%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW553_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:48 AM UTC 2026
% Result : Theorem 24.38s 10.30s
% Output : Refutation 24.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 104
% Syntax : Number of formulae : 210 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 2062 ( 255 equ; 0 cnn)
% Maximal formula atoms : 47 ( 9 avg)
% Number of connectives : 8724 ( 69 ~; 3 |; 52 &;8373 @)
% ( 20 <=>; 207 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 20 con; 0-6 aty)
% Number of variables : 1026 ( 0 ^;1001 !; 25 ?;1026 :)
% 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_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(conf_decl,type,
conf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > val > ty > $o ) ).
thf(hconf_decl,type,
hconf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > $o ) ).
thf(lconf_decl,type,
lconf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val @ option @ ( char @ list @ fun ) ) > ( ty @ option @ ( char @ list @ fun ) ) > $o ) ).
thf(oconf_decl,type,
oconf:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) ) > $o ) ).
thf(is_type_decl,type,
is_type:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ty > $o ) ).
thf(preallocated_decl,type,
preallocated: ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > $o ).
thf(start_heap_decl,type,
start_heap:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) ) ).
thf(fAss_decl,type,
fAss:
!>[TA: $tType] : ( ( TA @ exp ) > ( char @ list ) > ( char @ list ) > ( TA @ exp ) > ( TA @ exp ) ) ).
thf(val1_decl,type,
val1:
!>[TA: $tType] : ( val > ( TA @ exp ) ) ).
thf(fun_upd_decl,type,
fun_upd:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA > ( TA @ ( TB @ fun ) ) ) ).
thf(map_comp_decl,type,
map_comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ option @ ( TC @ fun ) ) > ( TC @ option @ ( TA @ fun ) ) > TA > ( TB @ option ) ) ).
thf(hext_decl,type,
hext: ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > $o ).
thf(typeof_h_decl,type,
typeof_h: ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > val > ( ty @ option ) ).
thf(none_decl,type,
none:
!>[TA: $tType] : ( TA @ option ) ).
thf(some_decl,type,
some:
!>[TA: $tType] : ( TA > ( TA @ option ) ) ).
thf(option_rec_decl,type,
option_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) > ( TA @ option ) > TB ) ).
thf(set_decl,type,
set:
!>[TA: $tType] : ( ( TA @ option ) > ( bool @ ( TA @ fun ) ) ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(has_field_decl,type,
has_field:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( char @ list ) > ( char @ list ) > ty > ( char @ list ) > $o ) ).
thf(widen_decl,type,
widen:
!>[TA: $tType] : ( ( TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ty > ty > $o ) ).
thf(default_val_decl,type,
default_val: ty > val ).
thf(the_Addr_decl,type,
the_Addr: val > nat ).
thf(addr_decl,type,
addr: nat > val ).
thf(wTrt_decl,type,
wTrt: ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( ty @ option @ ( char @ list @ fun ) ) > ( char @ list @ exp ) > ty > $o ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(c_decl,type,
c: char @ list ).
thf(d_decl,type,
d: char @ list ).
thf(e_decl,type,
e: ty @ option @ ( char @ list @ fun ) ).
thf(f_decl,type,
f: char @ list ).
thf(p_decl,type,
p: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list ).
thf(tf_decl,type,
tf: ty ).
thf(t_decl,type,
t: ty ).
thf(tv_decl,type,
tv: ty ).
thf(a_decl,type,
a: nat ).
thf(fs_decl,type,
fs: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) ).
thf(ha_decl,type,
ha: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(v_decl,type,
v: val ).
thf(70,axiom,
! [TA: $tType,A: ty,B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( A @ default_val @ ( B @ ( C @ ( TA @ conf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_defval__conf) ).
thf(371,plain,
! [TA: $tType,A: ty,B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( A @ default_val @ ( B @ ( C @ ( TA @ conf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ( B @ addr )
= ( A @ addr ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_val_Osimps_I3_J) ).
thf(323,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ addr )
= ( A @ addr ) ) )
& ( ( ( B @ addr )
= ( A @ addr ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB] :
( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
<=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_pred__equals__eq2) ).
thf(482,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ) )
& ( ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(100,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( C @ preallocated )
=> ( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ preallocated ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_preallocated__new) ).
thf(479,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( C @ preallocated )
=> ( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ preallocated ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(62,axiom,
( ( a @ ( ha @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( fs @ ( c @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_RedFAss_Ohyps) ).
thf(347,plain,
( ( a @ ( ha @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( fs @ ( c @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(64,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( C @ ( D @ ( E @ ( TA @ oconf ) ) ) )
=> ( ( ( B @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( E @ ( TA @ oconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_oconf__new) ).
thf(352,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( C @ ( D @ ( E @ ( TA @ oconf ) ) ) )
=> ( ( ( B @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( E @ ( TA @ oconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [TA: $tType,A: val,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_exp_Osimps_I79_J) ).
thf(333,plain,
! [TA: $tType,A: val,B: TA @ exp,C: char @ list,D: char @ list,E: TA @ exp] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ fAss ) ) ) ) )
!= ( A @ ( TA @ val1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ ( TB @ fun )] :
( ( ( A @ ( B @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) )
= C )
<=> ( ( B @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_fun__upd__idem__iff) ).
thf(249,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ ( TB @ fun )] :
( ( ( ( B @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A )
=> ( ( A @ ( B @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) )
= C ) )
& ( ( ( A @ ( B @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) )
= C )
=> ( ( B @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Pair__eq) ).
thf(217,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ option] :
( ( A
!= ( TA @ none ) )
=> ~ ! [B: TA] :
( A
!= ( B @ ( TA @ some ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_option_Oexhaust) ).
thf(308,plain,
! [TA: $tType,A: TA @ option] :
( ( A
!= ( TA @ none ) )
=> ~ ! [B: TA] :
( A
!= ( B @ ( TA @ some ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB @ ( TA @ fun ),C: TA,D: TA] :
( ( ( D != C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
& ( ( D = C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_fun__upd__apply) ).
thf(174,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB @ ( TA @ fun ),C: TA,D: TA] :
( ( ( D != C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
& ( ( D = C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(85,axiom,
( ( v @ ( ha @ typeof_h ) )
= ( tv @ ( ty @ some ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_typeofv) ).
thf(417,plain,
( ( v @ ( ha @ typeof_h ) )
= ( tv @ ( ty @ some ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB @ ( TA @ fun ),C: TA,D: TA] :
( ( D != C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_fun__upd__other) ).
thf(288,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB @ ( TA @ fun ),C: TA,D: TA] :
( ( D != C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(54,axiom,
! [A: ty,B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( C @ ( D @ hext ) )
=> ( ( ( B @ ( D @ typeof_h ) )
= ( A @ ( ty @ some ) ) )
=> ( ( B @ ( C @ typeof_h ) )
= ( A @ ( ty @ some ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_hext__typeof__mono) ).
thf(320,plain,
! [A: ty,B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( C @ ( D @ hext ) )
=> ( ( ( B @ ( D @ typeof_h ) )
= ( A @ ( ty @ some ) ) )
=> ( ( B @ ( C @ typeof_h ) )
= ( A @ ( ty @ some ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(77,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( A @ ( B @ ( TA @ hconf ) ) )
<=> ( ( A @ preallocated )
& ! [C: nat,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod )] :
( ( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( D @ ( A @ ( B @ ( TA @ oconf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_hconf__def) ).
thf(389,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( ( ( A @ preallocated )
& ! [C: nat,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod )] :
( ( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( D @ ( A @ ( B @ ( TA @ oconf ) ) ) ) ) )
=> ( A @ ( B @ ( TA @ hconf ) ) ) )
& ( ( A @ ( B @ ( TA @ hconf ) ) )
=> ( ( A @ preallocated )
& ! [C: nat,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod )] :
( ( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( D @ ( A @ ( B @ ( TA @ oconf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ option] :
( ! [B: TA] :
( A
!= ( B @ ( TA @ some ) ) )
<=> ( A
= ( TA @ none ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_not__Some__eq) ).
thf(110,plain,
! [TA: $tType,A: TA @ option] :
( ( ( A
= ( TA @ none ) )
=> ! [B: TA] :
( A
!= ( B @ ( TA @ some ) ) ) )
& ( ! [B: TA] :
( A
!= ( B @ ( TA @ some ) ) )
=> ( A
= ( TA @ none ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_prod__induct5) ).
thf(344,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: TA @ option @ ( TB @ fun )] :
( ( ( B @ ( C @ ( TA @ some ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some ) ) )
<=> ( ( ( ( B @ ( E @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some ) ) )
& ( B != D ) )
| ( ( C = A )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_map__upd__Some__unfold) ).
thf(152,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: TA @ option @ ( TB @ fun )] :
( ( ( ( ( ( B @ ( E @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some ) ) )
& ( B != D ) )
| ( ( C = A )
& ( B = D ) ) )
=> ( ( B @ ( C @ ( TA @ some ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some ) ) ) )
& ( ( ( B @ ( C @ ( TA @ some ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some ) ) )
=> ( ( ( ( B @ ( E @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some ) ) )
& ( B != D ) )
| ( ( C = A )
& ( B = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(93,axiom,
! [TA: $tType,A: ty,B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),F: char @ list,G: nat,H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( G @ ( H @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( E @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( ( A @ ( B @ ( C @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( D @ ( TA @ conf ) ) ) ) )
<=> ( A @ ( B @ ( H @ ( D @ ( TA @ conf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_conf__upd__obj) ).
thf(448,plain,
! [TA: $tType,A: ty,B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),F: char @ list,G: nat,H: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( G @ ( H @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( E @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( ( ( A @ ( B @ ( H @ ( D @ ( TA @ conf ) ) ) ) )
=> ( A @ ( B @ ( C @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( D @ ( TA @ conf ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( G @ ( H @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( D @ ( TA @ conf ) ) ) ) )
=> ( A @ ( B @ ( H @ ( D @ ( TA @ conf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_fun__upd__triv) ).
thf(211,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
tf @ ( v @ ( ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ conf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( tf @ ( v @ ( ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ conf ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(106,plain,
~ ( tf @ ( v @ ( ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ conf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(78,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list,E: ty,F: char @ list,G: char @ list,H: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( D @ ( E @ ( F @ ( G @ ( H @ ( TA @ has_field ) ) ) ) ) )
=> ( ( E @ ( B @ ( C @ ( H @ ( TA @ conf ) ) ) ) )
=> ( ( A @ ( G @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( C @ ( H @ ( TA @ oconf ) ) ) )
=> ( B @ ( val @ some ) @ ( D @ ( F @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun_upd ) ) ) ) @ ( G @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( C @ ( H @ ( TA @ oconf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_oconf__fupd) ).
thf(397,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: char @ list,E: ty,F: char @ list,G: char @ list,H: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( D @ ( E @ ( F @ ( G @ ( H @ ( TA @ has_field ) ) ) ) ) )
=> ( ( E @ ( B @ ( C @ ( H @ ( TA @ conf ) ) ) ) )
=> ( ( A @ ( G @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( C @ ( H @ ( TA @ oconf ) ) ) )
=> ( B @ ( val @ some ) @ ( D @ ( F @ ( char @ list @ ( char @ list @ product_Pair ) ) ) @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun_upd ) ) ) ) @ ( G @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( C @ ( H @ ( TA @ oconf ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TA @ fun ),B: TA,C: TC,D: TA @ option @ ( TC @ fun )] :
( ( ( C @ ( D @ ( TA @ option @ ( TC @ aa ) ) ) )
= ( B @ ( TA @ some ) ) )
=> ( ( C @ ( D @ ( A @ ( TC @ ( TB @ ( TA @ map_comp ) ) ) ) ) )
= ( B @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_map__comp__simps_I2_J) ).
thf(293,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TA @ fun ),B: TA,C: TC,D: TA @ option @ ( TC @ fun )] :
( ( ( C @ ( D @ ( TA @ option @ ( TC @ aa ) ) ) )
= ( B @ ( TA @ some ) ) )
=> ( ( C @ ( D @ ( A @ ( TC @ ( TB @ ( TA @ map_comp ) ) ) ) ) )
= ( B @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(89,axiom,
! [TA: $tType,A: ty @ option @ ( char @ list @ fun ),B: val @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ lconf ) ) ) ) )
<=> ! [E: char @ list,F: val] :
( ( ( E @ ( B @ ( val @ option @ ( char @ list @ aa ) ) ) )
= ( F @ ( val @ some ) ) )
=> ? [G: ty] :
( ( G @ ( F @ ( C @ ( D @ ( TA @ conf ) ) ) ) )
& ( ( E @ ( A @ ( ty @ option @ ( char @ list @ aa ) ) ) )
= ( G @ ( ty @ some ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_lconf__def) ).
thf(428,plain,
! [TA: $tType,A: ty @ option @ ( char @ list @ fun ),B: val @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( ! [E: char @ list,F: val] :
( ( ( E @ ( B @ ( val @ option @ ( char @ list @ aa ) ) ) )
= ( F @ ( val @ some ) ) )
=> ? [G: ty] :
( ( G @ ( F @ ( C @ ( D @ ( TA @ conf ) ) ) ) )
& ( ( E @ ( A @ ( ty @ option @ ( char @ list @ aa ) ) ) )
= ( G @ ( ty @ some ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ lconf ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ lconf ) ) ) ) )
=> ! [E: char @ list,F: val] :
( ( ( E @ ( B @ ( val @ option @ ( char @ list @ aa ) ) ) )
= ( F @ ( val @ some ) ) )
=> ? [G: ty] :
( ( G @ ( F @ ( C @ ( D @ ( TA @ conf ) ) ) ) )
& ( ( E @ ( A @ ( ty @ option @ ( char @ list @ aa ) ) ) )
= ( G @ ( ty @ some ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ ( TB @ fun )] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_fun__upd__same) ).
thf(265,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ ( TB @ fun )] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(90,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: ty,D: val] :
( ( ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none @ ( nat @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ combk ) ) @ typeof_h ) )
= ( C @ ( ty @ some ) ) )
=> ( C @ ( D @ ( A @ ( B @ ( TA @ conf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_typeof__lit__conf) ).
thf(439,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: ty,D: val] :
( ( ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none @ ( nat @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ combk ) ) @ typeof_h ) )
= ( C @ ( ty @ some ) ) )
=> ( C @ ( D @ ( A @ ( B @ ( TA @ conf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(68,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( C @ ( D @ ( TA @ hconf ) ) )
=> ( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( A @ ( C @ ( D @ ( TA @ oconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_hconfD) ).
thf(366,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( C @ ( D @ ( TA @ hconf ) ) )
=> ( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( A @ ( C @ ( D @ ( TA @ oconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_prod__induct6) ).
thf(380,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(5,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] : ( A @ ( A @ hext ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_hext__refl) ).
thf(117,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] : ( A @ ( A @ hext ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63,axiom,
! [TA: $tType,A: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: ty,C: val,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( C @ ( D @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( B @ ( C @ ( D @ ( A @ ( TA @ conf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_typeof__conf) ).
thf(349,plain,
! [TA: $tType,A: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: ty,C: val,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( C @ ( D @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( B @ ( C @ ( D @ ( A @ ( TA @ conf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: char @ list,G: char @ list,H: TA @ exp] :
( ( ( E @ ( F @ ( G @ ( H @ ( TA @ fAss ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) )
<=> ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_exp_Osimps_I8_J) ).
thf(192,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: TA @ exp,F: char @ list,G: char @ list,H: TA @ exp] :
( ( ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) )
=> ( ( E @ ( F @ ( G @ ( H @ ( TA @ fAss ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ) )
& ( ( ( E @ ( F @ ( G @ ( H @ ( TA @ fAss ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) )
=> ( ( E = A )
& ( F = B )
& ( G = C )
& ( H = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(96,axiom,
! [TA: $tType,A: char @ list,B: ty,C: val,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( D @ ( E @ ( F @ ( G @ ( TA @ lconf ) ) ) ) )
=> ( ( B @ ( C @ ( F @ ( G @ ( TA @ conf ) ) ) ) )
=> ( ( ( A @ ( D @ ( ty @ option @ ( char @ list @ aa ) ) ) )
= ( B @ ( ty @ some ) ) )
=> ( D @ ( C @ ( val @ some ) @ ( A @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) ) ) ) @ ( F @ ( G @ ( TA @ lconf ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_lconf__upd) ).
thf(467,plain,
! [TA: $tType,A: char @ list,B: ty,C: val,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( D @ ( E @ ( F @ ( G @ ( TA @ lconf ) ) ) ) )
=> ( ( B @ ( C @ ( F @ ( G @ ( TA @ conf ) ) ) ) )
=> ( ( ( A @ ( D @ ( ty @ option @ ( char @ list @ aa ) ) ) )
= ( B @ ( ty @ some ) ) )
=> ( D @ ( C @ ( val @ some ) @ ( A @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) ) ) ) @ ( F @ ( G @ ( TA @ lconf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( B @ ( TA @ some ) )
= ( A @ ( TA @ some ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_option_Oinject) ).
thf(229,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ some ) )
= ( A @ ( TA @ some ) ) ) )
& ( ( ( B @ ( TA @ some ) )
= ( A @ ( TA @ some ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_split__paired__All) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(95,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( A @ ( B @ hext ) )
<=> ! [C: nat,D: char @ list,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( ( C @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( E @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ? [F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( F @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_hext__def) ).
thf(456,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ! [C: nat,D: char @ list,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( ( C @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( E @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ? [F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( F @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ) )
=> ( A @ ( B @ hext ) ) )
& ( ( A @ ( B @ hext ) )
=> ! [C: nat,D: char @ list,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( ( C @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( E @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ? [F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( F @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(15,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( A @ ( E @ hext ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ wTrt ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_WTrt__hext__mono) ).
thf(169,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: char @ list @ exp,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( F @ wTrt ) ) ) ) )
=> ( ( A @ ( E @ hext ) )
=> ( B @ ( C @ ( D @ ( A @ ( F @ wTrt ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( TA @ oconf ) ) ) )
=> ( ( A @ ( C @ hext ) )
=> ( B @ ( A @ ( D @ ( TA @ oconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_oconf__hext) ).
thf(141,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( TA @ oconf ) ) ) )
=> ( ( A @ ( C @ hext ) )
=> ( B @ ( A @ ( D @ ( TA @ oconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(103,axiom,
~ ! [A: ty,B: ty] :
( ( ( v @ ( ha @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( ( d @ ( A @ ( f @ ( c @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ) )
=> ~ ( A @ ( B @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) ) ) ),
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(499,plain,
~ ! [A: ty,B: ty] :
( ( ( v @ ( ha @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( ( d @ ( A @ ( f @ ( c @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ) )
=> ~ ( A @ ( B @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(256,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA @ ( TB @ fun ),D: TB,E: TB] :
( ( E != D )
=> ( ( A @ ( D @ ( B @ ( E @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ fun_upd ) ) ) ) )
= ( B @ ( E @ ( A @ ( D @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ fun_upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_fun__upd__twist) ).
thf(124,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA @ ( TB @ fun ),D: TB,E: TB] :
( ( E != D )
=> ( ( A @ ( D @ ( B @ ( E @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ fun_upd ) ) ) ) )
= ( B @ ( E @ ( A @ ( D @ ( C @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ fun_upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(99,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: char @ list,C: nat,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( D @ ( E @ hext ) )
=> ( ( ( C @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ? [F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( C @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( F @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_hext__objD) ).
thf(476,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: char @ list,C: nat,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( D @ ( E @ hext ) )
=> ( ( ( C @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ? [F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( C @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( F @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ option,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
<=> ( A
= ( B @ ( TA @ some ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_elem__set) ).
thf(134,plain,
! [TA: $tType,A: TA @ option,B: TA] :
( ( ( A
= ( B @ ( TA @ some ) ) )
=> ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( A
= ( B @ ( TA @ some ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(59,axiom,
ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_RedFAss_I3_J) ).
thf(343,plain,
ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TB @ some ) ) )
=> ( ( A @ ( TB @ some ) @ ( B @ ( C @ ( TB @ option @ ( TA @ fun_upd ) ) ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_map__upd__triv) ).
thf(205,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TB @ some ) ) )
=> ( ( A @ ( TB @ some ) @ ( B @ ( C @ ( TB @ option @ ( TA @ fun_upd ) ) ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(52,axiom,
! [TA: $tType,A: TA @ option] :
( ( A
!= ( TA @ none ) )
<=> ? [B: TA] :
( A
= ( B @ ( TA @ some ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_not__None__eq) ).
thf(311,plain,
! [TA: $tType,A: TA @ option] :
( ( ? [B: TA] :
( A
= ( B @ ( TA @ some ) ) )
=> ( A
!= ( TA @ none ) ) )
& ( ( A
!= ( TA @ none ) )
=> ? [B: TA] :
( A
= ( B @ ( TA @ some ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(88,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( E @ preallocated )
=> ( ( ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ preallocated ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_preallocated__upd__obj) ).
thf(425,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( E @ preallocated )
=> ( ( ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ preallocated ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( TA @ some ) @ ( B @ ( C @ ( TA @ ( TB @ option_rec ) ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_option_Orecs_I2_J) ).
thf(279,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( TA @ some ) @ ( B @ ( C @ ( TA @ ( TB @ option_rec ) ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(49,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ option] :
( ! [D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member ) ) )
=> ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( C
= ( A @ ( TA @ some ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_ospec) ).
thf(296,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ option] :
( ! [D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member ) ) )
=> ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( C
= ( A @ ( TA @ some ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(73,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( E @ hext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_hext__upd__obj) ).
thf(375,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( E @ hext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(45,axiom,
! [TA: $tType,A: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( TA @ start_heap ) @ preallocated ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_preallocated__start) ).
thf(286,plain,
! [TA: $tType,A: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( TA @ start_heap ) @ preallocated ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,axiom,
! [TA: $tType,A: ty,B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( A @ ( B @ ( TA @ widen ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_widen__refl) ).
thf(291,plain,
! [TA: $tType,A: ty,B: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( A @ ( B @ ( TA @ widen ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_prod_Orecs) ).
thf(259,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_prod__induct3) ).
thf(413,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__cases5) ).
thf(445,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(76,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ! [C: nat,D: char @ list,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( ( C @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( E @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ? [F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( F @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ) )
=> ( A @ ( B @ hext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_hextI) ).
thf(382,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ! [C: nat,D: char @ list,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( ( C @ ( B @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( E @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ? [F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun )] :
( ( C @ ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( F @ ( D @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) ) )
=> ( A @ ( B @ hext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(102,axiom,
t @ ( v @ ( char @ list @ val1 ) @ ( d @ ( f @ ( a @ addr @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_wt) ).
thf(498,plain,
t @ ( v @ ( char @ list @ val1 ) @ ( d @ ( f @ ( a @ addr @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TC @ fun ),B: TC] :
( ( B @ ( A @ ( TA @ none @ ( TB @ ( TA @ option @ combk ) ) @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_map__comp__empty_I2_J) ).
thf(236,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TC @ fun ),B: TC] :
( ( B @ ( A @ ( TA @ none @ ( TB @ ( TA @ option @ combk ) ) @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(18,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ lconf ) ) ) ) )
=> ( ( A @ ( D @ hext ) )
=> ( B @ ( C @ ( A @ ( E @ ( TA @ lconf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_lconf__hext) ).
thf(181,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ option @ ( char @ list @ fun ),C: val @ option @ ( char @ list @ fun ),D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ lconf ) ) ) ) )
=> ( ( A @ ( D @ hext ) )
=> ( B @ ( C @ ( A @ ( E @ ( TA @ lconf ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(80,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( E @ ( F @ ( G @ ( TA @ oconf ) ) ) )
=> ( ( ( D @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( E @ ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( G @ ( TA @ oconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_oconf__upd__obj) ).
thf(406,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( E @ ( F @ ( G @ ( TA @ oconf ) ) ) )
=> ( ( ( D @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( E @ ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( F @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( G @ ( TA @ oconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(41,axiom,
! [A: nat] :
( ( A @ addr @ the_Addr )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_the__Addr_Osimps) ).
thf(274,plain,
! [A: nat] :
( ( A @ addr @ the_Addr )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(86,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: val] :
( ( ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none @ ( nat @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ combk ) ) @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( ( C @ ( A @ typeof_h ) )
= ( B @ ( ty @ some ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_typeof__lit__typeof) ).
thf(419,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty,C: val] :
( ( ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none @ ( nat @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ combk ) ) @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( ( C @ ( A @ typeof_h ) )
= ( B @ ( ty @ some ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(32,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(245,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(53,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(318,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(105,axiom,
ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hconf) ).
thf(509,plain,
ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_prod_Oexhaust) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ some ) )
!= ( TA @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_option_Osimps_I3_J) ).
thf(208,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ some ) )
!= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(79,axiom,
! [TA: $tType,A: ty,B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ conf ) ) ) ) )
<=> ? [E: ty] :
( ( A @ ( E @ ( D @ ( TA @ widen ) ) ) )
& ( ( B @ ( C @ typeof_h ) )
= ( E @ ( ty @ some ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_conf__def) ).
thf(399,plain,
! [TA: $tType,A: ty,B: val,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( ? [E: ty] :
( ( A @ ( E @ ( D @ ( TA @ widen ) ) ) )
& ( ( B @ ( C @ typeof_h ) )
= ( E @ ( ty @ some ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ conf ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ conf ) ) ) ) )
=> ? [E: ty] :
( ( A @ ( E @ ( D @ ( TA @ widen ) ) ) )
& ( ( B @ ( C @ typeof_h ) )
= ( E @ ( ty @ some ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(226,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(98,axiom,
! [A: ty @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: ty,D: val,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( D @ ( E @ typeof_h ) )
= ( C @ ( ty @ some ) ) )
=> ( C @ ( D @ ( char @ list @ val1 ) @ ( A @ ( E @ ( B @ wTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_WTrtVal) ).
thf(473,plain,
! [A: ty @ option @ ( char @ list @ fun ),B: char @ list @ exp @ ( char @ list @ list @ product_prod ) @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,C: ty,D: val,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( D @ ( E @ typeof_h ) )
= ( C @ ( ty @ some ) ) )
=> ( C @ ( D @ ( char @ list @ val1 ) @ ( A @ ( E @ ( B @ wTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(72,axiom,
tf @ ( tv @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_sub) ).
thf(374,plain,
tf @ ( tv @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ widen ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(65,axiom,
! [TA: $tType,A: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: ty,C: val] :
( ( ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none @ ( nat @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ combk ) ) @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( B @ ( A @ ( TA @ is_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_typeof__lit__is__type) ).
thf(355,plain,
! [TA: $tType,A: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,B: ty,C: val] :
( ( ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none @ ( nat @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ combk ) ) @ typeof_h ) )
= ( B @ ( ty @ some ) ) )
=> ( B @ ( A @ ( TA @ is_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= A )
=> ( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun_upd ) ) ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_fun__upd__idem) ).
thf(282,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= A )
=> ( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun_upd ) ) ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(13,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ ( C @ hext ) )
=> ( ( A @ ( B @ hext ) )
=> ( A @ ( C @ hext ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_hext__trans) ).
thf(150,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ ( C @ hext ) )
=> ( ( A @ ( B @ hext ) )
=> ( A @ ( C @ hext ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(81,axiom,
t @ ( v @ ( char @ list @ val1 ) @ ( d @ ( f @ ( a @ addr @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_RedFAss_I2_J) ).
thf(409,plain,
t @ ( v @ ( char @ list @ val1 ) @ ( d @ ( f @ ( a @ addr @ ( char @ list @ val1 ) @ ( char @ list @ fAss ) ) ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(9,axiom,
! [TA: $tType,A: val,B: val] :
( ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_exp_Osimps_I3_J) ).
thf(127,plain,
! [TA: $tType,A: val,B: val] :
( ( ( B = A )
=> ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) ) )
& ( ( ( B @ ( TA @ val1 ) )
= ( A @ ( TA @ val1 ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(97,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( C @ hext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_hext__new) ).
thf(470,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( C @ hext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_split__paired__Ex) ).
thf(336,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB @ ( TA @ fun ),C: TA,D: TA] :
( ( ( D != C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
& ( ( D = C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_fun__upd__def) ).
thf(143,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB @ ( TA @ fun ),C: TA,D: TA] :
( ( ( D != C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
& ( ( D = C )
=> ( ( D @ ( A @ ( C @ ( B @ ( TB @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(50,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(304,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Pair__inject) ).
thf(186,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB] :
( ( B @ ( TA @ none @ ( A @ ( TA @ none @ ( TB @ ( TA @ option @ combk ) ) @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_empty__upd__none) ).
thf(171,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB] :
( ( B @ ( TA @ none @ ( A @ ( TA @ none @ ( TB @ ( TA @ option @ combk ) ) @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ option @ ( TB @ fun ),B: TC,C: TB @ option @ ( TC @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( TB @ none ) )
=> ( ( B @ ( C @ ( A @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_map__comp__simps_I1_J) ).
thf(246,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ option @ ( TB @ fun ),B: TC,C: TB @ option @ ( TC @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( TB @ none ) )
=> ( ( B @ ( C @ ( A @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(61,axiom,
d @ ( tf @ ( f @ ( c @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_has) ).
thf(346,plain,
d @ ( tf @ ( f @ ( c @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ has_field ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ option @ ( TB @ fun )] :
~ ! [D: TB] :
( ( D @ ( A @ ( TA @ some ) @ ( B @ ( C @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_map__upd__nonempty) ).
thf(214,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ option @ ( TB @ fun )] :
~ ! [D: TB] :
( ( D @ ( A @ ( TA @ some ) @ ( B @ ( C @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_exp_Osimps_I78_J) ).
thf(119,plain,
! [TA: $tType,A: TA @ exp,B: char @ list,C: char @ list,D: TA @ exp,E: val] :
( ( E @ ( TA @ val1 ) )
!= ( A @ ( B @ ( C @ ( D @ ( TA @ fAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,axiom,
! [TA: $tType,A: ty,B: ty,C: val,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ conf ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( TA @ widen ) ) ) )
=> ( A @ ( C @ ( D @ ( E @ ( TA @ conf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conf__widen) ).
thf(378,plain,
! [TA: $tType,A: ty,B: ty,C: val,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( E @ ( TA @ conf ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( TA @ widen ) ) ) )
=> ( A @ ( C @ ( D @ ( E @ ( TA @ conf ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_prod__cases3) ).
thf(410,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ option @ ( TB @ fun ),C: TA,D: TB,E: TA @ option @ ( TB @ fun )] :
( ( ( C @ ( TA @ some ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) )
= ( A @ ( TA @ some ) @ ( D @ ( B @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_map__upd__eqD1) ).
thf(262,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ option @ ( TB @ fun ),C: TA,D: TB,E: TA @ option @ ( TB @ fun )] :
( ( ( C @ ( TA @ some ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) )
= ( A @ ( TA @ some ) @ ( D @ ( B @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ option @ ( TB @ fun ),B: TC] :
( ( B @ ( TB @ none @ ( TC @ ( TB @ option @ combk ) ) @ ( A @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_map__comp__empty_I1_J) ).
thf(183,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ option @ ( TB @ fun ),B: TC] :
( ( B @ ( TB @ none @ ( TC @ ( TB @ option @ combk ) ) @ ( A @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_prod__cases4) ).
thf(422,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(71,axiom,
fs @ ( c @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ oconf ) ) ),
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(373,plain,
fs @ ( c @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ oconf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: TA] :
( ( TB @ none @ ( A @ ( B @ ( TB @ ( TA @ option_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_option_Orecs_I1_J) ).
thf(107,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: TA] :
( ( TB @ none @ ( A @ ( B @ ( TB @ ( TA @ option_rec ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(58,axiom,
! [TA: $tType,A: ty @ option @ ( char @ list @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( val @ none @ ( char @ list @ ( val @ option @ combk ) ) @ ( B @ ( C @ ( TA @ lconf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_lconf__empty) ).
thf(341,plain,
! [TA: $tType,A: ty @ option @ ( char @ list @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),C: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] : ( A @ ( val @ none @ ( char @ list @ ( val @ option @ combk ) ) @ ( B @ ( C @ ( TA @ lconf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(66,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( E @ ( F @ ( TA @ hconf ) ) )
=> ( ( ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ oconf ) ) ) )
=> ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( F @ ( TA @ hconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_hconf__upd__obj) ).
thf(358,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ),C: char @ list,D: nat,E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),F: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( E @ ( F @ ( TA @ hconf ) ) )
=> ( ( ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) ) )
=> ( ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( E @ ( F @ ( TA @ oconf ) ) ) )
=> ( A @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( F @ ( TA @ hconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(84,axiom,
! [TA: $tType,A: ty,B: val,C: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( D @ ( E @ hext ) )
=> ( ( A @ ( B @ ( E @ ( C @ ( TA @ conf ) ) ) ) )
=> ( A @ ( B @ ( D @ ( C @ ( TA @ conf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_conf__hext) ).
thf(415,plain,
! [TA: $tType,A: ty,B: val,C: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list,D: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),E: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( D @ ( E @ hext ) )
=> ( ( A @ ( B @ ( E @ ( C @ ( TA @ conf ) ) ) ) )
=> ( A @ ( B @ ( D @ ( C @ ( TA @ conf ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(30,axiom,
! [TA: $tType,A: TA] :
( ( TA @ none )
!= ( A @ ( TA @ some ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_option_Osimps_I2_J) ).
thf(239,plain,
! [TA: $tType,A: TA] :
( ( TA @ none )
!= ( A @ ( TA @ some ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_PairE) ).
thf(242,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(104,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( C @ ( D @ ( TA @ hconf ) ) )
=> ( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( ( A @ ( C @ ( D @ ( TA @ oconf ) ) ) )
=> ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( D @ ( TA @ hconf ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_hconf__new) ).
thf(506,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ),B: nat,C: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( C @ ( D @ ( TA @ hconf ) ) )
=> ( ( ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ aa ) ) ) )
= ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ none ) )
=> ( ( A @ ( C @ ( D @ ( TA @ oconf ) ) ) )
=> ( A @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ some ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( D @ ( TA @ hconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: TA @ ( TB @ fun )] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ fun_upd ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ fun_upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_fun__upd__upd) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: TA @ ( TB @ fun )] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( TA @ ( TB @ fun_upd ) ) ) ) @ ( TA @ ( TB @ fun_upd ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ fun_upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ preallocated )
=> ( ( A @ ( B @ hext ) )
=> ( A @ preallocated ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_preallocated__hext) ).
thf(277,plain,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( B @ preallocated )
=> ( ( A @ ( B @ hext ) )
=> ( A @ preallocated ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod__cases6) ).
thf(442,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(69,axiom,
! [TA: $tType,A: char @ list,B: ty,C: val,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( D @ ( E @ ( F @ ( G @ ( TA @ lconf ) ) ) ) )
=> ( ( B @ ( C @ ( F @ ( G @ ( TA @ conf ) ) ) ) )
=> ( B @ ( ty @ some ) @ ( A @ ( D @ ( ty @ option @ ( char @ list @ fun_upd ) ) ) ) @ ( C @ ( val @ some ) @ ( A @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) ) ) ) @ ( F @ ( G @ ( TA @ lconf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_lconf__upd2) ).
thf(369,plain,
! [TA: $tType,A: char @ list,B: ty,C: val,D: ty @ option @ ( char @ list @ fun ),E: val @ option @ ( char @ list @ fun ),F: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),G: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( D @ ( E @ ( F @ ( G @ ( TA @ lconf ) ) ) ) )
=> ( ( B @ ( C @ ( F @ ( G @ ( TA @ conf ) ) ) ) )
=> ( B @ ( ty @ some ) @ ( A @ ( D @ ( ty @ option @ ( char @ list @ fun_upd ) ) ) ) @ ( C @ ( val @ some ) @ ( A @ ( E @ ( val @ option @ ( char @ list @ fun_upd ) ) ) ) @ ( F @ ( G @ ( TA @ lconf ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(7,axiom,
! [TA: $tType,A: ty,B: ty,C: ty,D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( TA @ widen ) ) ) )
=> ( ( A @ ( B @ ( D @ ( TA @ widen ) ) ) )
=> ( A @ ( C @ ( D @ ( TA @ widen ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_widen__trans) ).
thf(122,plain,
! [TA: $tType,A: ty,B: ty,C: ty,D: TA @ ( ty @ product_prod ) @ ( ty @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list @ ( ty @ ( char @ list @ product_prod ) @ list @ product_prod ) @ ( char @ list @ product_prod ) @ ( char @ list @ product_prod ) @ list] :
( ( B @ ( C @ ( D @ ( TA @ widen ) ) ) )
=> ( ( A @ ( B @ ( D @ ( TA @ widen ) ) ) )
=> ( A @ ( C @ ( D @ ( TA @ widen ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_prod__induct4) ).
thf(454,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(527,plain,
$false,
inference(e,[status(thm)],[371,323,482,479,347,352,333,249,217,308,174,417,288,320,389,110,344,152,448,211,106,397,293,428,265,439,366,380,117,349,192,467,229,361,456,169,141,499,256,124,476,134,343,205,311,425,279,296,375,286,291,259,413,445,382,498,236,181,406,274,419,245,318,509,271,208,399,226,473,374,355,282,150,409,127,470,336,143,304,186,171,246,346,214,119,378,410,262,183,422,373,107,341,358,415,239,242,506,268,277,442,369,122,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW553_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.62 % Computer : n008.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sat Sep 26 16:13:27 UTC 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.63 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.94/1.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.60/1.46 % [INFO] Parsing done (322ms).
% 1.60/1.47 % [INFO] Running in sequential loop mode.
% 2.88/1.87 % [INFO] eprover registered as external prover.
% 2.88/1.88 % [INFO] Scanning for conjecture ...
% 3.60/2.06 % [INFO] Found a conjecture (or negated_conjecture) and 103 axioms. Running axiom selection ...
% 3.98/2.19 % [INFO] Axiom selection finished. Selected 103 axioms (removed 0 axioms).
% 5.03/2.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.38/2.52 % [INFO] Type checking passed.
% 5.38/2.52 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 23.70/10.30 % External prover 'e' found a proof!
% 24.38/10.30 % [INFO] Killing All external provers ...
% 24.38/10.30 % Time passed: 9574ms (effective reasoning time: 8817ms)
% 24.38/10.30 % 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)>
% 24.38/10.30 % 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
% 24.38/10.30 % No. of inferences in proof: 210
% 24.38/10.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9574 ms resp. 8817 ms w/o parsing
% 24.82/10.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.82/10.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------