%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW512_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 : n002.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 09:10:43 AM UTC 2026
% Result : Theorem 53.88s 39.73s
% Output : Refutation 54.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 126
% Syntax : Number of formulae : 254 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 1800 ( 142 equ; 0 cnn)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 7911 ( 60 ~; 24 |; 56 &;7424 @)
% ( 25 <=>; 322 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 12 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 8 con; 0-6 aty)
% Number of variables : 787 ( 0 ^; 780 !; 7 ?; 787 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(enum_decl,type,
enum:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : $o ).
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(enum_enum_all_decl,type,
enum_enum_all:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > $o ) ).
thf(hoare_992312373derivs_decl,type,
hoare_992312373derivs:
!>[TA: $tType] : ( ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > $o ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_Least_decl,type,
ord_Least:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(powp_decl,type,
powp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( bool @ ( TA @ fun ) @ fun ) ) ) ).
thf(inv_imagep_decl,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(pow_decl,type,
pow:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( bool @ ( TA @ fun ) @ fun ) ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(g_decl,type,
g: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(ga_decl,type,
ga: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(124,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(555,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(68,axiom,
bool @ bot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(357,plain,
bool @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(66,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(350,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)],[66]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_subsetD) ).
thf(276,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(45,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(269,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)],[45]) ).
thf(110,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot )
!= ( A @ ( B @ ( TA @ insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_empty__not__insert) ).
thf(500,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot )
!= ( A @ ( B @ ( TA @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(340,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(121,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_85_insertCI) ).
thf(538,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)],[121]) ).
thf(84,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(404,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(417,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(126,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Pow__bottom) ).
thf(559,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ insert ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_singleton__inject) ).
thf(152,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ insert ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(107,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( A @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Pow__top) ).
thf(475,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ pow ) @ ( A @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(20,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_insert__not__empty) ).
thf(179,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_order__antisym__conv) ).
thf(211,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( ( A = B )
=> ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(115,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_83_insert__iff) ).
thf(514,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)],[115]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] : ( A @ ( TA @ bot_bot @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_bot__least) ).
thf(348,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] : ( A @ ( TA @ bot_bot @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(67,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_predicate1I) ).
thf(353,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A
= ( TA @ bot_bot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_bot__unique) ).
thf(293,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( ( A
= ( TA @ bot_bot ) )
=> ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A
= ( TA @ bot_bot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( ( ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) )
= A )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_ord__le__eq__subst) ).
thf(453,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( ( ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) )
= A )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(81,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ powp ) @ ( B @ ( TA @ powp ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Powp__mono) ).
thf(396,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ powp ) @ ( B @ ( TA @ powp ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(87,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(411,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(93,axiom,
bool @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(428,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(112,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_84_insertE) ).
thf(507,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)],[112]) ).
thf(117,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_empty__def) ).
thf(527,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(55,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_PowI) ).
thf(312,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(35,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_predicate1D) ).
thf(233,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Collect__conv__if) ).
thf(248,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( B @ ( TA @ ord_Least ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Least__equality) ).
thf(380,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( B @ ( TA @ ord_Least ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(114,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_weaken) ).
thf(512,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(25,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 @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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_31_set__rev__mp) ).
thf(201,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 @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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)],[25]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_order__trans) ).
thf(534,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_set__mp) ).
thf(220,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(72,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_subset__empty) ).
thf(366,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_order__subst2) ).
thf(561,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [D: TA] :
( ( D @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( C @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_LeastI2) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [D: TA] :
( ( D @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( C @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(94,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_singleton__conv) ).
thf(429,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(6,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(137,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_le__funE) ).
thf(165,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(34,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 @ insert ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_subset__insert) ).
thf(229,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 @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ insert ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( C @ ( TA @ insert ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( TA @ ord_Least ) @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_LeastI) ).
thf(435,plain,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( TA @ ord_Least ) @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(116,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( 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_86_insert__subset) ).
thf(522,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( 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)],[116]) ).
thf(103,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_PowD) ).
thf(461,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
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
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_all__not__in__conv) ).
thf(493,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A
= ( TA @ bot_bot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_le__bot) ).
thf(324,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A
= ( TA @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(78,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(388,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Collect__conv__if2) ).
thf(169,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(59,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 ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_subsetI) ).
thf(328,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 ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(33,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_equalityD1) ).
thf(225,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_order__antisym) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(3,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(129,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_ord__eq__le__trans) ).
thf(503,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(5,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(134,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)],[5]) ).
thf(1,conjecture,
bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( ga @ ( a @ hoare_992312373derivs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( ga @ ( a @ hoare_992312373derivs ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ( bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( ga @ ( a @ hoare_992312373derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(205,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_linorder__linear) ).
thf(398,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ enum ) )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( TB @ ord_less_eq @ ( TA @ ( bool @ ( TB @ fun ) @ ( TB @ combb ) ) ) ) @ ( bool @ ( TB @ ( TA @ combs ) ) ) ) @ ( TA @ enum_enum_all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order__fun_I1_J) ).
thf(530,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ enum ) )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TB @ ord_less_eq @ ( TA @ ( bool @ ( TB @ fun ) @ ( TB @ combb ) ) ) ) @ ( bool @ ( TB @ ( TA @ combs ) ) ) ) @ ( TA @ enum_enum_all ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ord_less_eq @ ( TA @ ( bool @ ( TB @ fun ) @ ( TB @ combb ) ) ) ) @ ( bool @ ( TB @ ( TA @ combs ) ) ) ) @ ( TA @ enum_enum_all ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(10,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(148,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)],[10]) ).
thf(14,axiom,
bool @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(161,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ pow ) @ ( B @ ( TA @ pow ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Pow__mono) ).
thf(444,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ pow ) @ ( B @ ( TA @ pow ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(74,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) )
= ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ combc ) ) ) ) @ ( bool @ ( TA @ fun ) @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Pow__def) ).
thf(375,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) )
= ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ combc ) ) ) ) @ ( bool @ ( TA @ fun ) @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(91,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ pow ) )
= ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Pow__empty) ).
thf(423,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ pow ) )
= ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_order__refl) ).
thf(281,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ enum )
=> ! [A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ enum_enum_all ) )
<=> ! [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_enum__all) ).
thf(419,plain,
! [TA: $tType] :
( ( TA @ enum )
=> ! [A: bool @ ( TA @ fun )] :
( ( ! [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( TA @ enum_enum_all ) ) )
& ( ( A @ ( TA @ enum_enum_all ) )
=> ! [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(70,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_emptyE) ).
thf(362,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert ) ) @ ( D @ ( TA @ insert ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) ) )
<=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_doubleton__eq__iff) ).
thf(477,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert ) ) @ ( D @ ( TA @ insert ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert ) ) @ ( D @ ( TA @ insert ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) ) )
=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(7,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(140,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)],[7]) ).
thf(13,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_empty__Collect__eq) ).
thf(155,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,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(198,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)],[24]) ).
thf(48,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) )
!= ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Pow__not__empty) ).
thf(278,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) )
!= ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(44,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(267,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_subset__refl) ).
thf(167,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun )] : ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( TA @ hoare_992312373derivs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).
thf(473,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun )] : ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( TA @ hoare_992312373derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ord_Least ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Least__le) ).
thf(426,plain,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ord_Least ) @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(15,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_singleton__conv2) ).
thf(162,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_singleton__iff) ).
thf(548,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( B = A )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(63,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(342,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)],[63]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_order__subst1) ).
thf(194,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,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_82_insert__absorb2) ).
thf(145,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)],[9]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_bot__apply) ).
thf(414,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(58,axiom,
bool @ enum,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(327,plain,
bool @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(43,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_pred__subset__eq) ).
thf(263,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(54,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_subset__trans) ).
thf(310,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_equals0D) ).
thf(182,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] : ( B @ ( A @ ( TA @ insert ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_subset__insertI) ).
thf(463,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] : ( B @ ( A @ ( TA @ insert ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_order__eq__refl) ).
thf(544,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_le__fun__def) ).
thf(336,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
<=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_set__eq__subset) ).
thf(314,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ enum )
=> ! [A: bool @ ( TA @ fun )] :
( ! [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A @ ( TA @ enum_enum_all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_all__code) ).
thf(446,plain,
! [TA: $tType] :
( ( TA @ enum )
=> ! [A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ enum_enum_all ) )
=> ! [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ! [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( TA @ enum_enum_all ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(8,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(143,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_equalityD2) ).
thf(175,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_le__funD) ).
thf(386,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(105,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ~ ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_equalityE) ).
thf(465,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ~ ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_bot__fun__def) ).
thf(450,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) )
| ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_subset__singletonD) ).
thf(556,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) ) )
| ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_LeastI__ex) ).
thf(203,plain,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rev__predicate1D) ).
thf(218,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Pow__iff) ).
thf(258,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(79,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_equalityI) ).
thf(390,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_ord__eq__le__subst) ).
thf(186,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(75,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_empty__iff) ).
thf(378,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_linorder__le__cases) ).
thf(510,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_ord__le__eq__trans) ).
thf(207,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ fun ) @ ( TB @ fun ),C: TA,D: TA] :
( ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_inv__imagep__def) ).
thf(272,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ fun ) @ ( TB @ fun ),C: TA,D: TA] :
( ( ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(346,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(536,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(51,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Collect__empty__eq) ).
thf(287,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(36,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
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_ex__in__conv) ).
thf(235,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_in__mono) ).
thf(246,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(11,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(151,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_order__eq__iff) ).
thf(300,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( B @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(95,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
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_equals0I) ).
thf(432,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
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(42,axiom,
ga @ ( g @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(262,plain,
ga @ ( g @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_le__funI) ).
thf(405,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(73,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_empty__subsetI) ).
thf(373,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( TA @ powp ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Powp__Pow__eq) ).
thf(242,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( TA @ powp ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( TA @ powp ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( TA @ pow ) @ ( B @ ( bool @ ( TA @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(69,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(358,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)],[69]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [D: TA] :
( ( D @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA] :
( ( E @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( D @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( C @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_LeastI2__wellorder) ).
thf(437,plain,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [D: TA] :
( ( D @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [E: TA] :
( ( E @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( D @ ( TA @ ord_less_eq @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( C @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ? [C: TA] : ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( B @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_LeastI2__ex) ).
thf(400,plain,
! [TA: $tType] :
( ( TA @ wellorder )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ? [C: TA] : ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( B @ ( TA @ ord_Least ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_in__inv__imagep) ).
thf(283,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(60,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( TA @ collect ) @ ( B @ ( TA @ collect ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mono) ).
thf(332,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( TA @ collect ) @ ( B @ ( TA @ collect ) @ ( bool @ ( TA @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(131,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(98,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_asm) ).
thf(442,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(40,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_bot__empty__eq) ).
thf(254,plain,
! [TA: $tType,A: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_singletonE) ).
thf(222,plain,
! [TA: $tType,A: TA,B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(71,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( C @ ( A @ ( TA @ hoare_992312373derivs ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_cut) ).
thf(364,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( C @ ( A @ ( TA @ hoare_992312373derivs ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(566,plain,
$false,
inference(e,[status(thm)],[555,357,350,276,269,500,340,538,404,417,559,152,475,179,211,514,348,353,293,453,396,411,428,507,527,312,233,248,380,512,201,534,220,366,561,407,429,137,165,229,435,522,461,493,324,388,169,328,225,393,129,503,134,128,205,398,530,148,161,444,375,423,281,419,362,477,140,155,198,278,267,167,473,426,162,548,342,194,145,414,327,263,310,182,463,544,336,314,446,143,175,386,465,450,556,203,218,258,390,186,378,510,207,272,346,536,287,235,246,151,300,432,262,405,373,242,358,437,400,283,332,131,442,254,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW512_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % 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
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 16:12:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.85/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.50/1.29 % [INFO] Parsing done (325ms).
% 1.97/1.30 % [INFO] Running in sequential loop mode.
% 2.74/1.69 % [INFO] eprover registered as external prover.
% 2.98/1.70 % [INFO] Scanning for conjecture ...
% 3.16/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 3.41/2.02 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 4.38/2.29 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.60/2.32 % [INFO] Type checking passed.
% 4.60/2.33 % [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 ...
% 5.72/2.61 % [INFO] [Domain constraints] Detected constraint on bool
% 5.72/2.62 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 53.88/39.72 % External prover 'e' found a proof!
% 53.88/39.72 % [INFO] Killing All external provers ...
% 53.88/39.72 % Time passed: 39196ms (effective reasoning time: 38410ms)
% 53.88/39.72 % 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)>
% 53.88/39.72 % Axioms used in derivation (125): fact_33_equalityD2, fact_57_in__inv__imagep, arity_HOL_Obool___Orderings_Oorder, fact_92_doubleton__eq__iff, fact_4_empty__subsetI, help_COMBS_1_1_U, fact_86_insert__subset, fact_88_singleton__conv, fact_90_insert__not__empty, arity_HOL_Obool___Orderings_Oord, arity_HOL_Obool___Orderings_Opreorder, help_fconj_3_1_U, arity_fun___Orderings_Obot, fact_83_insert__iff, fact_12_emptyE, fact_56_Powp__mono, fact_1_asm, fact_13_order__refl, arity_fun___Orderings_Oord, fact_31_set__rev__mp, fact_0_empty, fact_26_ex__in__conv, fact_42_le__fun__def, fact_11_Collect__empty__eq, fact_78_LeastI2__ex, fact_81_Pow__empty, fact_85_insertCI, fact_69_all__code, arity_HOL_Obool___Orderings_Olinorder, arity_fun___Enum_Oenum, fact_70_enum__all, fact_49_ord__eq__le__subst, help_fFalse_1_1_T, fact_82_insert__absorb2, fact_39_bot__least, fact_45_Collect__mono, fact_43_subsetI, fact_52_rev__predicate1D, fact_20_ord__eq__le__trans, fact_59_Pow__mono, fact_23_order__eq__iff, help_COMBB_1_1_U, fact_60_order__fun_I1_J, arity_fun___Orderings_Oorder, arity_HOL_Obool___Enum_Oenum, fact_53_predicate1D, fact_46_pred__subset__eq, help_fconj_2_1_U, fact_37_le__bot, arity_fun___Orderings_Opreorder, fact_44_le__funI, fact_84_insertE, fact_34_equalityD1, fact_3_cut, fact_97_subset__singletonD, fact_10_empty__iff, fact_91_singleton__iff, fact_15_bot__apply, fact_40_le__funE, fact_29_subset__trans, fact_96_Collect__conv__if, fact_68_LeastI__ex, fact_95_Collect__conv__if2, fact_5_subset__empty, fact_8_all__not__in__conv, fact_89_empty__not__insert, fact_28_equalityE, help_fequal_1_1_T, fact_80_LeastI2__wellorder, fact_62_Pow__iff, fact_36_subset__refl, fact_48_order__subst1, fact_41_le__funD, fact_66_Pow__not__empty, fact_21_order__antisym__conv, fact_76_mem__def, fact_7_equalityI, fact_17_order__trans, help_COMBK_1_1_U, fact_16_linorder__le__cases, fact_71_Pow__bottom, fact_63_PowI, fact_30_set__mp, fact_93_singletonE, fact_6_subsetD, fact_55_ord__le__eq__subst, fact_65_PowD, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, help_fequal_2_1_T, fact_25_equals0D, fact_24_linorder__linear, fact_99_subset__insert, fact_94_singleton__inject, help_fconj_1_1_U, fact_74_Least__equality, fact_27_empty__def, fact_73_Powp__Pow__eq, help_fFalse_1_1_U, fact_9_empty__Collect__eq, fact_98_subset__insertI, fact_2_weaken, fact_77_Collect__def, fact_35_set__eq__subset, fact_87_singleton__conv2, fact_38_bot__unique, help_pp_1_1_U, fact_61_Least__le, fact_22_order__eq__refl, fact_58_inv__imagep__def, fact_19_ord__le__eq__trans, fact_51_bot__empty__eq, fact_32_in__mono, fact_50_order__subst2, fact_72_LeastI, fact_75_ext, fact_14_bot__fun__def, conj_0, help_pp_2_1_U, fact_47_equals0I, fact_67_Pow__top, fact_18_order__antisym, fact_54_predicate1I, fact_64_Pow__def, fact_79_LeastI2
% 53.88/39.72 % No. of inferences in proof: 254
% 53.88/39.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 39196 ms resp. 38410 ms w/o parsing
% 54.33/39.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 54.33/39.89 % [INFO] Killing All external provers ...
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