TSTP Solution File: SWW512_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW512_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:56 EDT 2023
% Result : Theorem 36.78s 24.08s
% Output : Refutation 37.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 158
% Syntax : Number of formulae : 286 ( 47 unt; 32 typ; 0 def)
% Number of atoms : 1800 ( 142 equ; 0 cnn)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 7995 ( 60 ~; 24 |; 56 &;7508 @)
% ( 25 <=>; 322 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 12 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 8 con; 0-6 aty)
% Number of variables : 820 ( 0 ^; 780 !; 7 ?; 820 :)
% ( 33 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(enum_type,type,
enum:
!>[TA: $tType] : $o ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(enum_enum_all_type,type,
enum_enum_all:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > $o ) ).
thf(hoare_992312373derivs_type,type,
hoare_992312373derivs:
!>[TA: $tType] : ( ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > $o ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_Least_type,type,
ord_Least:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(powp_type,type,
powp:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(pow_type,type,
pow:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(g_type,type,
g: fun @ ( hoare_28830079triple @ a ) @ bool ).
thf(ga_type,type,
ga: fun @ ( hoare_28830079triple @ a ) @ bool ).
thf(79,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_equalityI) ).
thf(365,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(87,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(384,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_singletonE) ).
thf(217,plain,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] : ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ B @ C ) ) @ ( aa @ TA @ TB @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_le__funI) ).
thf(379,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] : ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ B @ C ) ) @ ( aa @ TA @ TB @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(95,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_equals0I) ).
thf(404,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(100,axiom,
! [TA: $tType] :
( ( enum @ TA )
=> ! [A: fun @ TA @ bool] :
( ! [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) )
<=> ( enum_enum_all @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_all__code) ).
thf(417,plain,
! [TA: $tType] :
( ( enum @ TA )
=> ! [A: fun @ TA @ bool] :
( ( ! [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( enum_enum_all @ TA @ A ) )
& ( ( enum_enum_all @ TA @ A )
=> ! [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(257,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( D
= ( aa @ TA @ TB @ C @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ! [E: TA,F: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ E ) @ F ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ E ) ) @ ( aa @ TA @ TB @ C @ F ) ) ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_ord__eq__le__subst) ).
thf(184,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( D
= ( aa @ TA @ TB @ C @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ! [E: TA,F: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ E ) @ F ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ E ) ) @ ( aa @ TA @ TB @ C @ F ) ) ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(109,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_all__not__in__conv) ).
thf(460,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(53,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_order__eq__iff) ).
thf(284,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) ) )
& ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(325,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_singleton__inject) ).
thf(152,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) )
<=> ! [C: TA] : ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ B @ C ) ) @ ( aa @ TA @ TB @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_le__fun__def) ).
thf(316,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) )
=> ! [C: TA] : ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ B @ C ) ) @ ( aa @ TA @ TB @ A @ C ) ) ) )
& ( ! [C: TA] : ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ B @ C ) ) @ ( aa @ TA @ TB @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ C ) @ B ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ A ) ) @ ( aa @ TA @ TB @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_le__funE) ).
thf(164,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ C ) @ B ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ A ) ) @ ( aa @ TA @ TB @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(107,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ A ) @ ( pow @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Pow__top) ).
thf(443,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ A ) @ ( pow @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(321,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_in__mono) ).
thf(238,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
<=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_insert__iff) ).
thf(480,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(54,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_subset__trans) ).
thf(293,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(48,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( pow @ TA @ A )
!= ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Pow__not__empty) ).
thf(265,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( pow @ TA @ A )
!= ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(41,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pow__iff) ).
thf(248,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_in__inv__imagep) ).
thf(270,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) )
=> ( inv_imagep @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(201,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(86,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ C @ D ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_LeastI2) ).
thf(381,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ C @ D ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(33,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_equalityD1) ).
thf(220,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(14,axiom,
ord @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(160,plain,
ord @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(90,axiom,
! [TA: $tType] :
( ( enum @ TA )
=> ! [A: fun @ TA @ bool] :
( ( enum_enum_all @ TA @ A )
<=> ! [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_enum__all) ).
thf(392,plain,
! [TA: $tType] :
( ( enum @ TA )
=> ! [A: fun @ TA @ bool] :
( ( ( enum_enum_all @ TA @ A )
=> ! [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( enum_enum_all @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(56,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_set__eq__subset) ).
thf(297,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( B = A )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(96,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ ( ord_Least @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_LeastI) ).
thf(407,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ ( ord_Least @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(6,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(137,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TB @ ( fun @ TB @ bool ),C: TA,D: TA] :
( ( inv_imagep @ TB @ TA @ B @ A @ C @ D )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_inv__imagep__def) ).
thf(260,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TB @ ( fun @ TB @ bool ),C: TA,D: TA] :
( ( ( inv_imagep @ TB @ TA @ B @ A @ C @ D )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) )
=> ( inv_imagep @ TB @ TA @ B @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(73,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_empty__subsetI) ).
thf(349,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(36,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_ex__in__conv) ).
thf(229,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(43,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_pred__subset__eq) ).
thf(252,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(25,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_set__rev__mp) ).
thf(197,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ C ) @ B ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ A ) ) @ ( aa @ TA @ TB @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_le__funD) ).
thf(361,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ C ) @ B ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ A ) ) @ ( aa @ TA @ TB @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(329,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ C ) ) @ A ) )
=> ( ! [E: TB,F: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ E ) @ F ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ E ) ) @ ( aa @ TB @ TA @ B @ F ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_order__subst2) ).
thf(522,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ C ) ) @ A ) )
=> ( ! [E: TB,F: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ E ) @ F ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ E ) ) @ ( aa @ TB @ TA @ B @ F ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(34,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ ( insert @ TA @ C @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_subset__insert) ).
thf(224,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ ( insert @ TA @ C @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ ( insert @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(76,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ C ) ) )
=> ( ( ord_Least @ TA @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Least__equality) ).
thf(356,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ C ) ) )
=> ( ( ord_Least @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_bot__fun__def) ).
thf(420,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(499,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(70,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_emptyE) ).
thf(339,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(113,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_linorder__le__cases) ).
thf(476,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_equalityD2) ).
thf(173,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(129,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(81,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( powp @ TA @ B ) ) @ ( powp @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Powp__mono) ).
thf(371,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( powp @ TA @ B ) ) @ ( powp @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(134,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(92,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( ord_Least @ TA @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Least__le) ).
thf(398,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( ord_Least @ TA @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1,conjecture,
hoare_992312373derivs @ a @ ga @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( hoare_992312373derivs @ a @ ga @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ( hoare_992312373derivs @ a @ ga @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_subset__empty) ).
thf(343,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(103,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_PowD) ).
thf(430,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(17,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_subset__refl) ).
thf(166,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(148,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_singleton__conv2) ).
thf(161,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_equals0D) ).
thf(180,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(83,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ? [C: TA] : ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_LeastI2__ex) ).
thf(375,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ? [C: TA] : ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ C ) )
=> ( ( ( aa @ TB @ TA @ B @ C )
= A )
=> ( ! [E: TB,F: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ E ) @ F ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ E ) ) @ ( aa @ TB @ TA @ B @ F ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_ord__le__eq__subst) ).
thf(423,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ C ) )
=> ( ( ( aa @ TB @ TA @ B @ C )
= A )
=> ( ! [E: TB,F: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ E ) @ F ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ E ) ) @ ( aa @ TB @ TA @ B @ F ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ ( aa @ TA @ TB @ C @ B ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ! [E: TA,F: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ E ) @ F ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ E ) ) @ ( aa @ TA @ TB @ C @ F ) ) ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_order__subst1) ).
thf(191,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ ( aa @ TA @ TB @ C @ B ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ! [E: TA,F: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ E ) @ F ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ ( aa @ TA @ TB @ C @ E ) ) @ ( aa @ TA @ TB @ C @ F ) ) ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( ord_less_eq @ TB ) @ D ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(98,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ B ) @ A ) )
=> ( hoare_992312373derivs @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_asm) ).
thf(413,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ B ) @ A ) )
=> ( hoare_992312373derivs @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_doubleton__eq__iff) ).
thf(445,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( ( insert @ TA @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( insert @ TA @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(60,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( collect @ TA @ B ) ) @ ( collect @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__mono) ).
thf(313,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( collect @ TA @ B ) ) @ ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(110,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( bot_bot @ ( fun @ TA @ bool ) )
!= ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_empty__not__insert) ).
thf(466,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( bot_bot @ ( fun @ TA @ bool ) )
!= ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(68,axiom,
bot @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(335,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(40,axiom,
! [TA: $tType,A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_bot__empty__eq) ).
thf(245,plain,
! [TA: $tType,A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(105,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_equalityE) ).
thf(434,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_bot__apply) ).
thf(387,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( order @ TB ) )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) )
<=> ( enum_enum_all @ TA @ ( combs @ TA @ TB @ bool @ ( combb @ TB @ ( fun @ TB @ bool ) @ TA @ ( ord_less_eq @ TB ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_order__fun_I1_J) ).
thf(494,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( order @ TB ) )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) )
=> ( enum_enum_all @ TA @ ( combs @ TA @ TB @ bool @ ( combb @ TB @ ( fun @ TB @ bool ) @ TA @ ( ord_less_eq @ TB ) @ B ) @ A ) ) )
& ( ( enum_enum_all @ TA @ ( combs @ TA @ TB @ bool @ ( combb @ TB @ ( fun @ TB @ bool ) @ TA @ ( ord_less_eq @ TB ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ TB ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(140,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rev__predicate1D) ).
thf(213,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(126,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ ( pow @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Pow__bottom) ).
thf(520,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ ( pow @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(13,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_empty__Collect__eq) ).
thf(155,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Collect__conv__if) ).
thf(240,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
pp @ ( aa @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ bool @ ( aa @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) @ g ) @ ga ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(251,plain,
pp @ ( aa @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ bool @ ( aa @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) @ g ) @ ga ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(52,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ ( bot_bot @ TA ) ) )
<=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_bot__unique) ).
thf(278,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ ( bot_bot @ TA ) ) )
=> ( A
= ( bot_bot @ TA ) ) )
& ( ( A
= ( bot_bot @ TA ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ ( bot_bot @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(57,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ ( bot_bot @ TA ) ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_le__bot) ).
thf(306,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ ( bot_bot @ TA ) ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(112,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insertE) ).
thf(473,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(44,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(255,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(116,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( insert @ TA @ C @ B ) ) @ A ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__subset) ).
thf(487,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( insert @ TA @ C @ B ) ) @ A ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ ( insert @ TA @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(124,axiom,
preorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(516,plain,
preorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(194,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_insert__absorb2) ).
thf(145,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(55,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_PowI) ).
thf(295,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(65,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] : ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( bot_bot @ TA ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_bot__least) ).
thf(327,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] : ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ ( bot_bot @ TA ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(97,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ C @ D ) )
=> ( ! [E: TA] :
( ( pp @ ( aa @ TA @ bool @ C @ E ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ D ) @ E ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_LeastI2__wellorder) ).
thf(409,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ C @ D ) )
=> ( ! [E: TA] :
( ( pp @ ( aa @ TA @ bool @ C @ E ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ D ) @ E ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subsetD) ).
thf(263,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(59,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_subsetI) ).
thf(310,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(26,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_LeastI__ex) ).
thf(199,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( ord_Least @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_insert__not__empty) ).
thf(177,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(106,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ A @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
thf(441,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ A @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(336,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(8,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(143,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(119,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_order__trans) ).
thf(497,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(78,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(363,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ B ) )
=> ( ( B = A )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_ord__le__eq__trans) ).
thf(203,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ B ) )
=> ( ( B = A )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(80,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_order__antisym) ).
thf(368,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ( B
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_subset__singletonD) ).
thf(517,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ( B
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(319,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(74,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( pow @ TA @ A )
= ( collect @ ( fun @ TA @ bool ) @ ( combc @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ bool @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Pow__def) ).
thf(351,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( pow @ TA @ A )
= ( collect @ ( fun @ TA @ bool ) @ ( combc @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ bool @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(390,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(94,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_singleton__conv) ).
thf(401,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(84,axiom,
order @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(378,plain,
order @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(37,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( powp @ TA @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) @ B ) )
<=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Powp__Pow__eq) ).
thf(235,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( powp @ TA @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ bool ) ) @ B ) @ ( pow @ TA @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( powp @ TA @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_singleton__iff) ).
thf(510,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(29,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_order__antisym__conv) ).
thf(207,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(114,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ A ) @ B ) )
=> ( hoare_992312373derivs @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weaken) ).
thf(478,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( pp @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ A ) @ B ) )
=> ( hoare_992312373derivs @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(11,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(151,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ ( insert @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_subset__insertI) ).
thf(432,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ ( insert @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Collect__conv__if2) ).
thf(168,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(51,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Collect__empty__eq) ).
thf(273,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(82,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_linorder__linear) ).
thf(373,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(71,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( hoare_992312373derivs @ TA @ A @ C )
=> ( hoare_992312373derivs @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cut) ).
thf(341,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( hoare_992312373derivs @ TA @ A @ C )
=> ( hoare_992312373derivs @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(93,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(400,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(99,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( pow @ TA @ B ) ) @ ( pow @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Pow__mono) ).
thf(415,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( pow @ TA @ B ) ) @ ( pow @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(122,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_order__eq__refl) ).
thf(506,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(49,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_order__refl) ).
thf(268,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(91,axiom,
! [TA: $tType] :
( ( pow @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( insert @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Pow__empty) ).
thf(395,plain,
! [TA: $tType] :
( ( pow @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( insert @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(67,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_predicate1I) ).
thf(332,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(4,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(131,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_insertCI) ).
thf(501,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(35,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_predicate1D) ).
thf(227,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ord__eq__le__trans) ).
thf(469,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less_eq @ TA ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(75,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_empty__iff) ).
thf(354,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(58,axiom,
enum @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(309,plain,
enum @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_set__mp) ).
thf(215,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ TA @ bool ) ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(117,axiom,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_empty__def) ).
thf(491,plain,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(525,plain,
$false,
inference(e,[status(thm)],[365,384,217,379,404,417,257,184,460,284,325,152,316,164,443,321,238,480,293,265,248,270,201,381,220,160,392,297,407,137,260,349,229,252,197,361,329,522,224,356,420,499,339,476,173,129,371,134,398,128,343,430,166,148,161,180,375,423,191,413,445,313,466,335,245,434,387,494,140,213,520,155,240,251,278,306,473,255,487,516,194,145,295,327,409,263,310,199,177,441,336,143,497,363,203,368,517,319,351,390,401,378,235,510,207,478,151,432,168,273,373,341,400,415,506,268,395,332,131,501,227,469,354,309,215,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW512_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 22:28:13 EDT 2023
% 0.15/0.37 % CPUTime :
% 1.01/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.13 % [INFO] Parsing done (220ms).
% 1.58/1.14 % [INFO] Running in sequential loop mode.
% 2.32/1.34 % [INFO] eprover registered as external prover.
% 2.32/1.34 % [INFO] cvc4 registered as external prover.
% 2.32/1.35 % [INFO] Scanning for conjecture ...
% 2.57/1.46 % [INFO] Found a conjecture and 125 axioms. Running axiom selection ...
% 3.08/1.54 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 3.55/1.70 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.94/1.73 % [INFO] Type checking passed.
% 3.94/1.73 % [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 ...
% 4.32/1.89 % [INFO] [Domain constraints] Detected constraint on bool
% 4.32/1.90 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 36.78/24.08 % External prover 'e' found a proof!
% 36.78/24.08 % [INFO] Killing All external provers ...
% 36.78/24.08 % Time passed: 23549ms (effective reasoning time: 22937ms)
% 36.78/24.08 % 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)>
% 36.78/24.08 % 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
% 36.78/24.08 % No. of inferences in proof: 254
% 36.78/24.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23549 ms resp. 22937 ms w/o parsing
% 37.12/24.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.12/24.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------