
thf(t_type,type,
t: ty ).
thf(tv_type,type,
tv: ty ).
thf(a_type,type,
a: nat ).
thf(fs_type,type,
fs: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ).
thf(ha_type,type,
ha: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ).
thf(v_type,type,
v: val ).
thf(11,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ D @ C @ B )
=> ( ( hext @ C @ A )
=> ( oconf @ TA @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_oconf__hext) ).
thf(138,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ D @ C @ B )
=> ( ( hext @ C @ A )
=> ( oconf @ TA @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(80,axiom,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ G @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( oconf @ TA @ G @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_oconf__upd__obj) ).
thf(385,plain,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ G @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( oconf @ TA @ G @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ F @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB] :
( ( fun_upd @ TA @ TB @ B @ A @ ( aa @ TA @ TB @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_fun__upd__triv) ).
thf(203,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB] :
( ( fun_upd @ TA @ TB @ B @ A @ ( aa @ TA @ TB @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_hext__trans) ).
thf(146,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ C @ B )
=> ( ( hext @ B @ A )
=> ( hext @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(217,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(98,axiom,
! [A: fun @ ( list @ char ) @ ( option @ ty ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: ty,D: val,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( typeof_h @ E @ D )
= ( some @ ty @ C ) )
=> ( wTrt @ B @ E @ A @ ( val1 @ ( list @ char ) @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_WTrtVal) ).
thf(449,plain,
! [A: fun @ ( list @ char ) @ ( option @ ty ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ),C: ty,D: val,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( typeof_h @ E @ D )
= ( some @ ty @ C ) )
=> ( wTrt @ B @ E @ A @ ( val1 @ ( list @ char ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(79,axiom,
! [TA: $tType,A: ty,B: val,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( conf @ TA @ D @ C @ B @ A )
<=> ? [E: ty] :
( ( ( typeof_h @ C @ B )
= ( some @ ty @ E ) )
& ( widen @ TA @ D @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_conf__def) ).
thf(379,plain,
! [TA: $tType,A: ty,B: val,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( ( conf @ TA @ D @ C @ B @ A )
=> ? [E: ty] :
( ( ( typeof_h @ C @ B )
= ( some @ ty @ E ) )
& ( widen @ TA @ D @ E @ A ) ) )
& ( ? [E: ty] :
( ( ( typeof_h @ C @ B )
= ( some @ ty @ E ) )
& ( widen @ TA @ D @ E @ A ) )
=> ( conf @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(88,axiom,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_preallocated__upd__obj) ).
thf(404,plain,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(21,axiom,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA,F: list @ char,G: list @ char,H: exp @ TA] :
( ( ( fAss @ TA @ H @ G @ F @ E )
= ( fAss @ TA @ D @ C @ B @ A ) )
<=> ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_exp_Osimps_I8_J) ).
thf(185,plain,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: exp @ TA,F: list @ char,G: list @ char,H: exp @ TA] :
( ( ( ( fAss @ TA @ H @ G @ F @ E )
= ( fAss @ TA @ D @ C @ B @ A ) )
=> ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) ) )
& ( ( ( H = D )
& ( G = C )
& ( F = B )
& ( E = A ) )
=> ( ( fAss @ TA @ H @ G @ F @ E )
= ( fAss @ TA @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(90,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),C: ty,D: val] :
( ( ( typeof_h @ ( combk @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ nat @ ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ D )
= ( some @ ty @ C ) )
=> ( conf @ TA @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_typeof__lit__conf) ).
thf(417,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),C: ty,D: val] :
( ( ( typeof_h @ ( combk @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ nat @ ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ D )
= ( some @ ty @ C ) )
=> ( conf @ TA @ B @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_split__paired__Ex) ).
thf(320,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: fun @ TB @ TA] :
( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ D @ C @ B ) @ C @ A )
= ( fun_upd @ TB @ TA @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_fun__upd__upd) ).
thf(257,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: fun @ TB @ TA] :
( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ D @ C @ B ) @ C @ A )
= ( fun_upd @ TB @ TA @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_prod__cases3) ).
thf(389,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(4,axiom,
! [TA: $tType,A: option @ TA] :
( ! [B: TA] :
( A
!= ( some @ TA @ B ) )
<=> ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_not__Some__eq) ).
thf(110,plain,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( some @ TA @ B ) )
=> ( A
= ( none @ TA ) ) )
& ( ( A
= ( none @ TA ) )
=> ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_split__paired__All) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(73,axiom,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( hext @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_hext__upd__obj) ).
thf(357,plain,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( hext @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(15,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_WTrt__hext__mono) ).
thf(164,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: exp @ ( list @ char ),D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) )] :
( ( wTrt @ F @ E @ D @ C @ B )
=> ( ( hext @ E @ A )
=> ( wTrt @ F @ A @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(96,axiom,
! [TA: $tType,A: list @ char,B: ty,C: val,D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ ( list @ char ) @ ( option @ val ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ G @ F @ E @ D )
=> ( ( conf @ TA @ G @ F @ C @ B )
=> ( ( ( aa @ ( list @ char ) @ ( option @ ty ) @ D @ A )
= ( some @ ty @ B ) )
=> ( lconf @ TA @ G @ F @ ( fun_upd @ ( list @ char ) @ ( option @ val ) @ E @ A @ ( some @ val @ C ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_lconf__upd) ).
thf(443,plain,
! [TA: $tType,A: list @ char,B: ty,C: val,D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ ( list @ char ) @ ( option @ val ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ G @ F @ E @ D )
=> ( ( conf @ TA @ G @ F @ C @ B )
=> ( ( ( aa @ ( list @ char ) @ ( option @ ty ) @ D @ A )
= ( some @ ty @ B ) )
=> ( lconf @ TA @ G @ F @ ( fun_upd @ ( list @ char ) @ ( option @ val ) @ E @ A @ ( some @ val @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1,conjecture,
conf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha @ v @ tf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( conf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha @ v @ tf ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(106,plain,
~ ( conf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha @ v @ tf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [TA: $tType,A: ty,B: ty,C: ty,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ D @ C @ B )
=> ( ( widen @ TA @ D @ B @ A )
=> ( widen @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_widen__trans) ).
thf(121,plain,
! [TA: $tType,A: ty,B: ty,C: ty,D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( widen @ TA @ D @ C @ B )
=> ( ( widen @ TA @ D @ B @ A )
=> ( widen @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(68,axiom,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) )
=> ( oconf @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_hconfD) ).
thf(348,plain,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) )
=> ( oconf @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(70,axiom,
! [TA: $tType,A: ty,B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( conf @ TA @ C @ B @ ( default_val @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_defval__conf) ).
thf(353,plain,
! [TA: $tType,A: ty,B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( conf @ TA @ C @ B @ ( default_val @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(104,axiom,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( ( oconf @ TA @ D @ C @ A )
=> ( hconf @ TA @ D @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_hconf__new) ).
thf(480,plain,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( ( oconf @ TA @ D @ C @ A )
=> ( hconf @ TA @ D @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(47,axiom,
! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_widen__refl) ).
thf(280,plain,
! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(10,axiom,
! [TA: $tType,A: option @ TA,B: TA] :
( ( member @ TA @ B @ ( set @ TA @ A ) )
<=> ( A
= ( some @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_elem__set) ).
thf(132,plain,
! [TA: $tType,A: option @ TA,B: TA] :
( ( ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( A
= ( some @ TA @ B ) ) )
& ( ( A
= ( some @ TA @ B ) )
=> ( member @ TA @ B @ ( set @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(85,axiom,
( ( typeof_h @ ha @ v )
= ( some @ ty @ tv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_typeofv) ).
thf(396,plain,
( ( typeof_h @ ha @ v )
= ( some @ ty @ tv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(5,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] : ( hext @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_hext__refl) ).
thf(116,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] : ( hext @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( option @ TA )] :
~ ! [D: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ C @ B @ ( some @ TA @ A ) ) @ D )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_map__upd__nonempty) ).
thf(206,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( option @ TA )] :
~ ! [D: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ C @ B @ ( some @ TA @ A ) ) @ D )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(50,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(292,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(99,axiom,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: list @ char,C: nat,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ E @ D )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ A ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_hext__objD) ).
thf(452,plain,
! [A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: list @ char,C: nat,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ E @ D )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ A ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_prod_Orecs) ).
thf(248,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( some @ TA @ B )
= ( some @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_option_Oinject) ).
thf(220,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( ( some @ TA @ B )
= ( some @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( some @ TA @ B )
= ( some @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_prod_Oexhaust) ).
thf(260,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_prod__induct3) ).
thf(392,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(89,axiom,
! [TA: $tType,A: fun @ ( list @ char ) @ ( option @ ty ),B: fun @ ( list @ char ) @ ( option @ val ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ D @ C @ B @ A )
<=> ! [E: list @ char,F: val] :
( ( ( aa @ ( list @ char ) @ ( option @ val ) @ B @ E )
= ( some @ val @ F ) )
=> ? [G: ty] :
( ( ( aa @ ( list @ char ) @ ( option @ ty ) @ A @ E )
= ( some @ ty @ G ) )
& ( conf @ TA @ D @ C @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_lconf__def) ).
thf(407,plain,
! [TA: $tType,A: fun @ ( list @ char ) @ ( option @ ty ),B: fun @ ( list @ char ) @ ( option @ val ),C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( ( lconf @ TA @ D @ C @ B @ A )
=> ! [E: list @ char,F: val] :
( ( ( aa @ ( list @ char ) @ ( option @ val ) @ B @ E )
= ( some @ val @ F ) )
=> ? [G: ty] :
( ( ( aa @ ( list @ char ) @ ( option @ ty ) @ A @ E )
= ( some @ ty @ G ) )
& ( conf @ TA @ D @ C @ F @ G ) ) ) )
& ( ! [E: list @ char,F: val] :
( ( ( aa @ ( list @ char ) @ ( option @ val ) @ B @ E )
= ( some @ val @ F ) )
=> ? [G: ty] :
( ( ( aa @ ( list @ char ) @ ( option @ ty ) @ A @ E )
= ( some @ ty @ G ) )
& ( conf @ TA @ D @ C @ F @ G ) ) )
=> ( lconf @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(45,axiom,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( preallocated @ ( start_heap @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_preallocated__start) ).
thf(275,plain,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( preallocated @ ( start_heap @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(30,axiom,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_option_Osimps_I2_J) ).
thf(229,plain,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( some @ TB @ A ) )
=> ( ( fun_upd @ TA @ ( option @ TB ) @ C @ B @ ( some @ TB @ A ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_map__upd__triv) ).
thf(197,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( option @ TB )] :
( ( ( aa @ TA @ ( option @ TB ) @ C @ B )
= ( some @ TB @ A ) )
=> ( ( fun_upd @ TA @ ( option @ TB ) @ C @ B @ ( some @ TB @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(61,axiom,
has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ c @ f @ tf @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_has) ).
thf(329,plain,
has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ c @ f @ tf @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(58,axiom,
! [TA: $tType,A: fun @ ( list @ char ) @ ( option @ ty ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( lconf @ TA @ C @ B @ ( combk @ ( option @ val ) @ ( list @ char ) @ ( none @ val ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_lconf__empty) ).
thf(324,plain,
! [TA: $tType,A: fun @ ( list @ char ) @ ( option @ ty ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( lconf @ TA @ C @ B @ ( combk @ ( option @ val ) @ ( list @ char ) @ ( none @ val ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(49,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: option @ TA] :
( ! [D: TA] :
( ( member @ TA @ D @ ( set @ TA @ C ) )
=> ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( ( C
= ( some @ TA @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_ospec) ).
thf(285,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: option @ TA] :
( ! [D: TA] :
( ( member @ TA @ D @ ( set @ TA @ C ) )
=> ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( ( C
= ( some @ TA @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(56,axiom,
! [TA: $tType,A: val,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAss @ TA @ E @ D @ C @ B )
!= ( val1 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_exp_Osimps_I79_J) ).
thf(317,plain,
! [TA: $tType,A: val,B: exp @ TA,C: list @ char,D: list @ char,E: exp @ TA] :
( ( fAss @ TA @ E @ D @ C @ B )
!= ( val1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(81,axiom,
wTrt @ p @ ha @ e @ ( fAss @ ( list @ char ) @ ( val1 @ ( list @ char ) @ ( addr @ a ) ) @ f @ d @ ( val1 @ ( list @ char ) @ v ) ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_RedFAss_I2_J) ).
thf(388,plain,
wTrt @ p @ ha @ e @ ( fAss @ ( list @ char ) @ ( val1 @ ( list @ char ) @ ( addr @ a ) ) @ f @ d @ ( val1 @ ( list @ char ) @ v ) ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(72,axiom,
widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ tv @ tf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_sub) ).
thf(356,plain,
widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ tv @ tf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_fun__upd__apply) ).
thf(169,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod__cases6) ).
thf(420,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(42,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ B )
=> ( ( hext @ B @ A )
=> ( preallocated @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_preallocated__hext) ).
thf(266,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ B )
=> ( ( hext @ B @ A )
=> ( preallocated @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(74,axiom,
! [TA: $tType,A: ty,B: ty,C: val,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( conf @ TA @ E @ D @ C @ B )
=> ( ( widen @ TA @ E @ B @ A )
=> ( conf @ TA @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conf__widen) ).
thf(360,plain,
! [TA: $tType,A: ty,B: ty,C: val,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( conf @ TA @ E @ D @ C @ B )
=> ( ( widen @ TA @ E @ B @ A )
=> ( conf @ TA @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(86,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: val] :
( ( ( typeof_h @ ( combk @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ nat @ ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ C )
= ( some @ ty @ B ) )
=> ( ( typeof_h @ A @ C )
= ( some @ ty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_typeof__lit__typeof) ).
thf(398,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: ty,C: val] :
( ( ( typeof_h @ ( combk @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ nat @ ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ C )
= ( some @ ty @ B ) )
=> ( ( typeof_h @ A @ C )
= ( some @ ty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(52,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
<=> ? [B: TA] :
( A
= ( some @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_not__None__eq) ).
thf(298,plain,
! [TA: $tType,A: option @ TA] :
( ( ( A
!= ( none @ TA ) )
=> ? [B: TA] :
( A
= ( some @ TA @ B ) ) )
& ( ? [B: TA] :
( A
= ( some @ TA @ B ) )
=> ( A
!= ( none @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ ( none @ TA ) ) @ B )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_empty__upd__none) ).
thf(166,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB] :
( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ ( none @ TA ) ) @ B )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( some @ TA @ C ) ) @ B )
= ( some @ TA @ A ) )
<=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( aa @ TB @ ( option @ TA ) @ E @ B )
= ( some @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_map__upd__Some__unfold) ).
thf(148,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( some @ TA @ C ) ) @ B )
= ( some @ TA @ A ) )
=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( aa @ TB @ ( option @ TA ) @ E @ B )
= ( some @ TA @ A ) ) ) ) )
& ( ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( aa @ TB @ ( option @ TA ) @ E @ B )
= ( some @ TA @ A ) ) ) )
=> ( ( aa @ TB @ ( option @ TA ) @ ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( some @ TA @ C ) ) @ B )
= ( some @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Pair__inject) ).
thf(180,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__cases5) ).
thf(423,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(6,axiom,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: val] :
( ( val1 @ TA @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_exp_Osimps_I78_J) ).
thf(118,plain,
! [TA: $tType,A: exp @ TA,B: list @ char,C: list @ char,D: exp @ TA,E: val] :
( ( val1 @ TA @ E )
!= ( fAss @ TA @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(64,axiom,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ E @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( oconf @ TA @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_oconf__new) ).
thf(335,plain,
! [TA: $tType,A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( oconf @ TA @ E @ D @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( oconf @ TA @ E @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ D @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC,C: fun @ TC @ ( option @ TB )] :
( ( ( aa @ TC @ ( option @ TB ) @ C @ B )
= ( none @ TB ) )
=> ( ( map_comp @ TB @ TA @ TC @ A @ C @ B )
= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_map__comp__simps_I1_J) ).
thf(236,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC,C: fun @ TC @ ( option @ TB )] :
( ( ( aa @ TC @ ( option @ TB ) @ C @ B )
= ( none @ TB ) )
=> ( ( map_comp @ TB @ TA @ TC @ A @ C @ B )
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: val,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ char,E: ty,F: list @ char,G: list @ char,H: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( has_field @ TA @ H @ G @ F @ E @ D )
=> ( ( conf @ TA @ H @ C @ B @ E )
=> ( ( oconf @ TA @ H @ C @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ G @ A ) )
=> ( oconf @ TA @ H @ C @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ G @ ( fun_upd @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) @ A @ ( product_Pair @ ( list @ char ) @ ( list @ char ) @ F @ D ) @ ( some @ val @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_oconf__fupd) ).
thf(377,plain,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: val,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: list @ char,E: ty,F: list @ char,G: list @ char,H: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( has_field @ TA @ H @ G @ F @ E @ D )
=> ( ( conf @ TA @ H @ C @ B @ E )
=> ( ( oconf @ TA @ H @ C @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ G @ A ) )
=> ( oconf @ TA @ H @ C @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ G @ ( fun_upd @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) @ A @ ( product_Pair @ ( list @ char ) @ ( list @ char ) @ F @ D ) @ ( some @ val @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_prod__induct6) ).
thf(362,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(245,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ TB] :
( ( ( aa @ TA @ TB @ C @ B )
= A )
=> ( ( fun_upd @ TA @ TB @ C @ B @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_fun__upd__idem) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ TB] :
( ( ( aa @ TA @ TB @ C @ B )
= A )
=> ( ( fun_upd @ TA @ TB @ C @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_fun__upd__def) ).
thf(140,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( ( D = C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= A ) )
& ( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(105,axiom,
hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hconf) ).
thf(483,plain,
hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( option @ TA ),C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( some @ TA @ C ) )
= ( fun_upd @ TB @ ( option @ TA ) @ B @ D @ ( some @ TA @ A ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_map__upd__eqD1) ).
thf(251,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( option @ TA ),C: TA,D: TB,E: fun @ TB @ ( option @ TA )] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ E @ D @ ( some @ TA @ C ) )
= ( fun_upd @ TB @ ( option @ TA ) @ B @ D @ ( some @ TA @ A ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(62,axiom,
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ha @ a )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ c @ fs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_RedFAss_Ohyps) ).
thf(330,plain,
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ ha @ a )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ c @ fs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(100,axiom,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_preallocated__new) ).
thf(455,plain,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( preallocated @ C )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( preallocated @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TC @ ( option @ TB ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ B )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_map__comp__empty_I2_J) ).
thf(226,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TC @ ( option @ TB ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ ( combk @ ( option @ TA ) @ TB @ ( none @ TA ) ) @ A @ B )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_prod__induct4) ).
thf(431,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(84,axiom,
! [TA: $tType,A: ty,B: val,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ E @ D )
=> ( ( conf @ TA @ C @ E @ B @ A )
=> ( conf @ TA @ C @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_conf__hext) ).
thf(394,plain,
! [TA: $tType,A: ty,B: val,C: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ E @ D )
=> ( ( conf @ TA @ C @ E @ B @ A )
=> ( conf @ TA @ C @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(54,axiom,
! [A: ty,B: val,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ D @ C )
=> ( ( ( typeof_h @ D @ B )
= ( some @ ty @ A ) )
=> ( ( typeof_h @ C @ B )
= ( some @ ty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_hext__typeof__mono) ).
thf(306,plain,
! [A: ty,B: val,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ D @ C )
=> ( ( ( typeof_h @ D @ B )
= ( some @ ty @ A ) )
=> ( ( typeof_h @ C @ B )
= ( some @ ty @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(102,axiom,
wTrt @ p @ ha @ e @ ( fAss @ ( list @ char ) @ ( val1 @ ( list @ char ) @ ( addr @ a ) ) @ f @ d @ ( val1 @ ( list @ char ) @ v ) ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_wt) ).
thf(473,plain,
wTrt @ p @ ha @ e @ ( fAss @ ( list @ char ) @ ( val1 @ ( list @ char ) @ ( addr @ a ) ) @ f @ d @ ( val1 @ ( list @ char ) @ v ) ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(93,axiom,
! [TA: $tType,A: ty,B: val,C: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),F: list @ char,G: nat,H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ H @ G )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ F @ E ) ) )
=> ( ( conf @ TA @ D @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ H @ G @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ F @ C ) ) ) @ B @ A )
<=> ( conf @ TA @ D @ H @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_conf__upd__obj) ).
thf(426,plain,
! [TA: $tType,A: ty,B: val,C: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),D: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),F: list @ char,G: nat,H: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ H @ G )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ F @ E ) ) )
=> ( ( ( conf @ TA @ D @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ H @ G @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ F @ C ) ) ) @ B @ A )
=> ( conf @ TA @ D @ H @ B @ A ) )
& ( ( conf @ TA @ D @ H @ B @ A )
=> ( conf @ TA @ D @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ H @ G @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ F @ C ) ) ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Pair__eq) ).
thf(209,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ TA,D: TB,E: TB] :
( ( E != D )
=> ( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ E @ B ) @ D @ A )
= ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ D @ A ) @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_fun__upd__twist) ).
thf(123,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ TA,D: TB,E: TB] :
( ( E != D )
=> ( ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ E @ B ) @ D @ A )
= ( fun_upd @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ D @ A ) @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(71,axiom,
oconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ c @ fs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096P_Mh_A_092_060turnstile_062_A_IC_M_Afs_J_A_092_060surd_062_096) ).
thf(355,plain,
oconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ c @ fs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_pred__equals__eq2) ).
thf(458,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(51,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_option_Oexhaust) ).
thf(295,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: TA,C: TC,D: fun @ TC @ ( option @ TA )] :
( ( ( aa @ TC @ ( option @ TA ) @ D @ C )
= ( some @ TA @ B ) )
=> ( ( map_comp @ TA @ TB @ TC @ A @ D @ C )
= ( aa @ TA @ ( option @ TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_map__comp__simps_I2_J) ).
thf(282,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( option @ TB ),B: TA,C: TC,D: fun @ TC @ ( option @ TA )] :
( ( ( aa @ TC @ ( option @ TA ) @ D @ C )
= ( some @ TA @ B ) )
=> ( ( map_comp @ TA @ TB @ TC @ A @ D @ C )
= ( aa @ TA @ ( option @ TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_prod__induct5) ).
thf(327,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(41,axiom,
! [A: nat] :
( ( the_Addr @ ( addr @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_the__Addr_Osimps) ).
thf(263,plain,
! [A: nat] :
( ( the_Addr @ ( addr @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ A @ ( combk @ ( option @ TB ) @ TC @ ( none @ TB ) ) @ B )
= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_map__comp__empty_I1_J) ).
thf(177,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TB @ ( option @ TA ),B: TC] :
( ( map_comp @ TB @ TA @ TC @ A @ ( combk @ ( option @ TB ) @ TC @ ( none @ TB ) ) @ B )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(77,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ B @ A )
<=> ( ! [C: nat,D: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ D ) )
=> ( oconf @ TA @ B @ A @ D ) )
& ( preallocated @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_hconf__def) ).
thf(370,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( ( hconf @ TA @ B @ A )
=> ( ! [C: nat,D: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ D ) )
=> ( oconf @ TA @ B @ A @ D ) )
& ( preallocated @ A ) ) )
& ( ( ! [C: nat,D: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ D ) )
=> ( oconf @ TA @ B @ A @ D ) )
& ( preallocated @ A ) )
=> ( hconf @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(65,axiom,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),B: ty,C: val] :
( ( ( typeof_h @ ( combk @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ nat @ ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ C )
= ( some @ ty @ B ) )
=> ( is_type @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_typeof__lit__is__type) ).
thf(338,plain,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),B: ty,C: val] :
( ( ( typeof_h @ ( combk @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ nat @ ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) ) @ C )
= ( some @ ty @ B ) )
=> ( is_type @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(18,axiom,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ ( list @ char ) @ ( option @ ty ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ E @ D @ C @ B )
=> ( ( hext @ D @ A )
=> ( lconf @ TA @ E @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_lconf__hext) ).
thf(175,plain,
! [TA: $tType,A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ ( list @ char ) @ ( option @ ty ),C: fun @ ( list @ char ) @ ( option @ val ),D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),E: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ E @ D @ C @ B )
=> ( ( hext @ D @ A )
=> ( lconf @ TA @ E @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(97,axiom,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( hext @ C @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_hext__new) ).
thf(446,plain,
! [A: product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ),B: nat,C: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B )
= ( none @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) )
=> ( hext @ C @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ C @ B @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(53,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(304,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(69,axiom,
! [TA: $tType,A: list @ char,B: ty,C: val,D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ ( list @ char ) @ ( option @ val ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ G @ F @ E @ D )
=> ( ( conf @ TA @ G @ F @ C @ B )
=> ( lconf @ TA @ G @ F @ ( fun_upd @ ( list @ char ) @ ( option @ val ) @ E @ A @ ( some @ val @ C ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ ty ) @ D @ A @ ( some @ ty @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_lconf__upd2) ).
thf(351,plain,
! [TA: $tType,A: list @ char,B: ty,C: val,D: fun @ ( list @ char ) @ ( option @ ty ),E: fun @ ( list @ char ) @ ( option @ val ),F: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),G: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( lconf @ TA @ G @ F @ E @ D )
=> ( ( conf @ TA @ G @ F @ C @ B )
=> ( lconf @ TA @ G @ F @ ( fun_upd @ ( list @ char ) @ ( option @ val ) @ E @ A @ ( some @ val @ C ) ) @ ( fun_upd @ ( list @ char ) @ ( option @ ty ) @ D @ A @ ( some @ ty @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_prod__cases4) ).
thf(401,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(32,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(235,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(95,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( hext @ B @ A )
<=> ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_hext__def) ).
thf(433,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( hext @ B @ A )
=> ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) ) )
& ( ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) )
=> ( hext @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( ( fun_upd @ TB @ TA @ C @ B @ A )
= C )
<=> ( ( aa @ TB @ TA @ C @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_fun__upd__idem__iff) ).
thf(239,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( ( ( fun_upd @ TB @ TA @ C @ B @ A )
= C )
=> ( ( aa @ TB @ TA @ C @ B )
= A ) )
& ( ( ( aa @ TB @ TA @ C @ B )
= A )
=> ( ( fun_upd @ TB @ TA @ C @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
! [TA: $tType,A: val,B: val] :
( ( ( val1 @ TA @ B )
= ( val1 @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_exp_Osimps_I3_J) ).
thf(126,plain,
! [TA: $tType,A: val,B: val] :
( ( ( ( val1 @ TA @ B )
= ( val1 @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( val1 @ TA @ B )
= ( val1 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( ( oconf @ TA @ F @ E @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) )
=> ( hconf @ TA @ F @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_hconf__upd__obj) ).
thf(341,plain,
! [TA: $tType,A: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),B: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ),C: list @ char,D: nat,E: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),F: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] :
( ( hconf @ TA @ F @ E )
=> ( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ B ) ) )
=> ( ( oconf @ TA @ F @ E @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) )
=> ( hconf @ TA @ F @ ( fun_upd @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ E @ D @ ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB,C: TB] :
( ( option_rec @ TB @ TA @ C @ B @ ( some @ TA @ A ) )
= ( aa @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_option_Orecs_I2_J) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ TB,C: TB] :
( ( option_rec @ TB @ TA @ C @ B @ ( some @ TA @ A ) )
= ( aa @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(103,axiom,
~ ! [A: ty,B: ty] :
( ( ( typeof_h @ ha @ v )
= ( some @ ty @ B ) )
=> ( ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ c @ f @ A @ d )
=> ~ ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_B_Bthesis_O_A_I_B_BTF_ATv_O_A_091_124_Atypeof_092_060_094bsub_062h_092_060_094esub_062_Av_A_061_A_092_060lfloor_062Tv_092_060rfloor_062_059_AP_A_092_060turnstile_062_AC_Ahas_AF_058TF_Ain_AD_059_AP_A_092_060turnstile_062_ATv_A_092_060le_062_ATF_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(474,plain,
~ ! [A: ty,B: ty] :
( ( ( typeof_h @ ha @ v )
= ( some @ ty @ B ) )
=> ( ( has_field @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ c @ f @ A @ d )
=> ~ ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(59,axiom,
hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_RedFAss_I3_J) ).
thf(326,plain,
hconf @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ ha,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: TA] :
( ( option_rec @ TA @ TB @ B @ A @ ( none @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_option_Orecs_I1_J) ).
thf(107,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: TA] :
( ( option_rec @ TA @ TB @ B @ A @ ( none @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,axiom,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),B: ty,C: val,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( typeof_h @ D @ C )
= ( some @ ty @ B ) )
=> ( conf @ TA @ A @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_typeof__conf) ).
thf(332,plain,
! [TA: $tType,A: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),B: ty,C: val,D: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ( ( typeof_h @ D @ C )
= ( some @ ty @ B ) )
=> ( conf @ TA @ A @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(23,axiom,
! [TA: $tType,A: TA] :
( ( some @ TA @ A )
!= ( none @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_option_Osimps_I3_J) ).
thf(200,plain,
! [TA: $tType,A: TA] :
( ( some @ TA @ A )
!= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_fun__upd__other) ).
thf(277,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ TB,C: TA,D: TA] :
( ( D != C )
=> ( ( aa @ TA @ TB @ ( fun_upd @ TA @ TB @ B @ C @ A ) @ D )
= ( aa @ TA @ TB @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( aa @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_fun__upd__same) ).
thf(254,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ TA] :
( ( aa @ TB @ TA @ ( fun_upd @ TB @ TA @ C @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ( addr @ B )
= ( addr @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_val_Osimps_I3_J) ).
thf(309,plain,
! [A: nat,B: nat] :
( ( ( ( addr @ B )
= ( addr @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( addr @ B )
= ( addr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(76,axiom,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) )
=> ( hext @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_hextI) ).
thf(364,plain,
! [A: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ),B: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) )] :
( ! [C: nat,D: list @ char,E: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ B @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ E ) ) )
=> ? [F: fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val )] :
( ( aa @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) ) @ A @ C )
= ( some @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) ) @ ( product_Pair @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val ) ) @ D @ F ) ) ) )
=> ( hext @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_PairE) ).
thf(232,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(484,plain,
$false,
inference(e,[status(thm)],[138,385,203,146,217,449,379,404,185,417,320,257,389,110,344,357,164,443,106,121,348,353,480,280,132,396,116,206,292,452,248,220,260,392,407,275,229,197,329,324,285,317,388,356,169,420,266,360,398,298,166,148,180,423,118,335,236,377,362,245,271,140,483,251,330,455,226,431,394,306,473,426,209,123,355,458,295,282,327,263,177,370,338,175,446,304,351,401,235,433,239,126,341,268,474,326,107,332,200,277,254,309,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW553_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 22:39:29 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.97/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.13 % [INFO] Parsing done (225ms).
% 1.58/1.14 % [INFO] Running in sequential loop mode.
% 2.41/1.34 % [INFO] eprover registered as external prover.
% 2.41/1.34 % [INFO] cvc4 registered as external prover.
% 2.41/1.34 % [INFO] Scanning for conjecture ...
% 2.63/1.46 % [INFO] Found a conjecture and 103 axioms. Running axiom selection ...
% 3.14/1.53 % [INFO] Axiom selection finished. Selected 103 axioms (removed 0 axioms).
% 3.60/1.69 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.84/1.71 % [INFO] Type checking passed.
% 3.84/1.71 % [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 ...
% 20.65/9.80 % External prover 'e' found a proof!
% 20.65/9.80 % [INFO] Killing All external provers ...
% 20.65/9.80 % Time passed: 9280ms (effective reasoning time: 8658ms)
% 20.65/9.80 % 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)>
% 20.65/9.80 % Axioms used in derivation (103): fact_49_fun__upd__upd, fact_11_wt, fact_7__096P_Mh_A_092_060turnstile_062_A_IC_M_Afs_J_A_092_060surd_062_096, fact_26_hext__trans, fact_62_hconf__upd__obj, fact_39_preallocated__hext, fact_27_exp_Osimps_I79_J, fact_19_hext__refl, fact_16_oconf__hext, fact_35_hconf__def, fact_23_option_Oinject, fact_65_lconf__upd2, fact_96_map__comp__empty_I2_J, fact_45_oconf__fupd, fact_63_map__upd__eqD1, fact_52_conf__upd__obj, fact_70_lconf__def, fact_2_hconf, fact_95_lconf__empty, fact_85_option_Orecs_I1_J, fact_48_fun__upd__triv, fact_92_typeof__lit__conf, fact_84_map__upd__nonempty, fact_4_RedFAss_I3_J, fact_20_exp_Osimps_I8_J, fact_14_RedFAss_I2_J, fact_43_ospec, fact_6_conf__widen, fact_13_RedFAss_Ohyps, fact_61_fun__upd__idem__iff, fact_22_val_Osimps_I3_J, fact_74_prod__induct5, fact_50_fun__upd__apply, fact_8_typeof__conf, fact_44_preallocated__start, fact_33_split__paired__All, fact_66_lconf__upd, fact_87_option_Osimps_I2_J, fact_94_typeof__lit__is__type, fact_83_empty__upd__none, fact_93_option_Oexhaust, fact_59_fun__upd__twist, fact_56_fun__upd__def, fact_64_map__upd__triv, fact_25_widen__trans, fact_98_map__comp__simps_I1_J, fact_40_prod_Orecs, fact_29_WTrt__hext__mono, fact_57_fun__upd__idem, fact_73_prod__cases5, fact_77_prod__induct4, fact_30_hext__def, fact_41_elem__set, fact_71_prod__induct6, fact_97_map__comp__empty_I1_J, fact_90_preallocated__new, fact_3_has, fact_5__096_B_Bthesis_O_A_I_B_BTF_ATv_O_A_091_124_Atypeof_092_060_094bsub_062h_092_060_094esub_062_Av_A_061_A_092_060lfloor_062Tv_092_060rfloor_062_059_AP_A_092_060turnstile_062_AC_Ahas_AF_058TF_Ain_AD_059_AP_A_092_060turnstile_062_ATv_A_092_060le_062_ATF_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_9_defval__conf, fact_86_option_Osimps_I3_J, fact_53_hext__upd__obj, fact_18_hext__typeof__mono, fact_91_oconf__new, fact_36_the__Addr_Osimps, fact_80_hconf__new, fact_54_preallocated__upd__obj, fact_99_map__comp__simps_I2_J, fact_21_widen__refl, fact_67_PairE, fact_42_option_Orecs_I2_J, fact_51_map__upd__Some__unfold, fact_81_not__None__eq, fact_68_prod__cases3, fact_55_oconf__upd__obj, fact_79_prod__induct3, fact_1_typeofv, fact_76_mem__def, fact_88_typeof__lit__typeof, fact_15_hconfD, help_COMBK_1_1_U, fact_72_prod__cases6, fact_89_hext__new, fact_34_hextI, fact_10_conf__def, fact_60_fun__upd__same, fact_31_hext__objD, fact_12_conf__hext, fact_58_fun__upd__other, fact_46_pred__equals__eq2, fact_24_exp_Osimps_I3_J, fact_32_Pair__eq, fact_0_sub, fact_69_lconf__hext, fact_78_prod__cases4, help_pp_1_1_U, fact_37_Pair__inject, fact_47_prod_Oexhaust, fact_28_exp_Osimps_I78_J, fact_75_ext, fact_38_split__paired__Ex, fact_17_WTrtVal, help_pp_2_1_U, fact_82_not__Some__eq
% 20.65/9.80 % No. of inferences in proof: 210
% 20.65/9.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9280 ms resp. 8658 ms w/o parsing
% 20.86/9.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.86/9.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------