%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW551_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 76.70s 59.77s
% Output : Refutation 77.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 117
% Syntax : Number of formulae : 236 ( 86 unt; 0 typ; 0 def)
% Number of atoms : 2796 ( 320 equ; 0 cnn)
% Maximal formula atoms : 46 ( 11 avg)
% Number of connectives : 9501 ( 86 ~; 36 |; 59 &;9100 @)
% ( 22 <=>; 198 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 19 con; 0-6 aty)
% Number of variables : 954 ( 0 ^; 923 !; 31 ?; 954 :)
% 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(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
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(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(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(new_decl,type,
new:
!>[TA: $tType] : ( ( char @ list ) > ( 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(ran_decl,type,
ran:
!>[TA: $tType,TB: $tType] : ( ( TA @ option @ ( TB @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
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(init_fields_decl,type,
init_fields: ( ty @ ( char @ list @ ( char @ list @ product_prod ) @ product_prod ) @ list ) > ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) ) ).
thf(new_Addr_decl,type,
new_Addr: ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ) > ( nat @ option ) ).
thf(bind_decl,type,
bind:
!>[TA: $tType,TB: $tType] : ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ fun ) @ ( TB @ option @ fun ) ) ).
thf(is_none_decl,type,
is_none:
!>[TA: $tType] : ( ( TA @ option ) > $o ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TA @ option @ ( TB @ option @ fun ) ) ) ).
thf(none_decl,type,
none:
!>[TA: $tType] : ( TA @ option ) ).
thf(some_decl,type,
some:
!>[TA: $tType] : ( TA @ option @ ( TA @ fun ) ) ).
thf(option_case_decl,type,
option_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) > ( TB @ ( TA @ option @ fun ) ) ) ).
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(quickcheck_orelse_decl,type,
quickcheck_orelse:
!>[TA: $tType] : ( ( TA @ option ) > ( TA @ option ) > ( TA @ option ) ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(fields_decl,type,
fields:
!>[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 ) > ( ty @ ( char @ list @ ( char @ list @ product_prod ) @ product_prod ) @ list ) > $o ) ).
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(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(fimplies_decl,type,
fimplies: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(c_decl,type,
c: char @ list ).
thf(e_decl,type,
e: ty @ option @ ( char @ list @ fun ) ).
thf(fDTs_decl,type,
fDTs: ty @ ( char @ list @ ( char @ list @ product_prod ) @ product_prod ) @ 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(t_decl,type,
t: ty ).
thf(a_decl,type,
a: nat ).
thf(h_a_decl,type,
h_a: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(ha_decl,type,
ha: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(343,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(365,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',fact_29_map__comp__simps_I1_J) ).
thf(479,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)],[97]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_17_empty__upd__none) ).
thf(333,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)],[57]) ).
thf(77,axiom,
( ( ha @ new_Addr )
= ( a @ ( nat @ some @ ( nat @ option @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_RedNew_I1_J) ).
thf(408,plain,
( ( ha @ new_Addr )
= ( a @ ( nat @ some @ ( nat @ option @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(36,axiom,
! [TA: $tType,A: TA @ option] :
( ( A
!= ( TA @ none ) )
=> ~ ! [B: TA] :
( A
!= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_option_Oexhaust) ).
thf(247,plain,
! [TA: $tType,A: TA @ option] :
( ( A
!= ( TA @ none ) )
=> ~ ! [B: TA] :
( A
!= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_54_prod_Orecs) ).
thf(440,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)],[88]) ).
thf(109,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_insert__absorb) ).
thf(533,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(94,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_57_hconf__new) ).
thf(472,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[94]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(340,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)],[60]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',fact_72_preallocated__hext) ).
thf(185,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)],[21]) ).
thf(86,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( E @ hext ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_hext__upd__obj) ).
thf(436,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[86]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ option @ ( TB @ fun )] :
~ ! [D: TB] :
( ( D @ ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_map__upd__nonempty) ).
thf(257,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA @ option @ ( TB @ fun )] :
~ ! [D: TB] :
( ( D @ ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: TB @ option @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ bind ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ aa ) ) ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_bind__lunit) ).
thf(570,plain,
! [TA: $tType,TB: $tType,A: TB @ option @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ bind ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ aa ) ) ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(69,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ ( C @ hext ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_hext__new) ).
thf(372,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[69]) ).
thf(23,axiom,
! [A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] : ( A @ ( A @ hext ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_hext__refl) ).
thf(189,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)],[23]) ).
thf(80,axiom,
! [TA: $tType,A: TA] :
( ( TA @ none )
!= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_option_Osimps_I2_J) ).
thf(416,plain,
! [TA: $tType,A: TA] :
( ( TA @ none )
!= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(10,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insert__compr) ).
thf(152,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ? [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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_hext__objD) ).
thf(228,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ? [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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',fact_42_split__paired__All) ).
thf(316,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)],[52]) ).
thf(95,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(475,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: TA] :
( ( TB @ none @ ( A @ ( B @ ( TB @ ( TA @ option_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_option_Orecs_I1_J) ).
thf(164,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)],[15]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',fact_48_fun__upd__other) ).
thf(443,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)],[89]) ).
thf(53,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C != B )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insertE) ).
thf(321,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C != B )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(29,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ? [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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_hext__def) ).
thf(211,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ? [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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ? [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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_19_map__comp__empty_I1_J) ).
thf(238,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)],[34]) ).
thf(3,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(121,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(397,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TA @ option,B: TB @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TB @ ( TA @ map ) ) @ ( TB @ option @ ( TA @ option @ aa ) ) ) )
= ( TB @ none ) )
<=> ( A
= ( TA @ none ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_option__map__is__None) ).
thf(280,plain,
! [TA: $tType,TB: $tType,A: TA @ option,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ none ) )
=> ( ( A @ ( B @ ( TB @ ( TA @ map ) ) @ ( TB @ option @ ( TA @ option @ aa ) ) ) )
= ( TB @ none ) ) )
& ( ( ( A @ ( B @ ( TB @ ( TA @ map ) ) @ ( TB @ option @ ( TA @ option @ aa ) ) ) )
= ( TB @ none ) )
=> ( A
= ( TA @ none ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [TA: $tType,A: char @ list,B: char @ list] :
( ( ( B @ ( TA @ new ) )
= ( A @ ( TA @ new ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_exp_Osimps_I1_J) ).
thf(133,plain,
! [TA: $tType,A: char @ list,B: char @ list] :
( ( ( B = A )
=> ( ( B @ ( TA @ new ) )
= ( A @ ( TA @ new ) ) ) )
& ( ( ( B @ ( TA @ new ) )
= ( A @ ( TA @ new ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(87,axiom,
ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_RedNew_I5_J) ).
thf(439,plain,
ha @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ hconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(42,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(270,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(112,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun ),D: TA] :
( ~ ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( C @ ( D @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) )
<=> ( ( ( D != B )
=> ? [E: bool @ ( TA @ fun )] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( E @ ( D @ ( TA @ insert ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_insert__eq__iff) ).
thf(546,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun ),D: TA] :
( ~ ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( ( ( D != B )
=> ? [E: bool @ ( TA @ fun )] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( E @ ( D @ ( TA @ insert ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) )
=> ( ( C @ ( D @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) )
=> ( ( ( D != B )
=> ? [E: bool @ ( TA @ fun )] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( E @ ( D @ ( TA @ insert ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB @ option @ ( TC @ fun ),C: TA @ option @ ( TB @ fun )] :
( ( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) )
<=> ( ? [D: TB] :
( ( ( D @ ( C @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) )
& ( ( A @ ( B @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( D @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) )
| ( ( A @ ( B @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( TB @ none ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_map__comp__None__iff) ).
thf(201,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB @ option @ ( TC @ fun ),C: TA @ option @ ( TB @ fun )] :
( ( ( ? [D: TB] :
( ( ( D @ ( C @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) )
& ( ( A @ ( B @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( D @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) )
| ( ( A @ ( B @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( TB @ none ) ) )
=> ( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) ) )
& ( ( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( TA @ none ) )
=> ( ? [D: TB] :
( ( ( D @ ( C @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( TA @ none ) )
& ( ( A @ ( B @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( D @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) )
| ( ( A @ ( B @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( TB @ none ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(13,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(160,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(72,axiom,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ ( char @ list @ ( char @ list @ product_prod ) @ product_prod ) @ list,C: char @ list,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 @ fields ) ) ) )
=> ( B @ init_fields @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( A @ ( D @ ( TA @ oconf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_oconf__init__fields) ).
thf(392,plain,
! [TA: $tType,A: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun ),B: ty @ ( char @ list @ ( char @ list @ product_prod ) @ product_prod ) @ list,C: char @ list,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 @ fields ) ) ) )
=> ( B @ init_fields @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_Pair ) ) ) @ ( A @ ( D @ ( TA @ oconf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(83,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(424,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(85,axiom,
! [TA: $tType,A: TA @ option] :
( ( A
!= ( TA @ none ) )
<=> ? [B: TA] :
( A
= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_not__None__eq) ).
thf(429,plain,
! [TA: $tType,A: TA @ option] :
( ( ? [B: TA] :
( A
= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( A
!= ( TA @ none ) ) )
& ( ( A
!= ( TA @ none ) )
=> ? [B: TA] :
( A
= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(44,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( B @ pp )
| ~ ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(275,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( B @ pp )
| ~ ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_47_fun__upd__idem) ).
thf(260,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)],[39]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',fact_46_fun__upd__def) ).
thf(349,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)],[63]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( B @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_insert__ident) ).
thf(484,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(329,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(101,axiom,
t @ ( c @ ( char @ list @ new ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_RedNew_I4_J) ).
thf(493,plain,
t @ ( c @ ( char @ list @ new ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: TA] :
( ( TB @ none @ ( A @ ( B @ ( TB @ ( TA @ option_case ) ) ) @ ( TA @ ( TB @ option @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_option_Osimps_I4_J) ).
thf(324,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: TA] :
( ( TB @ none @ ( A @ ( B @ ( TB @ ( TA @ option_case ) ) ) @ ( TA @ ( TB @ option @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(356,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',fact_43_Pair__eq) ).
thf(169,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)],[17]) ).
thf(118,axiom,
! [A: nat,B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( B @ new_Addr )
= ( A @ ( nat @ some @ ( nat @ option @ ( nat @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_new__Addr__SomeD) ).
thf(593,plain,
! [A: nat,B: val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun )] :
( ( ( B @ new_Addr )
= ( A @ ( nat @ some @ ( nat @ option @ ( nat @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_50_fun__upd__same) ).
thf(499,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)],[104]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_51_fun__upd__idem__iff) ).
thf(526,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)],[108]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ none @ ( A @ ( TA @ ( TB @ map ) ) @ ( TA @ option @ ( TB @ option @ aa ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_option__map__None) ).
thf(590,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ none @ ( A @ ( TA @ ( TB @ map ) ) @ ( TA @ option @ ( TB @ option @ aa ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ option] :
( ( A @ ( TA @ is_none ) )
<=> ( A
= ( TA @ none ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_is__none__def) ).
thf(124,plain,
! [TA: $tType,A: TA @ option] :
( ( ( A
= ( TA @ none ) )
=> ( A @ ( TA @ is_none ) ) )
& ( ( A @ ( TA @ is_none ) )
=> ( A
= ( TA @ none ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun )] :
( ( A @ ( TB @ ( TA @ map ) ) )
= ( A @ ( TB @ some @ ( TA @ ( TB @ option @ ( TB @ combb ) ) ) ) @ ( TB @ none @ ( TA @ ( TB @ option @ option_case ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Option_Omap__def) ).
thf(225,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun )] :
( ( A @ ( TB @ ( TA @ map ) ) )
= ( A @ ( TB @ some @ ( TA @ ( TB @ option @ ( TB @ combb ) ) ) ) @ ( TB @ none @ ( TA @ ( TB @ option @ option_case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(264,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',fact_49_fun__upd__twist) ).
thf(161,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)],[14]) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ option] :
( ! [D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( C
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_ospec) ).
thf(573,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ option] :
( ! [D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( C
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(9,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_insert__commute) ).
thf(149,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(70,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( D @ ( A @ ( B @ ( TA @ oconf ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_hconf__def) ).
thf(375,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( D @ ( A @ ( B @ ( TA @ oconf ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insertCI) ).
thf(584,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',fact_39_fun__upd__upd) ).
thf(191,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)],[24]) ).
thf(79,axiom,
! [TA: $tType,A: TA @ option,B: TA @ option] :
( ( A @ ( B @ ( TA @ quickcheck_orelse ) ) )
= ( B @ ( TA @ some @ ( A @ ( TA @ ( TA @ option @ option_case ) ) ) @ ( TA @ option @ ( TA @ option @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_) ).
thf(413,plain,
! [TA: $tType,A: TA @ option,B: TA @ option] :
( ( A @ ( B @ ( TA @ quickcheck_orelse ) ) )
= ( B @ ( TA @ some @ ( A @ ( TA @ ( TA @ option @ option_case ) ) ) @ ( TA @ option @ ( TA @ option @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(92,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) )
!= ( TA @ none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_option_Osimps_I3_J) ).
thf(466,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) )
!= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_67_hext__trans) ).
thf(181,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)],[19]) ).
thf(22,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(187,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(81,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( B @ ( C @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ preallocated ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_preallocated__new) ).
thf(419,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[81]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ option_case ) ) ) @ ( TB @ ( TA @ option @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_option_Osimps_I5_J) ).
thf(362,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ option_case ) ) ) @ ( TB @ ( TA @ option @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_insert__iff) ).
thf(509,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) )
=> ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(49,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_60_oconf__upd__obj) ).
thf(303,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[49]) ).
thf(96,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] : ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_insertI1) ).
thf(477,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] : ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(102,axiom,
( h_a
= ( fDTs @ init_fields @ ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( a @ ( ha @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_RedNew_I3_J) ).
thf(494,plain,
( h_a
= ( fDTs @ init_fields @ ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( a @ ( ha @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',fact_45_Pair__inject) ).
thf(140,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)],[7]) ).
thf(11,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( TA @ collect ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fimplies @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insert__Collect) ).
thf(155,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( TA @ collect ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fimplies @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ option_rec ) ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_option_Orecs_I2_J) ).
thf(198,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ option_rec ) ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(41,axiom,
! [TA: $tType,A: TA @ option] :
( ( TA @ some @ ( A @ ( TA @ ( TA @ bind ) @ ( TA @ option @ ( TA @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TA @ fun ) @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_bind__runit) ).
thf(267,plain,
! [TA: $tType,A: TA @ option] :
( ( TA @ some @ ( A @ ( TA @ ( TA @ bind ) @ ( TA @ option @ ( TA @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TA @ fun ) @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB,C: bool @ ( TB @ fun ),D: TA @ option,E: bool @ ( TA @ fun ),F: bool] :
( ( D @ ( E @ ( F @ ( TA @ ( bool @ option_case ) ) ) @ ( bool @ ( TA @ option @ aa ) ) ) @ pp )
=> ( ( ( F @ pp )
=> ( B @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( ! [G: TA] :
( ( G @ ( E @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( G @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( D @ ( A @ ( B @ ( TA @ ( TB @ option_case ) ) ) @ ( TB @ ( TA @ option @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_disjE__realizer2) ).
thf(241,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB,C: bool @ ( TB @ fun ),D: TA @ option,E: bool @ ( TA @ fun ),F: bool] :
( ( D @ ( E @ ( F @ ( TA @ ( bool @ option_case ) ) ) @ ( bool @ ( TA @ option @ aa ) ) ) @ pp )
=> ( ( ( F @ pp )
=> ( B @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( ! [G: TA] :
( ( G @ ( E @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( G @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( D @ ( A @ ( B @ ( TA @ ( TB @ option_case ) ) ) @ ( TB @ ( TA @ option @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',fact_68_oconf__hext) ).
thf(167,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)],[16]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TB @ option] :
( ( TA @ none @ ( TB @ ( TA @ option @ combk ) ) @ ( A @ ( TA @ ( TB @ bind ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ fun ) @ ( TB @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_bind__rzero) ).
thf(394,plain,
! [TA: $tType,TB: $tType,A: TB @ option] :
( ( TA @ none @ ( TB @ ( TA @ option @ combk ) ) @ ( A @ ( TA @ ( TB @ bind ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ fun ) @ ( TB @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TA @ fun ),B: TA @ option @ ( TC @ fun ),C: TC @ option] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ bind ) @ ( TA @ option @ ( TA @ option @ ( TC @ fun ) @ fun ) @ ( TC @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ bind ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ aa ) ) ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ bind ) @ ( TC @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ combb ) ) ) ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ ( TC @ combc ) ) ) ) @ ( C @ ( TB @ ( TC @ bind ) @ ( TB @ option @ ( TB @ option @ ( TC @ fun ) @ fun ) @ ( TC @ option @ aa ) ) ) @ ( TB @ option @ ( TB @ option @ ( TC @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_bind__assoc) ).
thf(306,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TA @ fun ),B: TA @ option @ ( TC @ fun ),C: TC @ option] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ bind ) @ ( TA @ option @ ( TA @ option @ ( TC @ fun ) @ fun ) @ ( TC @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ bind ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ aa ) ) ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ bind ) @ ( TC @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ fun ) @ ( TA @ option @ combb ) ) ) ) @ ( TB @ option @ ( TB @ option @ ( TA @ fun ) @ ( TC @ combc ) ) ) ) @ ( C @ ( TB @ ( TC @ bind ) @ ( TB @ option @ ( TB @ option @ ( TC @ fun ) @ fun ) @ ( TC @ option @ aa ) ) ) @ ( TB @ option @ ( TB @ option @ ( TC @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( TB @ ( TA @ map ) ) @ ( TB @ option @ ( TA @ option @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_option__map__Some) ).
thf(426,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( B @ ( TB @ ( TA @ map ) ) @ ( TB @ option @ ( TA @ option @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(25,axiom,
fDTs @ ( c @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ fields ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_RedNew_I2_J) ).
thf(194,plain,
fDTs @ ( c @ ( p @ ( char @ list @ exp @ ( char @ list @ list @ product_prod ) @ fields ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_insert__code) ).
thf(295,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(55,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(327,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(105,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_option_Oinject) ).
thf(502,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_20_map__comp__empty_I2_J) ).
thf(463,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)],[91]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_insertI2) ).
thf(338,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(65,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( D @ ( E @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( nat @ fun_upd ) ) ) ) @ preallocated ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_preallocated__upd__obj) ).
thf(359,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[65]) ).
thf(58,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(336,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: TA @ option @ ( TB @ fun )] :
( ( ( B @ ( C @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
<=> ( ( ( ( B @ ( E @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
& ( B != D ) )
| ( ( C = A )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_map__upd__Some__unfold) ).
thf(446,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 @ ( TA @ option @ ( TA @ aa ) ) ) ) )
& ( B != D ) )
| ( ( C = A )
& ( B = D ) ) )
=> ( ( B @ ( C @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( ( ( ( B @ ( E @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
& ( B != D ) )
| ( ( C = A )
& ( B = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(111,axiom,
! [TA: $tType,A: TA @ option] :
( ! [B: TA] :
( A
!= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
<=> ( A
= ( TA @ none ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_not__Some__eq) ).
thf(539,plain,
! [TA: $tType,A: TA @ option] :
( ( ( A
= ( TA @ none ) )
=> ! [B: TA] :
( A
!= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) )
& ( ! [B: TA] :
( A
!= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( A
= ( TA @ none ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(98,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(482,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(115,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_58_hconf__upd__obj) ).
thf(581,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( ( 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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[115]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ option,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_elem__set) ).
thf(250,plain,
! [TA: $tType,A: TA @ option,B: TA] :
( ( ( A
= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( B @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(33,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ? [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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) ) )
=> ( A @ ( B @ hext ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_hextI) ).
thf(231,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ? [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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) ) )
=> ( A @ ( B @ hext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB @ option,C: TA @ ( TB @ fun )] :
( ( ( B @ ( C @ ( TA @ ( TB @ map ) ) @ ( TA @ option @ ( TB @ option @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
<=> ? [D: TB] :
( ( ( D @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A )
& ( B
= ( D @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_option__map__eq__Some) ).
thf(517,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB @ option,C: TA @ ( TB @ fun )] :
( ( ? [D: TB] :
( ( ( D @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A )
& ( B
= ( D @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) )
=> ( ( B @ ( C @ ( TA @ ( TB @ map ) ) @ ( TA @ option @ ( TB @ option @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ ( TB @ map ) ) @ ( TA @ option @ ( TB @ option @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ? [D: TB] :
( ( ( D @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A )
& ( B
= ( D @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(12,axiom,
! [TA: $tType] : ( TA @ none @ ( TA @ is_none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_is__none__code_I1_J) ).
thf(158,plain,
! [TA: $tType] : ( TA @ none @ ( TA @ is_none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
( ( ha @ new_Addr )
= ( a @ ( nat @ some @ ( nat @ option @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ha @ new_Addr )
!= ( a @ ( nat @ some @ ( nat @ option @ ( nat @ aa ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
( ( ha @ new_Addr )
!= ( a @ ( nat @ some @ ( nat @ option @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TA @ fun ),B: TC @ option @ ( TB @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TA @ ( TC @ ( TB @ map_comp ) ) ) ) ) )
= ( C @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) @ ( B @ ( TC @ none @ ( TB @ ( TC @ option @ option_case ) ) ) @ ( TC @ option @ ( TB @ option @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_map__comp__def) ).
thf(272,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ option @ ( TA @ fun ),B: TC @ option @ ( TB @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TA @ ( TC @ ( TB @ map_comp ) ) ) ) ) )
= ( C @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) @ ( B @ ( TC @ none @ ( TB @ ( TC @ option @ option_case ) ) ) @ ( TC @ option @ ( TB @ option @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ option,B: bool @ ( TA @ fun ),C: bool] :
( ( A @ ( B @ ( C @ ( TA @ ( bool @ option_case ) ) ) @ ( bool @ ( TA @ option @ aa ) ) ) @ pp )
=> ( ( ( A
= ( TA @ none ) )
=> ~ ( C @ pp ) )
=> ~ ! [D: TA] :
( ( A
= ( D @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ~ ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_option__caseE) ).
thf(383,plain,
! [TA: $tType,A: TA @ option,B: bool @ ( TA @ fun ),C: bool] :
( ( A @ ( B @ ( C @ ( TA @ ( bool @ option_case ) ) ) @ ( bool @ ( TA @ option @ aa ) ) ) @ pp )
=> ( ( ( A
= ( TA @ none ) )
=> ~ ( C @ pp ) )
=> ~ ! [D: TA] :
( ( A
= ( D @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ~ ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(62,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( A @ ( C @ ( D @ ( TA @ oconf ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_hconfD) ).
thf(346,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) ) )
=> ( A @ ( C @ ( D @ ( TA @ oconf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(110,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 @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( ( C @ ( D @ ( A @ ( TC @ ( TB @ ( TA @ map_comp ) ) ) ) ) )
= ( B @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_map__comp__simps_I2_J) ).
thf(536,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 @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ( ( C @ ( D @ ( A @ ( TC @ ( TB @ ( TA @ map_comp ) ) ) ) ) )
= ( B @ ( A @ ( TB @ option @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ option @ ( TC @ fun ),D: TA @ option @ ( TB @ fun )] :
( ( ( B @ ( C @ ( D @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
<=> ? [E: TB] :
( ( ( E @ ( D @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
& ( ( B @ ( C @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( E @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_map__comp__Some__iff) ).
thf(287,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ option @ ( TC @ fun ),D: TA @ option @ ( TB @ fun )] :
( ( ? [E: TB] :
( ( ( E @ ( D @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
& ( ( B @ ( C @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( E @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) )
=> ( ( B @ ( C @ ( D @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( TC @ ( TA @ ( TB @ map_comp ) ) ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
=> ? [E: TB] :
( ( ( E @ ( D @ ( TA @ option @ ( TB @ aa ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) ) )
& ( ( B @ ( C @ ( TB @ option @ ( TC @ aa ) ) ) )
= ( E @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) )
=> ( ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) @ ( B @ ( C @ ( TB @ option @ ( TA @ fun_upd ) ) ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_map__upd__triv) ).
thf(410,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) )
=> ( ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) @ ( B @ ( C @ ( TB @ option @ ( TA @ fun_upd ) ) ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( TA @ insert ) ) )
= ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_insert__compr__raw) ).
thf(146,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( TA @ insert ) ) )
= ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( TB @ none ) )
=> ( ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) @ ( B @ ( C @ ( TB @ option @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ ran ) ) )
= ( C @ ( TB @ ( TA @ ran ) ) @ ( A @ ( TB @ insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ran__map__upd) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( TB @ none ) )
=> ( ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) @ ( B @ ( C @ ( TB @ option @ ( TA @ fun_upd ) ) ) ) @ ( TB @ ( TA @ ran ) ) )
= ( C @ ( TB @ ( TA @ ran ) ) @ ( A @ ( TB @ insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',fact_79_preallocated__start) ).
thf(183,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)],[20]) ).
thf(82,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(422,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ option @ ( TB @ fun ),C: TA,D: TB,E: TA @ option @ ( TB @ fun )] :
( ( ( C @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_map__upd__eqD1) ).
thf(195,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ option @ ( TB @ fun ),C: TA,D: TB,E: TA @ option @ ( TB @ fun )] :
( ( ( C @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( D @ ( E @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) )
= ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TA @ option @ ( TB @ fun_upd ) ) ) ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',fact_52_split__paired__Ex) ).
thf(400,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)],[75]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_74_WTrt__hext__mono) ).
thf(131,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)],[5]) ).
thf(18,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_insert__absorb2) ).
thf(178,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_61_oconf__new) ).
thf(277,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 @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ option @ ( val @ option @ ( char @ list @ ( char @ list @ product_prod ) @ fun ) @ ( char @ list @ product_prod ) @ aa ) ) ) @ ( 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)],[45]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) )
=> ( C @ ( TB @ ( TA @ ran ) ) @ ( A @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ranI) ).
thf(369,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB @ option @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ option @ ( TA @ aa ) ) ) )
= ( A @ ( TB @ some @ ( TB @ option @ ( TB @ aa ) ) ) ) )
=> ( C @ ( TB @ ( TA @ ran ) ) @ ( A @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(469,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)],[93]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_40_fun__upd__apply) ).
thf(309,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)],[51]) ).
thf(100,axiom,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( TA @ is_none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_is__none__code_I2_J) ).
thf(491,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ some @ ( TA @ option @ ( TA @ aa ) ) ) @ ( TA @ is_none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA @ option @ ( TB @ fun )] :
( ( A @ ( TB @ none @ ( TA @ ( TB @ bind ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ fun ) @ ( TB @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_bind__lzero) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: TA @ option @ ( TB @ fun )] :
( ( A @ ( TB @ none @ ( TA @ ( TB @ bind ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ fun ) @ ( TB @ option @ aa ) ) ) @ ( TA @ option @ ( TA @ option @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_38_fun__upd__triv) ).
thf(496,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)],[103]) ).
thf(597,plain,
$false,
inference(e,[status(thm)],[343,365,479,333,408,247,440,533,472,340,185,436,257,570,372,189,416,152,228,316,475,164,443,321,211,238,121,397,280,133,439,270,546,201,160,392,424,429,275,260,349,484,329,493,324,356,169,593,499,526,590,124,225,264,161,573,149,375,584,191,413,466,181,187,419,362,509,303,477,494,140,155,198,267,241,167,394,306,426,194,295,327,502,463,338,359,336,446,539,482,581,250,231,517,158,119,272,383,346,536,287,410,146,405,183,422,195,400,131,178,277,369,469,309,491,222,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW551_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n026.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 16:15:10 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.67/0.73 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/0.98 % [INFO] Parsing done (245ms).
% 1.31/0.98 % [INFO] Running in sequential loop mode.
% 2.25/1.20 % [INFO] eprover registered as external prover.
% 2.45/1.20 % [INFO] Scanning for conjecture ...
% 2.73/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 3.17/1.41 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 4.13/1.61 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.13/1.63 % [INFO] Type checking passed.
% 4.13/1.63 % [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 ...
% 76.70/59.76 % External prover 'e' found a proof!
% 76.70/59.76 % [INFO] Killing All external provers ...
% 76.70/59.77 % Time passed: 59256ms (effective reasoning time: 58779ms)
% 76.70/59.77 % 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)>
% 76.70/59.77 % Axioms used in derivation (116): fact_30_map__upd__eqD1, help_fimplies_2_1_U, fact_67_hext__trans, fact_8_bind__lunit, help_COMBS_1_1_U, fact_41_option_Oexhaust, fact_63_hconf__def, fact_73_hext__def, fact_42_split__paired__All, fact_34_option_Osimps_I2_J, fact_90_insert__absorb, fact_97_insert__compr, fact_81_ran__map__upd, fact_93_insert__ident, fact_31_map__upd__triv, fact_37_option__caseE, fact_72_preallocated__hext, fact_18_bind__rzero, fact_12_map__comp__simps_I2_J, fact_29_map__comp__simps_I1_J, fact_95_insert__commute, fact_7_option_Osimps_I5_J, fact_49_fun__upd__twist, fact_33_option_Osimps_I3_J, fact_55_, fact_46_fun__upd__def, help_fNot_2_1_U, fact_13_bind__assoc, fact_69_preallocated__new, fact_89_insertE, fact_92_insert__eq__iff, fact_74_WTrt__hext__mono, fact_15_not__Some__eq, fact_4_option_Orecs_I2_J, help_fNot_1_1_U, fact_25_map__comp__def, fact_20_map__comp__empty_I2_J, fact_11_ranI, fact_48_fun__upd__other, fact_36_ospec, fact_0_RedNew_I1_J, fact_14_not__None__eq, fact_71_hext__objD, fact_54_prod_Orecs, fact_70_preallocated__upd__obj, help_COMBB_1_1_U, fact_87_insert__iff, fact_35_bind__runit, fact_44_RedNew_I4_J, fact_53_exp_Osimps_I1_J, fact_38_fun__upd__triv, fact_24_is__none__def, help_fdisj_1_1_U, fact_79_preallocated__start, fact_28_option_Osimps_I4_J, fact_62_oconf__init__fields, fact_88_insertCI, fact_22_map__upd__nonempty, fact_78_hextI, fact_10_map__comp__Some__iff, fact_1_option_Oinject, fact_52_split__paired__Ex, fact_40_fun__upd__apply, fact_50_fun__upd__same, help_fequal_1_1_T, fact_76_mem__def, fact_27_option_Orecs_I1_J, fact_66_hext__refl, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_68_oconf__hext, fact_84_option__map__is__None, fact_45_Pair__inject, fact_3_elem__set, fact_17_empty__upd__none, fact_96_insert__Collect, fact_83_option__map__eq__Some, help_COMBC_1_1_U, fact_51_fun__upd__idem__iff, fact_64_hext__new, fact_16_bind__lzero, help_fequal_2_1_T, fact_85_option__map__None, fact_80_Option_Omap__def, fact_82_option__map__Some, help_fdisj_3_1_U, fact_98_insertI1, fact_6_RedNew_I3_J, fact_57_hconf__new, fact_65_hext__upd__obj, fact_43_Pair__eq, fact_2_new__Addr__SomeD, fact_23_is__none__code_I1_J, fact_9_RedNew_I5_J, fact_77_Collect__def, fact_60_oconf__upd__obj, fact_59_hconfD, help_pp_1_1_U, fact_99_insert__compr__raw, fact_56_disjE__realizer2, help_fimplies_1_1_U, fact_61_oconf__new, fact_5_is__none__code_I2_J, fact_75_ext, fact_58_hconf__upd__obj, help_fimplies_3_1_U, fact_86_insert__absorb2, fact_47_fun__upd__idem, fact_32_map__upd__Some__unfold, fact_26_map__comp__None__iff, fact_19_map__comp__empty_I1_J, help_pp_2_1_U, fact_94_insert__code, fact_21_RedNew_I2_J, fact_39_fun__upd__upd, fact_91_insertI2
% 76.70/59.77 % No. of inferences in proof: 236
% 76.70/59.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 59256 ms resp. 58779 ms w/o parsing
% 77.52/59.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 77.52/59.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------