TSTP Solution File: ITP199^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP199^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : Tue May 7 07:48:46 EDT 2024
% Result : Theorem 52.01s 23.13s
% Output : Refutation 52.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 368
% Syntax : Number of formulae : 671 ( 282 unt; 67 typ; 0 def)
% Number of atoms : 1777 ( 752 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 6520 ( 162 ~; 27 |; 86 &;5843 @)
% ( 0 <=>; 402 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 579 ( 579 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 12 con; 0-7 aty)
% Number of variables : 1743 ( 112 ^1569 !; 26 ?;1743 :)
% ( 36 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(denotational_interp_type,type,
denotational_interp: $tType ).
thf(variable_type,type,
variable: $tType ).
thf(game_type,type,
game: $tType ).
thf(char_type,type,
char: $tType ).
thf(trm_type,type,
trm: $tType ).
thf(fml_type,type,
fml: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(bounded_lattice_type,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(uminus_type,type,
uminus:
!>[TA: $tType] : $o ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(boolean_algebra_type,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(semilattice_inf_type,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(semilattice_sup_type,type,
semilattice_sup:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(bounde1808546759up_bot_type,type,
bounde1808546759up_bot:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(statediff_type,type,
statediff: ( variable > real ) > ( variable > real ) > ( set @ variable ) ).
thf(stateinterpol_type,type,
stateinterpol: ( variable > real ) > ( variable > real ) > ( set @ variable ) > variable > real ).
thf(denota1419872369iation_type,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
thf(denotational_Vagree_type,type,
denotational_Vagree: ( variable > real ) > ( variable > real ) > ( set @ variable ) > $o ).
thf(denotational_repv_type,type,
denotational_repv: ( variable > real ) > variable > real > variable > real ).
thf(denota1778088425es_ODE_type,type,
denota1778088425es_ODE: denotational_interp > ( real > variable > real ) > char > trm > $o ).
thf(denota1863255036rm_sem_type,type,
denota1863255036rm_sem: denotational_interp > trm > ( variable > real ) > real ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sup_sup_type,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(none_type,type,
none:
!>[TA: $tType] : ( option @ TA ) ).
thf(some_type,type,
some:
!>[TA: $tType] : ( TA > ( option @ TA ) ) ).
thf(case_option_type,type,
case_option:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > TB ) > ( option @ TA ) > TB ) ).
thf(set_option_type,type,
set_option:
!>[TA: $tType] : ( ( option @ TA ) > ( set @ TA ) ) ).
thf(the_type,type,
the:
!>[TA: $tType] : ( ( option @ TA ) > TA ) ).
thf(these_type,type,
these:
!>[TA: $tType] : ( ( set @ ( option @ TA ) ) > ( set @ TA ) ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_type,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(static_FVT_type,type,
static_FVT: trm > ( set @ variable ) ).
thf(static_selectlike_type,type,
static_selectlike: ( set @ ( variable > real ) ) > ( variable > real ) > ( set @ variable ) > ( set @ ( variable > real ) ) ).
thf(times_type,type,
times: trm > trm > trm ).
thf(dVar_type,type,
dVar: char > variable ).
thf(rVar_type,type,
rVar: char > variable ).
thf(rec_variable_type,type,
rec_variable:
!>[TA: $tType] : ( ( char > TA ) > ( char > TA ) > variable > TA ) ).
thf(size_variable_type,type,
size_variable: variable > nat ).
thf(uSubst277968634Timeso_type,type,
uSubst277968634Timeso: ( option @ trm ) > ( option @ trm ) > ( option @ trm ) ).
thf(uSubst2091380086djoint_type,type,
uSubst2091380086djoint: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > denotational_interp > ( variable > real ) > denotational_interp ).
thf(uSubst95898992stappt_type,type,
uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_type,type,
f: real > variable > real ).
thf(i_type,type,
i: denotational_interp ).
thf(u_type,type,
u: set @ variable ).
thf(omega_type,type,
omega: variable > real ).
thf(sigma_type,type,
sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
thf(theta_type,type,
theta: trm ).
thf(rr_type,type,
rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real ).
thf(x_type,type,
x: char ).
thf(115,axiom,
! [A: set @ ( variable > real ),B: variable > real] :
( ( static_selectlike @ A @ B @ ( bot_bot @ ( set @ variable ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_selectlike__empty) ).
thf(645,plain,
! [A: set @ ( variable > real ),B: variable > real] :
( ( static_selectlike @ A @ B @ ( bot_bot @ ( set @ variable ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_bot__apply) ).
thf(809,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(246,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_9) ).
thf(1024,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(276,axiom,
! [A: variable,B: set @ variable,C: variable > real,D: variable > real] :
( ~ ( member @ variable @ A @ B )
=> ( ( stateinterpol @ C @ D @ B @ A )
= ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_stateinterpol__right) ).
thf(1105,plain,
! [A: variable,B: set @ variable,C: variable > real,D: variable > real] :
( ~ ( member @ variable @ A @ B )
=> ( ( stateinterpol @ C @ D @ B @ A )
= ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(183,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_UnE) ).
thf(846,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(200,axiom,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denota1419872369iation @ A @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) )
= ( denotational_Vagree @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Uvariation__Vagree) ).
thf(893,plain,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denota1419872369iation @ A @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) )
= ( denotational_Vagree @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(79,axiom,
! [A: option @ trm,B: option @ trm] :
( ( ( uSubst277968634Timeso @ A @ B )
= ( none @ trm ) )
= ( ( A
= ( none @ trm ) )
| ( B
= ( none @ trm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Timeso__undef) ).
thf(518,plain,
! [A: option @ trm,B: option @ trm] :
( ( ( uSubst277968634Timeso @ A @ B )
= ( none @ trm ) )
= ( ( A
= ( none @ trm ) )
| ( B
= ( none @ trm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(301,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_doubleton__eq__iff) ).
thf(1179,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(65,axiom,
! [A: variable > real,B: set @ variable] : ( denotational_Vagree @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_Vagree__refl) ).
thf(481,plain,
! [A: variable > real,B: set @ variable] : ( denotational_Vagree @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(224,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_all__not__in__conv) ).
thf(962,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(61,axiom,
! [A: variable > real,B: variable > real,C: trm,D: denotational_interp] :
( ( denotational_Vagree @ A @ B @ ( static_FVT @ C ) )
=> ( ( denota1863255036rm_sem @ D @ C @ A )
= ( denota1863255036rm_sem @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_coincidence__term) ).
thf(468,plain,
! [A: variable > real,B: variable > real,C: trm,D: denotational_interp] :
( ( denotational_Vagree @ A @ B @ ( static_FVT @ C ) )
=> ( ( denota1863255036rm_sem @ D @ C @ A )
= ( denota1863255036rm_sem @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(229,axiom,
! [A: variable > real,B: set @ ( variable > real ),C: set @ variable] :
( ( member @ ( variable > real ) @ A @ ( static_selectlike @ B @ A @ C ) )
= ( member @ ( variable > real ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_selectlike__self) ).
thf(977,plain,
! [A: variable > real,B: set @ ( variable > real ),C: set @ variable] :
( ( member @ ( variable > real ) @ A @ ( static_selectlike @ B @ A @ C ) )
= ( member @ ( variable > real ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(144,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_empty__Collect__eq) ).
thf(730,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(5,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( uSubst95898992stappt @ A @ B @ ( times @ C @ D ) )
= ( uSubst277968634Timeso @ ( uSubst95898992stappt @ A @ B @ C ) @ ( uSubst95898992stappt @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_usubstappt_Osimps_I6_J) ).
thf(308,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( uSubst95898992stappt @ A @ B @ ( times @ C @ D ) )
= ( uSubst277968634Timeso @ ( uSubst95898992stappt @ A @ B @ C ) @ ( uSubst95898992stappt @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(193,axiom,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_double__complement) ).
thf(873,plain,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_sup__apply) ).
thf(614,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(252,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_UnCI) ).
thf(1041,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(148,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ozero_16) ).
thf(741,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(264,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_insertE) ).
thf(1073,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(195,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( insert @ TA @ A @ B ) )
=> ( C @ D ) ) )
= ( ( C @ A )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_ball__insert) ).
thf(878,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( insert @ TA @ A @ B ) )
=> ( C @ D ) ) )
= ( ( C @ A )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(50,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( ? [B: TA] :
( A
= ( some @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_not__None__eq) ).
thf(440,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( ? [B: TA] :
( A
= ( some @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(266,axiom,
( ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta )
!= ( none @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_subdef) ).
thf(1078,plain,
( ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta )
!= ( none @ trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(139,axiom,
! [TA: $tType] : ( uminus @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_15) ).
thf(715,plain,
! [TA: $tType] : ( uminus @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( case_option @ TB @ TA @ A @ B @ ( some @ TA @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_option_Osimps_I5_J) ).
thf(472,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( case_option @ TB @ TA @ A @ B @ ( some @ TA @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(172,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(814,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(207,axiom,
lattice @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Olattice_28) ).
thf(913,plain,
lattice @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(260,axiom,
! [TA: $tType,A: set @ ( option @ TA )] :
( ( these @ TA @ ( insert @ ( option @ TA ) @ ( none @ TA ) @ A ) )
= ( these @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_these__insert__None) ).
thf(1063,plain,
! [TA: $tType,A: set @ ( option @ TA )] :
( ( these @ TA @ ( insert @ ( option @ TA ) @ ( none @ TA ) @ A ) )
= ( these @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(17,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inf_Oleft__idem) ).
thf(340,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(237,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insert__eq__iff) ).
thf(1001,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(160,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_bot__eq__sup__iff) ).
thf(782,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(48,axiom,
! [TA: $tType] :
( ( '?' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
| ? [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_split__option__ex) ).
thf(436,plain,
! [TA: $tType] :
( ( '?' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
| ? [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(117,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Un__commute) ).
thf(651,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(273,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sup__bot_Oleft__neutral) ).
thf(1095,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(36,axiom,
( ( some @ trm )
= ( some @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Aterm__Some) ).
thf(404,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(142,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_ball__Un) ).
thf(724,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(98,axiom,
! [A: option @ trm,B: option @ trm,C: option @ trm] :
( ( ( uSubst277968634Timeso @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some @ trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some @ trm @ E ) )
=> ( C
!= ( some @ trm @ ( times @ D @ E ) ) ) ) )
=> ( ( ( A
= ( none @ trm ) )
=> ( C
!= ( none @ trm ) ) )
=> ~ ( ? [D: trm] :
( A
= ( some @ trm @ D ) )
=> ( ( B
= ( none @ trm ) )
=> ( C
!= ( none @ trm ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Timeso_Oelims) ).
thf(570,plain,
! [A: option @ trm,B: option @ trm,C: option @ trm] :
( ( ( uSubst277968634Timeso @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some @ trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some @ trm @ E ) )
=> ( C
!= ( some @ trm @ ( times @ D @ E ) ) ) ) )
=> ( ( ( A
= ( none @ trm ) )
=> ( C
!= ( none @ trm ) ) )
=> ~ ( ? [D: trm] :
( A
= ( some @ trm @ D ) )
=> ( ( B
= ( none @ trm ) )
=> ( C
!= ( none @ trm ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_insertCI) ).
thf(785,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(106,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_sup_Oidem) ).
thf(619,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(134,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_emptyE) ).
thf(702,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(23,axiom,
semilattice_inf @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_4) ).
thf(357,plain,
semilattice_inf @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(258,axiom,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( ( static_selectlike @ A @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) )
= ( static_selectlike @ D @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) ) )
= ( ! [E: variable > real] :
( ( denota1419872369iation @ E @ B @ C )
=> ( ( member @ ( variable > real ) @ E @ A )
= ( member @ ( variable > real ) @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_selectlike__equal__cocond) ).
thf(1059,plain,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( ( static_selectlike @ A @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) )
= ( static_selectlike @ D @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) ) )
= ( ! [E: variable > real] :
( ( denota1419872369iation @ E @ B @ C )
=> ( ( member @ ( variable > real ) @ E @ A )
= ( member @ ( variable > real ) @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(285,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Un__insert__left) ).
thf(1132,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(174,axiom,
( denotational_repv
= ( ^ [A: variable > real,B: variable,C: real,D: variable] : ( if @ real @ ( B = D ) @ C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_repv__access) ).
thf(817,plain,
( denotational_repv
= ( ^ [A: variable > real,B: variable,C: real,D: variable] : ( if @ real @ ( B = D ) @ C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(270,axiom,
! [TA: $tType,A: char > TA,B: char > TA,C: char] :
( ( rec_variable @ TA @ A @ B @ ( rVar @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_variable_Osimps_I7_J) ).
thf(1087,plain,
! [TA: $tType,A: char > TA,B: char > TA,C: char] :
( ( rec_variable @ TA @ A @ B @ ( rVar @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(41,axiom,
( ( none @ trm )
= ( none @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_undeft__None) ).
thf(421,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(242,axiom,
! [TA: $tType,A: char > TA,B: char > TA,C: char] :
( ( rec_variable @ TA @ A @ B @ ( dVar @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_variable_Osimps_I8_J) ).
thf(1013,plain,
! [TA: $tType,A: char > TA,B: char > TA,C: char] :
( ( rec_variable @ TA @ A @ B @ ( dVar @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(196,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_insert__iff) ).
thf(881,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > TA] :
( ( case_option @ TA @ TB @ A @ B @ ( none @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_option_Osimps_I4_J) ).
thf(448,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > TA] :
( ( case_option @ TA @ TB @ A @ B @ ( none @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(279,axiom,
! [TA: $tType,A: set @ ( option @ TA )] :
( ( ( these @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ ( option @ TA ) ) ) )
| ( A
= ( insert @ ( option @ TA ) @ ( none @ TA ) @ ( bot_bot @ ( set @ ( option @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_these__empty__eq) ).
thf(1115,plain,
! [TA: $tType,A: set @ ( option @ TA )] :
( ( ( these @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ ( option @ TA ) ) ) )
| ( A
= ( insert @ ( option @ TA ) @ ( none @ TA ) @ ( bot_bot @ ( set @ ( option @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: option @ TA] :
( ( member @ TA @ A @ ( set_option @ TA @ B ) )
=> ( B
= ( some @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_option_Oset__cases) ).
thf(325,plain,
! [TA: $tType,A: TA,B: option @ TA] :
( ( member @ TA @ A @ ( set_option @ TA @ B ) )
=> ( B
= ( some @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(475,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(443,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_inf__apply) ).
thf(348,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(277,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ variable] :
( ( ( denotational_Vagree @ A @ B @ C )
& ( denotational_Vagree @ A @ B @ D ) )
= ( denotational_Vagree @ A @ B @ ( sup_sup @ ( set @ variable ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Vagree__and) ).
thf(1109,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ variable] :
( ( ( denotational_Vagree @ A @ B @ C )
& ( denotational_Vagree @ A @ B @ D ) )
= ( denotational_Vagree @ A @ B @ ( sup_sup @ ( set @ variable ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: option @ TA] :
( ( member @ TA @ A @ ( set_option @ TA @ B ) )
= ( B
= ( some @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_elem__set) ).
thf(321,plain,
! [TA: $tType,A: TA,B: option @ TA] :
( ( member @ TA @ A @ ( set_option @ TA @ B ) )
= ( B
= ( some @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(156,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_insertI1) ).
thf(766,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(190,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_neg__equal__0__iff__equal) ).
thf(866,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(33,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_equation__minus__iff) ).
thf(396,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(297,axiom,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( ( static_selectlike @ A @ B @ C )
= ( static_selectlike @ D @ B @ C ) )
= ( ! [E: variable > real] :
( ( denota1419872369iation @ E @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) )
=> ( ( member @ ( variable > real ) @ E @ A )
= ( member @ ( variable > real ) @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_selectlike__equal__cond) ).
thf(1169,plain,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( ( static_selectlike @ A @ B @ C )
= ( static_selectlike @ D @ B @ C ) )
= ( ! [E: variable > real] :
( ( denota1419872369iation @ E @ B @ ( uminus_uminus @ ( set @ variable ) @ C ) )
=> ( ( member @ ( variable > real ) @ E @ A )
= ( member @ ( variable > real ) @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(129,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_sup__bot_Oneutr__eq__iff) ).
thf(687,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(4,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(307,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(49,axiom,
bounded_lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(439,plain,
bounded_lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(529,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(211,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_singleton__iff) ).
thf(925,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(27,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( ( some @ TA @ ( the @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_option_Ocollapse) ).
thf(366,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( ( some @ TA @ ( the @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(86,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_order__refl) ).
thf(534,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_fun__Compl__def) ).
thf(546,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(163,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_neg__0__equal__iff__equal) ).
thf(793,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(292,axiom,
! [A: char] :
( ( size_size @ variable @ ( rVar @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_variable_Osize_I3_J) ).
thf(1153,plain,
! [A: char] :
( ( size_size @ variable @ ( rVar @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(154,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__sup__iff) ).
thf(761,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(254,axiom,
! [A: char] :
( ( size_variable @ ( rVar @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_variable_Osize__gen_I1_J) ).
thf(1047,plain,
! [A: char] :
( ( size_variable @ ( rVar @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(165,axiom,
! [A: variable > real,B: variable > real] :
( ( stateinterpol @ A @ B @ ( bot_bot @ ( set @ variable ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_stateinterpol__empty) ).
thf(798,plain,
! [A: variable > real,B: variable > real] :
( ( stateinterpol @ A @ B @ ( bot_bot @ ( set @ variable ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(206,axiom,
! [TA: $tType] :
( ( set_option @ TA @ ( none @ TA ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_option_Osimps_I14_J) ).
thf(910,plain,
! [TA: $tType] :
( ( set_option @ TA @ ( none @ TA ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insert__ident) ).
thf(746,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(177,axiom,
! [A: variable > real,B: set @ variable,C: set @ ( variable > real ),D: set @ ( variable > real )] :
( ! [E: variable > real] :
( ( denota1419872369iation @ E @ A @ B )
=> ( ( member @ ( variable > real ) @ E @ C )
= ( member @ ( variable > real ) @ E @ D ) ) )
=> ( ( static_selectlike @ C @ A @ ( uminus_uminus @ ( set @ variable ) @ B ) )
= ( static_selectlike @ D @ A @ ( uminus_uminus @ ( set @ variable ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_selectlike__equal__cocond__corule) ).
thf(825,plain,
! [A: variable > real,B: set @ variable,C: set @ ( variable > real ),D: set @ ( variable > real )] :
( ! [E: variable > real] :
( ( denota1419872369iation @ E @ A @ B )
=> ( ( member @ ( variable > real ) @ E @ C )
= ( member @ ( variable > real ) @ E @ D ) ) )
=> ( ( static_selectlike @ C @ A @ ( uminus_uminus @ ( set @ variable ) @ B ) )
= ( static_selectlike @ D @ A @ ( uminus_uminus @ ( set @ variable ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(245,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Un__left__absorb) ).
thf(1021,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(282,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_singletonD) ).
thf(1123,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(99,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( set_option @ TA @ ( some @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_option_Oset__intros) ).
thf(598,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( set_option @ TA @ ( some @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(95,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_inf__idem) ).
thf(561,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_uminus__apply) ).
thf(429,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(131,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__reorient) ).
thf(693,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(110,axiom,
! [A: char,B: char] :
( ( ( dVar @ A )
= ( dVar @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_variable_Oinject_I2_J) ).
thf(630,plain,
! [A: char,B: char] :
( ( ( dVar @ A )
= ( dVar @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(60,axiom,
semilattice_inf @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_19) ).
thf(467,plain,
semilattice_inf @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(249,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_neg__equal__zero) ).
thf(1032,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_UnI2) ).
thf(625,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(121,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Un__empty__right) ).
thf(665,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(178,axiom,
! [A: variable > real] :
( ( denota1419872369iation @ A @ ( f @ ( zero_zero @ real ) ) @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) )
=> ( ( denota1863255036rm_sem @ i @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) @ A )
= ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ sigma @ i @ ( f @ ( zero_zero @ real ) ) ) @ theta @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_IH) ).
thf(830,plain,
! [A: variable > real] :
( ( denota1419872369iation @ A @ ( f @ ( zero_zero @ real ) ) @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) )
=> ( ( denota1863255036rm_sem @ i @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) @ A )
= ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ sigma @ i @ ( f @ ( zero_zero @ real ) ) ) @ theta @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(294,axiom,
! [TA: $tType,A: TA] :
( ( set_option @ TA @ ( some @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_option_Osimps_I15_J) ).
thf(1159,plain,
! [TA: $tType,A: TA] :
( ( set_option @ TA @ ( some @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(127,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_11) ).
thf(682,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(137,axiom,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real,C: set @ variable] :
! [D: variable] :
( ~ ( member @ variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Uvariation__def) ).
thf(710,plain,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real,C: set @ variable] :
! [D: variable] :
( ~ ( member @ variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(10,axiom,
boolean_algebra @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_20) ).
thf(324,plain,
boolean_algebra @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ( static_selectlike @ D @ A @ C )
= ( static_selectlike @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_selectlike__Vagree) ).
thf(317,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ( static_selectlike @ D @ A @ C )
= ( static_selectlike @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(219,axiom,
! [A: variable > real,B: variable,C: real,D: set @ ( variable > real )] :
( ( member @ ( variable > real ) @ ( denotational_repv @ A @ B @ C ) @ ( static_selectlike @ D @ A @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) )
= ( ( C
= ( A @ B ) )
& ( member @ ( variable > real ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_repv__selectlike__self) ).
thf(948,plain,
! [A: variable > real,B: variable,C: real,D: set @ ( variable > real )] :
( ( member @ ( variable > real ) @ ( denotational_repv @ A @ B @ C ) @ ( static_selectlike @ D @ A @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) )
= ( ( C
= ( A @ B ) )
& ( member @ ( variable > real ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(281,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_12) ).
thf(1121,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(230,axiom,
! [A: trm,B: denotational_interp,C: trm,D: denotational_interp,E: char,F: real > variable > real] :
( ( ? [G: variable > real] :
( ( denota1419872369iation @ G @ ( F @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ E ) @ ( insert @ variable @ ( dVar @ E ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ D @ C @ G )
!= ( denota1863255036rm_sem @ B @ A @ G ) ) ) )
= ( ( denota1419872369iation @ ( rr @ A @ B @ C @ D @ E @ F ) @ ( F @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ E ) @ ( insert @ variable @ ( dVar @ E ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ D @ C @ ( rr @ A @ B @ C @ D @ E @ F ) )
!= ( denota1863255036rm_sem @ B @ A @ ( rr @ A @ B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062) ).
thf(980,plain,
! [A: trm,B: denotational_interp,C: trm,D: denotational_interp,E: char,F: real > variable > real] :
( ( ? [G: variable > real] :
( ( denota1419872369iation @ G @ ( F @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ E ) @ ( insert @ variable @ ( dVar @ E ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ D @ C @ G )
!= ( denota1863255036rm_sem @ B @ A @ G ) ) ) )
= ( ( denota1419872369iation @ ( rr @ A @ B @ C @ D @ E @ F ) @ ( F @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ E ) @ ( insert @ variable @ ( dVar @ E ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ D @ C @ ( rr @ A @ B @ C @ D @ E @ F ) )
!= ( denota1863255036rm_sem @ B @ A @ ( rr @ A @ B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(287,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_insert__absorb2) ).
thf(1138,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(191,axiom,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Uvariation__sym) ).
thf(869,plain,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(233,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_sup_Oassoc) ).
thf(989,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(40,axiom,
bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_23) ).
thf(420,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(280,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Compl__eq__Compl__iff) ).
thf(1118,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(328,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(197,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Set_Ois__empty__def) ).
thf(884,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(68,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_inf_Oright__idem) ).
thf(488,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(16,axiom,
semilattice_sup @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__sup_3) ).
thf(339,plain,
semilattice_sup @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(214,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_singleton__Un__iff) ).
thf(933,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(152,axiom,
! [A: real > variable > real,B: char,C: denotational_interp,D: trm,E: denotational_interp,F: trm] :
( ( ( denota1419872369iation @ ( rr @ F @ E @ D @ C @ B @ A ) @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ C @ D @ ( rr @ F @ E @ D @ C @ B @ A ) )
!= ( denota1863255036rm_sem @ E @ F @ ( rr @ F @ E @ D @ C @ B @ A ) ) ) )
| ( ( denota1778088425es_ODE @ C @ A @ B @ D )
= ( denota1778088425es_ODE @ E @ A @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_f2) ).
thf(753,plain,
! [A: real > variable > real,B: char,C: denotational_interp,D: trm,E: denotational_interp,F: trm] :
( ( ( denota1419872369iation @ ( rr @ F @ E @ D @ C @ B @ A ) @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ C @ D @ ( rr @ F @ E @ D @ C @ B @ A ) )
!= ( denota1863255036rm_sem @ E @ F @ ( rr @ F @ E @ D @ C @ B @ A ) ) ) )
| ( ( denota1778088425es_ODE @ C @ A @ B @ D )
= ( denota1778088425es_ODE @ E @ A @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(302,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_14) ).
thf(1182,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(114,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_insert__is__Un) ).
thf(642,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(243,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_is__singletonI) ).
thf(1016,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_bex__Un) ).
thf(679,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(107,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_inf__sup__aci_I5_J) ).
thf(622,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(32,axiom,
! [A: trm] :
( ( uSubst277968634Timeso @ ( some @ trm @ A ) @ ( none @ trm ) )
= ( none @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Timeso_Osimps_I3_J) ).
thf(393,plain,
! [A: trm] :
( ( uSubst277968634Timeso @ ( some @ trm @ A ) @ ( none @ trm ) )
= ( none @ trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(236,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: denotational_interp,E: real > variable > real] :
( ( ( uSubst95898992stappt @ A @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ C )
!= ( none @ trm ) )
=> ( ( denota1778088425es_ODE @ D @ E @ B @ ( the @ trm @ ( uSubst95898992stappt @ A @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ C ) ) )
= ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ A @ D @ ( E @ ( zero_zero @ real ) ) ) @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_usubst__ode) ).
thf(997,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: denotational_interp,E: real > variable > real] :
( ( ( uSubst95898992stappt @ A @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ C )
!= ( none @ trm ) )
=> ( ( denota1778088425es_ODE @ D @ E @ B @ ( the @ trm @ ( uSubst95898992stappt @ A @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ C ) ) )
= ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ A @ D @ ( E @ ( zero_zero @ real ) ) ) @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(147,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) )
= ( ~ ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_not__union__or) ).
thf(738,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) )
= ( ~ ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(118,axiom,
! [A: variable,B: variable,C: variable > real,D: real,E: set @ ( variable > real )] :
( ( A != B )
=> ( ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ E )
= ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ ( static_selectlike @ E @ C @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_repv__selectlike__other__converse) ).
thf(654,plain,
! [A: variable,B: variable,C: variable > real,D: real,E: set @ ( variable > real )] :
( ( A != B )
=> ( ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ E )
= ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ ( static_selectlike @ E @ C @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(255,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_inf__sup__aci_I8_J) ).
thf(1050,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(141,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Un__insert__right) ).
thf(721,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(159,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Collect__empty__eq__bot) ).
thf(779,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(29,axiom,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( some @ TA @ B ) ) )
= ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_not__Some__eq) ).
thf(371,plain,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( some @ TA @ B ) ) )
= ( A
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(605,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(78,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_le__inf__iff) ).
thf(515,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(291,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Un__empty__left) ).
thf(1150,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(343,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(269,axiom,
group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add) ).
thf(1086,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(111,axiom,
! [A: variable > real,B: variable,C: real] :
( ( denotational_Vagree @ A @ ( denotational_repv @ A @ B @ C ) @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) )
= ( C
= ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Vagree__repv__self) ).
thf(633,plain,
! [A: variable > real,B: variable,C: real] :
( ( denotational_Vagree @ A @ ( denotational_repv @ A @ B @ C ) @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) )
= ( C
= ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(508,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(311,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(210,axiom,
! [A: char,B: char] :
( ( rVar @ A )
!= ( dVar @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_variable_Odistinct_I1_J) ).
thf(921,plain,
! [A: char,B: char] :
( ( rVar @ A )
!= ( dVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(250,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_insert__absorb) ).
thf(1035,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(247,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: variable > real,E: set @ variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ( denota1419872369iation @ B @ D @ E )
=> ( denota1419872369iation @ A @ D @ ( sup_sup @ ( set @ variable ) @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Uvariation__trans) ).
thf(1026,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: variable > real,E: set @ variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ( denota1419872369iation @ B @ D @ E )
=> ( denota1419872369iation @ A @ D @ ( sup_sup @ ( set @ variable ) @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(94,axiom,
! [A: variable > ( option @ trm ) > $o,B: variable,C: option @ trm] :
( ! [D: variable,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: variable] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Assigno_Oinduct) ).
thf(558,plain,
! [A: variable > ( option @ trm ) > $o,B: variable,C: option @ trm] :
( ! [D: variable,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: variable] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(263,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_singletonI) ).
thf(1071,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(286,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sup__bot_Oeq__neutr__iff) ).
thf(1135,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(225,axiom,
! [A: char,B: char] :
( ( ( rVar @ A )
= ( rVar @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_variable_Oinject_I1_J) ).
thf(965,plain,
! [A: char,B: char] :
( ( ( rVar @ A )
= ( rVar @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(43,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_21) ).
thf(425,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(513,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(145,axiom,
! [A: real > variable > real,B: variable > real,C: set @ variable,D: denotational_interp,E: char,F: trm,G: real] :
( ( denota1419872369iation @ ( A @ ( zero_zero @ real ) ) @ B @ C )
=> ( ( denota1778088425es_ODE @ D @ A @ E @ F )
=> ( denota1419872369iation @ ( A @ G ) @ B @ ( sup_sup @ ( set @ variable ) @ C @ ( insert @ variable @ ( rVar @ E ) @ ( insert @ variable @ ( dVar @ E ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_solves__Vagree__trans) ).
thf(733,plain,
! [A: real > variable > real,B: variable > real,C: set @ variable,D: denotational_interp,E: char,F: trm,G: real] :
( ( denota1419872369iation @ ( A @ ( zero_zero @ real ) ) @ B @ C )
=> ( ( denota1778088425es_ODE @ D @ A @ E @ F )
=> ( denota1419872369iation @ ( A @ G ) @ B @ ( sup_sup @ ( set @ variable ) @ C @ ( insert @ variable @ ( rVar @ E ) @ ( insert @ variable @ ( dVar @ E ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(175,axiom,
! [A: set @ ( variable > real ),B: set @ ( variable > real ),C: variable > real,D: set @ variable] :
( ( static_selectlike @ ( sup_sup @ ( set @ ( variable > real ) ) @ A @ B ) @ C @ D )
= ( sup_sup @ ( set @ ( variable > real ) ) @ ( static_selectlike @ A @ C @ D ) @ ( static_selectlike @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_selectlike__union) ).
thf(819,plain,
! [A: set @ ( variable > real ),B: set @ ( variable > real ),C: variable > real,D: set @ variable] :
( ( static_selectlike @ ( sup_sup @ ( set @ ( variable > real ) ) @ A @ B ) @ C @ D )
= ( sup_sup @ ( set @ ( variable > real ) ) @ ( static_selectlike @ A @ C @ D ) @ ( static_selectlike @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(239,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: variable] : ( denotational_Vagree @ ( stateinterpol @ A @ B @ C ) @ ( stateinterpol @ A @ B @ ( insert @ variable @ D @ C ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ D @ ( bot_bot @ ( set @ variable ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_stateinterpol__insert) ).
thf(1007,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: variable] : ( denotational_Vagree @ ( stateinterpol @ A @ B @ C ) @ ( stateinterpol @ A @ B @ ( insert @ variable @ D @ C ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ D @ ( bot_bot @ ( set @ variable ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(182,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_equal__neg__zero) ).
thf(843,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(149,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Un__absorb) ).
thf(743,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(222,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( zero_zero @ ( set @ TA ) )
= ( insert @ TA @ ( zero_zero @ TA ) @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_set__zero) ).
thf(958,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( zero_zero @ ( set @ TA ) )
= ( insert @ TA @ ( zero_zero @ TA ) @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(204,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_is__singleton__def) ).
thf(904,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(228,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ComplI) ).
thf(975,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(215,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ( member @ ( variable > real ) @ A @ ( static_selectlike @ D @ B @ C ) )
= ( member @ ( variable > real ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_similar__selectlike__mem) ).
thf(936,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ ( variable > real )] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ( member @ ( variable > real ) @ A @ ( static_selectlike @ D @ B @ C ) )
= ( member @ ( variable > real ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_neg__le__iff__le) ).
thf(498,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Un__empty) ).
thf(1092,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(14,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(335,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(271,axiom,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( denota1419872369iation @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Uvariation__sym__rel) ).
thf(1090,plain,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( denota1419872369iation @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(167,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_the__elem__eq) ).
thf(804,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(135,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Set_Oset__insert) ).
thf(704,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(89,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(540,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(155,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_ComplD) ).
thf(764,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(241,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_empty__iff) ).
thf(1011,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(146,axiom,
! [A: variable > real,B: variable > real] : ( denotational_Vagree @ A @ B @ ( bot_bot @ ( set @ variable ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Vagree__empty) ).
thf(736,plain,
! [A: variable > real,B: variable > real] : ( denotational_Vagree @ A @ B @ ( bot_bot @ ( set @ variable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(289,axiom,
semilattice_inf @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__inf_26) ).
thf(1144,plain,
semilattice_inf @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1,conjecture,
denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(303,plain,
~ ( denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(202,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_sup_Oleft__commute) ).
thf(900,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(38,axiom,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( ( A
= ( none @ TA ) )
= ( B
= ( none @ TA ) ) )
=> ( ( ( A
!= ( none @ TA ) )
=> ( ( B
!= ( none @ TA ) )
=> ( ( the @ TA @ A )
= ( the @ TA @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_option_Oexpand) ).
thf(406,plain,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( ( A
= ( none @ TA ) )
= ( B
= ( none @ TA ) ) )
=> ( ( ( A
!= ( none @ TA ) )
=> ( ( B
!= ( none @ TA ) )
=> ( ( the @ TA @ A )
= ( the @ TA @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: set @ variable] :
( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ C )
!= ( none @ trm ) )
=> ( ( uSubst95898992stappt @ A @ B @ C )
= ( uSubst95898992stappt @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_usubstappt__det) ).
thf(362,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: set @ variable] :
( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ C )
!= ( none @ trm ) )
=> ( ( uSubst95898992stappt @ A @ B @ C )
= ( uSubst95898992stappt @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
! [A: option @ trm] :
( ! [B: trm] :
( A
!= ( some @ trm @ B ) )
=> ( A
= ( none @ trm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Differentialo_Ocases) ).
thf(451,plain,
! [A: option @ trm] :
( ! [B: trm] :
( A
!= ( some @ trm @ B ) )
=> ( A
= ( none @ trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(97,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( member @ TA @ ( the @ TA @ A ) @ ( set_option @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_option_Oset__sel) ).
thf(567,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( member @ TA @ ( the @ TA @ A ) @ ( set_option @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(189,axiom,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable,D: set @ variable] :
( ( static_selectlike @ ( static_selectlike @ A @ B @ C ) @ B @ D )
= ( static_selectlike @ A @ B @ ( sup_sup @ ( set @ variable ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_selectlike__compose) ).
thf(863,plain,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable,D: set @ variable] :
( ( static_selectlike @ ( static_selectlike @ A @ B @ C ) @ B @ D )
= ( static_selectlike @ A @ B @ ( sup_sup @ ( set @ variable ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(299,axiom,
preorder @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_27) ).
thf(1175,plain,
preorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(199,axiom,
! [A: variable > $o,B: variable] :
( ! [C: char] : ( A @ ( rVar @ C ) )
=> ( ! [C: char] : ( A @ ( dVar @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_variable_Oinduct) ).
thf(890,plain,
! [A: variable > $o,B: variable] :
( ! [C: char] : ( A @ ( rVar @ C ) )
=> ( ! [C: char] : ( A @ ( dVar @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(70,axiom,
! [TA: $tType,A: option @ TA,B: TA] :
( ( A
= ( some @ TA @ B ) )
=> ( A
!= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_option_OdiscI) ).
thf(494,plain,
! [TA: $tType,A: option @ TA,B: TA] :
( ( A
= ( some @ TA @ B ) )
=> ( A
!= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_subset__empty) ).
thf(758,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(173,axiom,
uminus @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ouminus_29) ).
thf(816,plain,
uminus @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(295,axiom,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable] :
( ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( static_selectlike @ A @ B @ C ) ) @ B @ C )
= ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ A ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_selectlike__co__selectlike) ).
thf(1162,plain,
! [A: set @ ( variable > real ),B: variable > real,C: set @ variable] :
( ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ ( static_selectlike @ A @ B @ C ) ) @ B @ C )
= ( static_selectlike @ ( uminus_uminus @ ( set @ ( variable > real ) ) @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(66,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_neg__equal__iff__equal) ).
thf(483,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(184,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_union__or) ).
thf(848,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(248,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_sup__idem) ).
thf(1029,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(217,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_le__zero__eq) ).
thf(943,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(122,axiom,
! [TA: $tType,A: TA,B: set @ ( option @ TA )] :
( ( these @ TA @ ( insert @ ( option @ TA ) @ ( some @ TA @ A ) @ B ) )
= ( insert @ TA @ A @ ( these @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_these__insert__Some) ).
thf(668,plain,
! [TA: $tType,A: TA,B: set @ ( option @ TA )] :
( ( these @ TA @ ( insert @ ( option @ TA ) @ ( some @ TA @ A ) @ B ) )
= ( insert @ TA @ A @ ( these @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(13,axiom,
! [TA: $tType,A: ( option @ TA ) > $o,B: option @ TA] :
( ( A @ ( none @ TA ) )
=> ( ! [C: TA] : ( A @ ( some @ TA @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_option_Oinducts) ).
thf(330,plain,
! [TA: $tType,A: ( option @ TA ) > $o,B: option @ TA] :
( ( A @ ( none @ TA ) )
=> ( ! [C: TA] : ( A @ ( some @ TA @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,axiom,
! [A: variable > real,B: variable] :
( ( denotational_repv @ A @ B @ ( A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_repv__self) ).
thf(462,plain,
! [A: variable > real,B: variable] :
( ( denotational_repv @ A @ B @ ( A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(278,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_sup__assoc) ).
thf(1112,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(19,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_double__compl) ).
thf(345,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(188,axiom,
~ ! [A: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real] :
~ ! [B: trm,C: denotational_interp,D: trm,E: denotational_interp,F: char,G: real > variable > real] :
( ( ? [H: variable > real] :
( ( denota1419872369iation @ H @ ( G @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ F ) @ ( insert @ variable @ ( dVar @ F ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ E @ D @ H )
!= ( denota1863255036rm_sem @ C @ B @ H ) ) ) )
= ( ( denota1419872369iation @ ( A @ B @ C @ D @ E @ F @ G ) @ ( G @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ F ) @ ( insert @ variable @ ( dVar @ F ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ E @ D @ ( A @ B @ C @ D @ E @ F @ G ) )
!= ( denota1863255036rm_sem @ C @ B @ ( A @ B @ C @ D @ E @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(858,plain,
~ ! [A: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real] :
~ ! [B: trm,C: denotational_interp,D: trm,E: denotational_interp,F: char,G: real > variable > real] :
( ( ? [H: variable > real] :
( ( denota1419872369iation @ H @ ( G @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ F ) @ ( insert @ variable @ ( dVar @ F ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ E @ D @ H )
!= ( denota1863255036rm_sem @ C @ B @ H ) ) ) )
= ( ( denota1419872369iation @ ( A @ B @ C @ D @ E @ F @ G ) @ ( G @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ F ) @ ( insert @ variable @ ( dVar @ F ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
& ( ( denota1863255036rm_sem @ E @ D @ ( A @ B @ C @ D @ E @ F @ G ) )
!= ( denota1863255036rm_sem @ C @ B @ ( A @ B @ C @ D @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(93,axiom,
! [A: ( option @ trm ) > $o,B: option @ trm] :
( ! [C: trm] : ( A @ ( some @ trm @ C ) )
=> ( ( A @ ( none @ trm ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Differentialo_Oinduct) ).
thf(552,plain,
! [A: ( option @ trm ) > $o,B: option @ trm] :
( ! [C: trm] : ( A @ ( some @ trm @ C ) )
=> ( ( A @ ( none @ trm ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(80,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( some @ TA @ A )
= ( some @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_option_Oinject) ).
thf(521,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( some @ TA @ A )
= ( some @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(231,axiom,
! [A: variable > real,B: variable > real] :
( ( denota1419872369iation @ A @ B @ ( bot_bot @ ( set @ variable ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Uvariation__empty) ).
thf(983,plain,
! [A: variable > real,B: variable > real] :
( ( denota1419872369iation @ A @ B @ ( bot_bot @ ( set @ variable ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(399,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(157,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_is__singletonI_H) ).
thf(768,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(261,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_sup__left__idem) ).
thf(1066,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(55,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_inf__right__idem) ).
thf(455,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(300,axiom,
! [TA: $tType,A: set @ ( option @ TA )] :
( ( ( these @ TA @ A )
!= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
!= ( bot_bot @ ( set @ ( option @ TA ) ) ) )
& ( A
!= ( insert @ ( option @ TA ) @ ( none @ TA ) @ ( bot_bot @ ( set @ ( option @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_these__not__empty__eq) ).
thf(1176,plain,
! [TA: $tType,A: set @ ( option @ TA )] :
( ( ( these @ TA @ A )
!= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
!= ( bot_bot @ ( set @ ( option @ TA ) ) ) )
& ( A
!= ( insert @ ( option @ TA ) @ ( none @ TA ) @ ( bot_bot @ ( set @ ( option @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(232,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_sup_Oright__idem) ).
thf(986,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(185,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_sup_Obounded__iff) ).
thf(851,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(74,axiom,
! [TA: $tType] :
( ( '!' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
& ! [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_split__option__all) ).
thf(505,plain,
! [TA: $tType] :
( ( '!' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
& ! [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(119,axiom,
! [A: variable > real,B: set @ variable,C: set @ ( variable > real ),D: set @ ( variable > real )] :
( ! [E: variable > real] :
( ( denota1419872369iation @ E @ A @ ( uminus_uminus @ ( set @ variable ) @ B ) )
=> ( ( member @ ( variable > real ) @ E @ C )
= ( member @ ( variable > real ) @ E @ D ) ) )
=> ( ( static_selectlike @ C @ A @ B )
= ( static_selectlike @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_selectlike__equal__cocond__rule) ).
thf(658,plain,
! [A: variable > real,B: set @ variable,C: set @ ( variable > real ),D: set @ ( variable > real )] :
( ! [E: variable > real] :
( ( denota1419872369iation @ E @ A @ ( uminus_uminus @ ( set @ variable ) @ B ) )
=> ( ( member @ ( variable > real ) @ E @ C )
= ( member @ ( variable > real ) @ E @ D ) ) )
=> ( ( static_selectlike @ C @ A @ B )
= ( static_selectlike @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_bot__fun__def) ).
thf(636,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(253,axiom,
! [A: real > variable > real,B: trm,C: real] :
( ( denota1778088425es_ODE @ i @ A @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ B ) ) )
=> ( denota1419872369iation @ ( A @ C ) @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_vaflow1) ).
thf(1044,plain,
! [A: real > variable > real,B: trm,C: real] :
( ( denota1778088425es_ODE @ i @ A @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ B ) ) )
=> ( denota1419872369iation @ ( A @ C ) @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(265,axiom,
( denotational_repv
= ( ^ [A: variable > real,B: variable,C: real,D: variable] : ( if @ real @ ( B = D ) @ C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_repv__def__correct) ).
thf(1076,plain,
( denotational_repv
= ( ^ [A: variable > real,B: variable,C: real,D: variable] : ( if @ real @ ( B = D ) @ C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(44,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add_Oinverse__inverse) ).
thf(426,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(85,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_option_Oexhaust) ).
thf(531,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(120,axiom,
! [A: variable > real,B: variable,C: real] : ( denotational_Vagree @ A @ ( denotational_repv @ A @ B @ C ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Vagree__repv) ).
thf(663,plain,
! [A: variable > real,B: variable,C: real] : ( denotational_Vagree @ A @ ( denotational_repv @ A @ B @ C ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: option @ TB,B: ( option @ TB ) > ( option @ TA ) > $o,C: option @ TA] :
( ( ( A
= ( none @ TB ) )
=> ( B @ A @ C ) )
=> ( ( ( C
= ( none @ TA ) )
=> ( B @ A @ C ) )
=> ( ! [D: TB,E: TA] :
( ( A
= ( some @ TB @ D ) )
=> ( ( C
= ( some @ TA @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_combine__options__cases) ).
thf(374,plain,
! [TA: $tType,TB: $tType,A: option @ TB,B: ( option @ TB ) > ( option @ TA ) > $o,C: option @ TA] :
( ( ( A
= ( none @ TB ) )
=> ( B @ A @ C ) )
=> ( ( ( C
= ( none @ TA ) )
=> ( B @ A @ C ) )
=> ( ! [D: TB,E: TA] :
( ( A
= ( some @ TB @ D ) )
=> ( ( C
= ( some @ TA @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_sup__fun__def) ).
thf(648,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(171,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_insertI2) ).
thf(812,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(105,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_10) ).
thf(617,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(180,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ A @ D )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_boolean__algebra__cancel_Osup1) ).
thf(836,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ A @ D )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(267,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_inf__sup__aci_I7_J) ).
thf(1081,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_mk__disjoint__insert) ).
thf(749,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(290,axiom,
! [A: real > variable > real,B: char,C: denotational_interp,D: trm,E: denotational_interp,F: trm] :
( ! [G: variable > real] :
( ( denota1419872369iation @ G @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
=> ( ( denota1863255036rm_sem @ C @ D @ G )
= ( denota1863255036rm_sem @ E @ F @ G ) ) )
=> ( ( denota1778088425es_ODE @ C @ A @ B @ D )
= ( denota1778088425es_ODE @ E @ A @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_same__ODE__same__sol) ).
thf(1145,plain,
! [A: real > variable > real,B: char,C: denotational_interp,D: trm,E: denotational_interp,F: trm] :
( ! [G: variable > real] :
( ( denota1419872369iation @ G @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ B ) @ ( insert @ variable @ ( dVar @ B ) @ ( bot_bot @ ( set @ variable ) ) ) ) )
=> ( ( denota1863255036rm_sem @ C @ D @ G )
= ( denota1863255036rm_sem @ E @ F @ G ) ) )
=> ( ( denota1778088425es_ODE @ C @ A @ B @ D )
= ( denota1778088425es_ODE @ E @ A @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(244,axiom,
! [A: denotational_interp,B: real > variable > real,C: char,D: trm,E: real] :
( ( denota1778088425es_ODE @ A @ B @ C @ D )
=> ( denotational_Vagree @ ( B @ E ) @ ( B @ ( zero_zero @ real ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ C ) @ ( insert @ variable @ ( dVar @ C ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_solves__Vagree) ).
thf(1018,plain,
! [A: denotational_interp,B: real > variable > real,C: char,D: trm,E: real] :
( ( denota1778088425es_ODE @ A @ B @ C @ D )
=> ( denotational_Vagree @ ( B @ E ) @ ( B @ ( zero_zero @ real ) ) @ ( uminus_uminus @ ( set @ variable ) @ ( insert @ variable @ ( rVar @ C ) @ ( insert @ variable @ ( dVar @ C ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(226,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Int__iff) ).
thf(968,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(56,axiom,
semilattice_sup @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_18) ).
thf(458,plain,
semilattice_sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(82,axiom,
! [A: option @ trm] :
( ( uSubst277968634Timeso @ ( none @ trm ) @ A )
= ( none @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Timeso_Osimps_I2_J) ).
thf(525,plain,
! [A: option @ trm] :
( ( uSubst277968634Timeso @ ( none @ trm ) @ A )
= ( none @ trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(138,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sup__eq__bot__iff) ).
thf(712,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_subsetI) ).
thf(855,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_insert__commute) ).
thf(690,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(293,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ variable] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ( denotational_Vagree @ A @ B @ D )
=> ( denotational_Vagree @ A @ B @ ( sup_sup @ ( set @ variable ) @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Vagree__union) ).
thf(1156,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: set @ variable] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ( denotational_Vagree @ A @ B @ D )
=> ( denotational_Vagree @ A @ B @ ( sup_sup @ ( set @ variable ) @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(198,axiom,
! [A: char] :
( ( size_variable @ ( dVar @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_variable_Osize__gen_I2_J) ).
thf(887,plain,
! [A: char] :
( ( size_variable @ ( dVar @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(227,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ D @ A )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_boolean__algebra__cancel_Osup2) ).
thf(971,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ D @ A )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(274,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_bot__set__def) ).
thf(1098,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(256,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_sup_Ocommute) ).
thf(1053,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(124,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Un__singleton__iff) ).
thf(673,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(251,axiom,
! [TA: $tType,A: option @ TA] :
( ( ( set_option @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_set__empty__eq) ).
thf(1038,plain,
! [TA: $tType,A: option @ TA] :
( ( ( set_option @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(140,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),E: trm,F: denotational_interp] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ( ( uSubst95898992stappt @ D @ C @ E )
!= ( none @ trm ) )
=> ( ( denota1863255036rm_sem @ F @ ( the @ trm @ ( uSubst95898992stappt @ D @ C @ E ) ) @ A )
= ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ D @ F @ B ) @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_usubst__term) ).
thf(717,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),E: trm,F: denotational_interp] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ( ( uSubst95898992stappt @ D @ C @ E )
!= ( none @ trm ) )
=> ( ( denota1863255036rm_sem @ F @ ( the @ trm @ ( uSubst95898992stappt @ D @ C @ E ) ) @ A )
= ( denota1863255036rm_sem @ ( uSubst2091380086djoint @ D @ F @ B ) @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( none @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
& ~ ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_option_Osplit__sel__asm) ).
thf(502,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( none @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
& ~ ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(181,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_sup_Oleft__idem) ).
thf(840,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(359,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(205,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_Compl__iff) ).
thf(907,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(220,axiom,
! [A: variable] :
( ! [B: char] :
( A
!= ( rVar @ B ) )
=> ~ ! [B: char] :
( A
!= ( dVar @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_variable_Oexhaust) ).
thf(951,plain,
! [A: variable] :
( ! [B: char] :
( A
!= ( rVar @ B ) )
=> ~ ! [B: char] :
( A
!= ( dVar @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(169,axiom,
semilattice_sup @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__sup_25) ).
thf(808,plain,
semilattice_sup @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(15,axiom,
! [A: option @ trm] :
( ( A
!= ( none @ trm ) )
= ( ? [B: trm] :
( A
= ( some @ trm @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_undeft__equiv) ).
thf(336,plain,
! [A: option @ trm] :
( ( A
!= ( none @ trm ) )
= ( ? [B: trm] :
( A
= ( some @ trm @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(288,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Collect__empty__eq) ).
thf(1141,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType] :
( ( case_option @ TA @ TB )
= ( ^ [A: TA,B: TB > TA,C: option @ TB] :
( if @ TA
@ ( C
= ( none @ TB ) )
@ A
@ ( B @ ( the @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_option_Ocase__eq__if) ).
thf(600,plain,
! [TA: $tType,TB: $tType] :
( ( case_option @ TA @ TB )
= ( ^ [A: TA,B: TB > TA,C: option @ TB] :
( if @ TA
@ ( C
= ( none @ TB ) )
@ A
@ ( B @ ( the @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(143,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_sup__commute) ).
thf(727,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(7,axiom,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_option_Odistinct_I1_J) ).
thf(314,plain,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1808546759up_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__sup__bot) ).
thf(446,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1808546759up_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(194,axiom,
( denotational_Vagree
= ( ^ [A: variable > real,B: variable > real,C: set @ variable] :
! [D: variable] :
( ( member @ variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Vagree__def) ).
thf(876,plain,
( denotational_Vagree
= ( ^ [A: variable > real,B: variable > real,C: set @ variable] :
! [D: variable] :
( ( member @ variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(465,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(109,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_subset__antisym) ).
thf(627,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(268,axiom,
! [A: variable > real,B: set @ variable] : ( denota1419872369iation @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Uvariation__refl) ).
thf(1084,plain,
! [A: variable > real,B: set @ variable] : ( denota1419872369iation @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(123,axiom,
( ( denota1778088425es_ODE @ i @ f @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) )
=> ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_l2r) ).
thf(671,plain,
( ( denota1778088425es_ODE @ i @ f @ x @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) @ theta ) ) )
=> ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(203,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add) ).
thf(903,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(81,axiom,
bounde1808546759up_bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_17) ).
thf(524,plain,
bounde1808546759up_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(283,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_is__singleton__the__elem) ).
thf(1126,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(213,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_13) ).
thf(931,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(88,axiom,
lattice @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_6) ).
thf(539,plain,
lattice @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(133,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_inf__sup__aci_I6_J) ).
thf(699,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(223,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add) ).
thf(961,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(201,axiom,
! [A: variable,B: variable,C: variable > real,D: real,E: set @ ( variable > real )] :
( ( A != B )
=> ( ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ ( static_selectlike @ E @ C @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) )
= ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_repv__selectlike__other) ).
thf(896,plain,
! [A: variable,B: variable,C: variable > real,D: real,E: set @ ( variable > real )] :
( ( A != B )
=> ( ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ ( static_selectlike @ E @ C @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ) )
= ( member @ ( variable > real ) @ ( denotational_repv @ C @ A @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(3,axiom,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( times @ A @ B )
= ( times @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_trm_Oinject_I6_J) ).
thf(304,plain,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( times @ A @ B )
= ( times @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(259,axiom,
denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_a1) ).
thf(1062,plain,
denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ f @ x @ theta,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( none @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
=> ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_option_Osplit__sel) ).
thf(351,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( none @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
=> ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_inf_Obounded__iff) ).
thf(390,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(35,axiom,
! [A: char > ( option @ trm ) > $o,B: char,C: option @ trm] :
( ! [D: char,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: char] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_ODEo_Oinduct) ).
thf(401,plain,
! [A: char > ( option @ trm ) > $o,B: char,C: option @ trm] :
( ! [D: char,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: char] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(235,axiom,
( stateinterpol
= ( ^ [A: variable > real,B: variable > real,C: set @ variable,D: variable] : ( if @ real @ ( member @ variable @ D @ C ) @ ( A @ D ) @ ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_stateinterpol__def) ).
thf(995,plain,
( stateinterpol
= ( ^ [A: variable > real,B: variable > real,C: set @ variable,D: variable] : ( if @ real @ ( member @ variable @ D @ C ) @ ( A @ D ) @ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(218,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_UnI1) ).
thf(946,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(275,axiom,
! [A: variable,B: set @ variable,C: variable > real,D: variable > real] :
( ( member @ variable @ A @ B )
=> ( ( stateinterpol @ C @ D @ B @ A )
= ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_stateinterpol__left) ).
thf(1101,plain,
! [A: variable,B: set @ variable,C: variable > real,D: variable > real] :
( ( member @ variable @ A @ B )
=> ( ( stateinterpol @ C @ D @ B @ A )
= ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(208,axiom,
! [A: variable,B: trm,C: denotational_interp,D: variable > real,E: variable > real,F: set @ variable] :
( ~ ( member @ variable @ A @ ( static_FVT @ B ) )
=> ( ( denota1863255036rm_sem @ C @ B @ ( stateinterpol @ D @ E @ F ) )
= ( denota1863255036rm_sem @ C @ B @ ( stateinterpol @ D @ E @ ( insert @ variable @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_stateinterpol__FVT) ).
thf(914,plain,
! [A: variable,B: trm,C: denotational_interp,D: variable > real,E: variable > real,F: set @ variable] :
( ~ ( member @ variable @ A @ ( static_FVT @ B ) )
=> ( ( denota1863255036rm_sem @ C @ B @ ( stateinterpol @ D @ E @ F ) )
= ( denota1863255036rm_sem @ C @ B @ ( stateinterpol @ D @ E @ ( insert @ variable @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(64,axiom,
! [A: trm,B: trm] :
( ( uSubst277968634Timeso @ ( some @ trm @ A ) @ ( some @ trm @ B ) )
= ( some @ trm @ ( times @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Timeso_Osimps_I1_J) ).
thf(478,plain,
! [A: trm,B: trm] :
( ( uSubst277968634Timeso @ ( some @ trm @ A ) @ ( some @ trm @ B ) )
= ( some @ trm @ ( times @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(128,axiom,
! [A: real > variable > real,B: trm,C: real] :
( ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ A @ x @ B )
=> ( denota1419872369iation @ ( A @ C ) @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_vaflow2) ).
thf(684,plain,
! [A: real > variable > real,B: trm,C: real] :
( ( denota1778088425es_ODE @ ( uSubst2091380086djoint @ sigma @ i @ omega ) @ A @ x @ B )
=> ( denota1419872369iation @ ( A @ C ) @ ( A @ ( zero_zero @ real ) ) @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(92,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_compl__eq__compl__iff) ).
thf(549,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(87,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_inf__left__idem) ).
thf(536,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(47,axiom,
! [A: variable > real,B: variable > real] :
( ( stateinterpol @ A @ B @ ( statediff @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_stateinterpol__diff) ).
thf(433,plain,
! [A: variable > real,B: variable > real] :
( ( stateinterpol @ A @ B @ ( statediff @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(76,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( A
= ( some @ TA @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_option_Oexhaust__sel) ).
thf(510,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( A
= ( some @ TA @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(46,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_5) ).
thf(432,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(179,axiom,
! [TA: $tType] :
( ( these @ TA @ ( bot_bot @ ( set @ ( option @ TA ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_these__empty) ).
thf(833,plain,
! [TA: $tType] :
( ( these @ TA @ ( bot_bot @ ( set @ ( option @ TA ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(37,axiom,
lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_22) ).
thf(405,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(186,axiom,
denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_uv) ).
thf(854,plain,
denota1419872369iation @ ( f @ ( zero_zero @ real ) ) @ omega @ ( sup_sup @ ( set @ variable ) @ u @ ( insert @ variable @ ( rVar @ x ) @ ( insert @ variable @ ( dVar @ x ) @ ( bot_bot @ ( set @ variable ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(101,axiom,
( denotational_Vagree
= ( ^ [A: variable > real,B: variable > real] : ( denotational_Vagree @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_Vagree__sym) ).
thf(603,plain,
( denotational_Vagree
= ( ^ [A: variable > real,B: variable > real] : ( denotational_Vagree @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: set @ ( option @ TA )] :
( ( member @ TA @ A @ ( these @ TA @ B ) )
= ( member @ ( option @ TA ) @ ( some @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_in__these__eq) ).
thf(422,plain,
! [TA: $tType,A: TA,B: set @ ( option @ TA )] :
( ( member @ TA @ A @ ( these @ TA @ B ) )
= ( member @ ( option @ TA ) @ ( some @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(162,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_sup__bot__right) ).
thf(790,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(96,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( some @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_option_Osel) ).
thf(564,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( some @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(298,axiom,
! [A: char] :
( ( size_size @ variable @ ( dVar @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_variable_Osize_I4_J) ).
thf(1172,plain,
! [A: char] :
( ( size_size @ variable @ ( dVar @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(257,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_equals0I) ).
thf(1056,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(132,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_bot__empty__eq) ).
thf(696,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(296,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_equals0D) ).
thf(1165,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(221,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ex__in__conv) ).
thf(955,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(164,axiom,
! [A: variable > real,B: variable,C: real] : ( denota1419872369iation @ A @ ( denotational_repv @ A @ B @ C ) @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Uvariation__repv) ).
thf(796,plain,
! [A: variable > real,B: variable,C: real] : ( denota1419872369iation @ A @ ( denotational_repv @ A @ B @ C ) @ ( insert @ variable @ B @ ( bot_bot @ ( set @ variable ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(209,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Un__left__commute) ).
thf(918,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(166,axiom,
! [A: variable,B: variable > real,C: variable > real] :
( ~ ( member @ variable @ A @ ( statediff @ B @ C ) )
=> ( ( B @ A )
= ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_nostatediff) ).
thf(801,plain,
! [A: variable,B: variable > real,C: variable > real] :
( ~ ( member @ variable @ A @ ( statediff @ B @ C ) )
=> ( ( B @ A )
= ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(24,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(358,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(168,axiom,
zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_30) ).
thf(807,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(212,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_singleton__inject) ).
thf(928,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(39,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898992stappt @ A @ B @ ( times @ C @ D ) )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
& ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_usubstappt__times__conv) ).
thf(415,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898992stappt @ A @ B @ ( times @ C @ D ) )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
& ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(284,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_sup__bot__left) ).
thf(1129,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(83,axiom,
uminus @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_24) ).
thf(528,plain,
uminus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(57,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_minus__equation__iff) ).
thf(459,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(234,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_is__singletonE) ).
thf(992,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(176,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_sup__bot_Oright__neutral) ).
thf(822,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(238,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add_Oinverse__neutral) ).
thf(1004,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(192,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_IntI) ).
thf(871,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(72,axiom,
bot @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Obot_7) ).
thf(501,plain,
bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(28,axiom,
! [A: variable > real,B: variable > real,C: set @ variable] : ( denotational_Vagree @ ( stateinterpol @ A @ B @ C ) @ A @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Vagree__stateinterpol) ).
thf(369,plain,
! [A: variable > real,B: variable > real,C: set @ variable] : ( denotational_Vagree @ ( stateinterpol @ A @ B @ C ) @ A @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(103,axiom,
! [TA: $tType,A: option @ TA,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( member @ TA @ D @ ( set_option @ TA @ A ) )
=> ( B @ D ) )
=> ( ( A
= ( some @ TA @ C ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ospec) ).
thf(607,plain,
! [TA: $tType,A: option @ TA,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( member @ TA @ D @ ( set_option @ TA @ A ) )
=> ( B @ D ) )
=> ( ( A
= ( some @ TA @ C ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(67,axiom,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denotational_Vagree @ A @ B @ C )
=> ( denotational_Vagree @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Vagree__sym__rel) ).
thf(486,plain,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denotational_Vagree @ A @ B @ C )
=> ( denotational_Vagree @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(216,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_insert__not__empty) ).
thf(940,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(22,axiom,
! [A: ( option @ trm ) > ( option @ trm ) > $o,B: option @ trm,C: option @ trm] :
( ! [D: trm,E: trm] : ( A @ ( some @ trm @ D ) @ ( some @ trm @ E ) )
=> ( ! [D: option @ trm] : ( A @ ( none @ trm ) @ D )
=> ( ! [D: trm] : ( A @ ( some @ trm @ D ) @ ( none @ trm ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Timeso_Oinduct) ).
thf(354,plain,
! [A: ( option @ trm ) > ( option @ trm ) > $o,B: option @ trm,C: option @ trm] :
( ! [D: trm,E: trm] : ( A @ ( some @ trm @ D ) @ ( some @ trm @ E ) )
=> ( ! [D: option @ trm] : ( A @ ( none @ trm ) @ D )
=> ( ! [D: trm] : ( A @ ( some @ trm @ D ) @ ( none @ trm ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(240,axiom,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8) ).
thf(1009,plain,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(90,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_inf_Oidem) ).
thf(543,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(158,axiom,
! [A: variable > real,B: variable > real,C: set @ variable,D: trm,E: denotational_interp] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ C )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( denota1863255036rm_sem @ E @ D @ A )
= ( denota1863255036rm_sem @ E @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_coincidence__term__cor) ).
thf(775,plain,
! [A: variable > real,B: variable > real,C: set @ variable,D: trm,E: denotational_interp] :
( ( denota1419872369iation @ A @ B @ C )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ C )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( denota1863255036rm_sem @ E @ D @ A )
= ( denota1863255036rm_sem @ E @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(113,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Un__assoc) ).
thf(639,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(125,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_sup__left__commute) ).
thf(676,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(69,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_compl__le__compl__iff) ).
thf(491,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(262,axiom,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ord_less_eq @ ( set @ variable ) @ ( statediff @ A @ B ) @ ( uminus_uminus @ ( set @ variable ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Vagree__statediff) ).
thf(1069,plain,
! [A: variable > real,B: variable > real,C: set @ variable] :
( ( denotational_Vagree @ A @ B @ C )
=> ( ord_less_eq @ ( set @ variable ) @ ( statediff @ A @ B ) @ ( uminus_uminus @ ( set @ variable ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(136,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_empty__subsetI) ).
thf(708,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1184,plain,
$false,
inference(e,[status(thm)],[645,809,1024,1105,846,893,518,1179,481,962,468,977,730,308,873,614,1041,741,1073,878,440,1078,715,472,814,913,1063,340,1001,782,436,651,1095,404,724,570,785,619,702,357,1059,1132,817,1087,421,1013,881,448,1115,325,475,443,348,1109,321,766,866,396,1169,687,307,439,529,925,366,534,546,793,1153,761,1047,798,910,746,825,1021,1123,598,561,429,693,630,467,1032,625,665,830,1159,682,710,324,317,948,1121,980,1138,869,989,420,1118,328,884,488,339,933,753,1182,642,1016,679,622,393,997,738,654,1050,721,779,371,605,515,1150,343,1086,633,508,311,921,1035,1026,558,1071,1135,965,425,513,733,819,1007,843,743,958,904,975,936,498,1092,335,1090,804,704,540,764,1011,736,1144,303,900,406,362,451,567,863,1175,890,494,758,816,1162,483,848,1029,943,668,330,462,1112,345,858,552,521,983,399,768,1066,455,1176,986,851,505,658,636,1044,1076,426,531,663,374,648,812,617,836,1081,749,1145,1018,968,458,525,712,855,690,1156,887,971,1098,1053,673,1038,717,502,840,359,907,951,808,336,1141,600,727,314,446,876,465,627,1084,671,903,524,1126,931,539,699,961,896,304,1062,351,390,401,995,946,1101,914,478,684,549,536,433,510,432,833,405,854,603,422,790,564,1172,1056,696,1165,955,796,918,801,358,807,928,415,1129,528,459,992,822,1004,871,501,369,607,486,940,354,1009,543,775,639,676,491,1069,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP199^2 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:22:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/1.09 % [INFO] Parsing done (235ms).
% 1.83/1.10 % [INFO] Running in sequential loop mode.
% 2.44/1.31 % [INFO] eprover registered as external prover.
% 2.44/1.31 % [INFO] cvc4 registered as external prover.
% 2.44/1.31 % [INFO] Scanning for conjecture ...
% 2.81/1.41 % [INFO] Found a conjecture and 301 axioms. Running axiom selection ...
% 3.23/1.51 % [INFO] Axiom selection finished. Selected 300 axioms (removed 1 axioms).
% 3.72/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 3.72/1.69 % [INFO] Type checking passed.
% 3.72/1.70 % [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 ...
% 52.01/23.12 % External prover 'e' found a proof!
% 52.01/23.12 % [INFO] Killing All external provers ...
% 52.01/23.12 % Time passed: 22614ms (effective reasoning time: 22023ms)
% 52.01/23.12 % 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)>
% 52.01/23.13 % Axioms used in derivation (300): fact_69_Uvariation__sym__rel, tcon_fun___Orderings_Obot, fact_62_Un__absorb, fact_170_similar__selectlike__mem, fact_55_inf__sup__aci_I5_J, tcon_Set_Oset___Groups_Ouminus_15, fact_180_Vagree__sym__rel, tcon_Set_Oset___Orderings_Obot_14, fact_208_ComplD, fact_104_is__singleton__the__elem, fact_16_empty__iff, fact_50_sup__assoc, fact_13_empty__Collect__eq, fact_147_selectlike__union, fact_11_sup__bot_Oneutr__eq__iff, fact_151_option_Oexhaust, fact_3_Un__insert__right, fact_206_fun__Compl__def, fact_175_ospec, fact_44_sup__commute, fact_25_sup__apply, fact_247_compl__le__compl__iff, fact_222_Vagree__stateinterpol, fact_21_sup__left__idem, fact_40_insertI1, tcon_HOL_Obool___Lattices_Olattice_22, tcon_Set_Oset___Lattices_Olattice_13, tcon_Nat_Onat___Orderings_Opreorder_5, fact_66_UnI2, fact_42_sup__left__commute, fact_130_repv__access, fact_184_option_Osimps_I14_J, fact_155_combine__options__cases, fact_94_f2, tcon_Set_Oset___Orderings_Opreorder_12, fact_8_sup__eq__bot__iff, fact_242_inf__right__idem, fact_108_is__singletonI_H, fact_163_option_Osplit__sel, fact_179_Vagree__refl, fact_2_Un__insert__left, fact_201_equal__neg__zero, fact_243_IntI, fact_24_sup_Oidem, fact_90_union__or, fact_95_zero__reorient, fact_200_neg__equal__0__iff__equal, fact_131_these__empty, fact_127_these__not__empty__eq, fact_214_selectlike__equal__cond, tcon_HOL_Obool___Groups_Ouminus_24, tcon_HOL_Obool___Lattices_Oboolean__algebra_20, fact_117_usubstappt__det, tcon_Nat_Onat___Orderings_Obot_7, fact_187_solves__Vagree, fact_252_empty__subsetI, fact_27_singletonI, fact_129_repv__self, tcon_Nat_Onat___Lattices_Olattice_6, fact_87_variable_Oinject_I1_J, fact_126_these__empty__eq, fact_185_option_Oset__sel, fact_72_Uvariation__def, fact_33_mk__disjoint__insert, fact_205_equation__minus__iff, fact_128_variable_Osimps_I7_J, fact_20_sup_Oright__idem, fact_198_add_Oinverse__neutral, fact_204_minus__equation__iff, fact_246_neg__le__iff__le, fact_38_Set_Oset__insert, fact_89_variable_Oinject_I2_J, tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_17, fact_15_all__not__in__conv, fact_192_compl__eq__compl__iff, tcon_fun___Lattices_Obounded__semilattice__sup__bot, fact_239_inf_Oleft__idem, fact_31_equals0D, fact_141_not__None__eq, fact_110_is__singletonE, fact_39_insertI2, fact_199_neg__0__equal__iff__equal, fact_135_these__insert__Some, fact_133_repv__def__correct, fact_26_UnCI, fact_227_stateinterpol__diff, fact_253_subset__empty, fact_234_subsetI, fact_125_Uvariation__repv, fact_165_option_Osimps_I15_J, fact_43_sup_Oleft__commute, fact_137_repv__selectlike__other, fact_46_Collect__mem__eq, tcon_HOL_Obool___Lattices_Osemilattice__inf_19, fact_142_not__Some__eq, tcon_Real_Oreal___Orderings_Opreorder_27, fact_12_sup__bot_Oright__neutral, fact_5_sup__bot__left, fact_140_selectlike__self, fact_68_UnE, fact_132_these__insert__None, fact_51_sup_Oassoc, fact_230_coincidence__term, fact_63_Un__assoc, fact_101_variable_Oexhaust, fact_105_vaflow2, fact_93_bot__apply, tcon_HOL_Obool___Orderings_Obot_23, fact_229_nostatediff, fact_28_bot__set__def, fact_197_ComplI, fact_167_elem__set, fact_76_singleton__iff, tcon_fun___Lattices_Obounded__lattice_2, fact_158_Timeso_Oinduct, help_If_1_1_T, fact_10_sup__bot_Oleft__neutral, fact_109_is__singleton__def, fact_70_Uvariation__refl, tcon_Real_Oreal___Groups_Oordered__ab__group__add, fact_34_insert__commute, fact_1_Uvariation__empty, fact_61_Un__commute, fact_98_same__ODE__same__sol, tcon_fun___Lattices_Osemilattice__sup, fact_96_bot__fun__def, fact_115_variable_Osize__gen_I1_J, fact_7_bot__eq__sup__iff, fact_4_Un__empty, fact_249_inf_Obounded__iff, tcon_Set_Oset___Lattices_Osemilattice__sup_9, fact_216_Timeso_Oelims, fact_49_sup_Ocommute, fact_35_insert__eq__iff, fact_237_inf_Oidem, fact_186_option_Ocase__eq__if, fact_88_set__zero, fact_217_trm_Oinject_I6_J, fact_36_insert__absorb, fact_235_subset__antisym, fact_145_option_Ocollapse, fact_215_stateinterpol__insert, fact_6_sup__bot__right, tcon_fun___Lattices_Osemilattice__inf, fact_100_variable_Oinduct, tcon_Nat_Onat___Groups_Ozero, tcon_Real_Oreal___Lattices_Olattice_28, fact_64_ball__Un, fact_144_selectlike__compose, fact_57_inf__sup__aci_I7_J, fact_193_double__compl, fact_157_undeft__equiv, fact_223_stateinterpol__def, fact_181_Vagree__empty, fact_45_mem__Collect__eq, fact_81_singleton__Un__iff, fact_138_repv__selectlike__self, fact_103_Collect__empty__eq__bot, fact_112_l2r, fact_248_le__inf__iff, fact_78_Un__empty__right, fact_73_singleton__inject, fact_91_ball__insert, fact_188_Vagree__repv, fact_250_le__sup__iff, fact_233_order__refl, tcon_Real_Oreal___Groups_Ozero_30, fact_146_in__these__eq, fact_164_option_Osplit__sel__asm, fact_118_undeft__None, tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8, fact_194_uminus__apply, fact_168_Vagree__and, fact_190_neg__equal__iff__equal, fact_251_sup_Obounded__iff, tcon_Real_Oreal___Lattices_Osemilattice__inf_26, fact_75_doubleton__eq__iff, fact_224_usubstappt__times__conv, fact_74_insert__not__empty, fact_241_inf_Oright__idem, fact_245_le__zero__eq, fact_71_Uvariation__sym, fact_150_option_OdiscI, fact_107_a1, fact_92_the__elem__eq, fact_121_option_Oexpand, fact_154_split__option__all, fact_32_emptyE, fact_79_Un__empty__left, fact_60_Un__left__absorb, fact_196_Compl__iff, fact_47_Collect__cong, fact_207_double__complement, fact_41_insertE, fact_195_Compl__eq__Compl__iff, help_If_3_1_T, tcon_Nat_Onat___Lattices_Osemilattice__inf_4, fact_149_option_Osel, help_If_2_1_T, fact_111_vaflow1, fact_67_UnI1, fact_114_subdef, tcon_fun___Lattices_Oboolean__algebra, fact_30_equals0I, fact_82_Un__singleton__iff, fact_177_Vagree__def, fact_29_ex__in__conv, tcon_Set_Oset___Lattices_Obounded__lattice_1, tcon_Set_Oset___Lattices_Oboolean__algebra_11, fact_156_ODEo_Oinduct, fact_161_Differentialo_Oinduct, fact_159_Assigno_Oinduct, fact_134_variable_Osimps_I8_J, fact_176_Vagree__union, tcon_Real_Oreal___Groups_Ogroup__add, fact_173_option_Oset__intros, tcon_HOL_Obool___Orderings_Opreorder_21, fact_77_singletonD, fact_56_inf__sup__aci_I6_J, fact_86__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062, fact_136_repv__selectlike__other__converse, fact_14_Collect__empty__eq, fact_166_Vagree__repv__self, fact_236_inf__apply, fact_139_option_Oinject, fact_212_selectlike__equal__cocond__rule, fact_209_Timeso_Osimps_I2_J, fact_189_Timeso_Osimps_I3_J, fact_225_usubstappt_Osimps_I6_J, fact_17_insert__absorb2, fact_240_inf__left__idem, tcon_fun___Orderings_Opreorder, fact_174_option_Oset__cases, fact_172_Aterm__Some, fact_211_selectlike__equal__cocond__corule, fact_153_split__option__ex, fact_119_usubst__ode, fact_84__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_226_Timeso_Osimps_I1_J, fact_221_stateinterpol__empty, fact_218_stateinterpol__left, fact_52_boolean__algebra__cancel_Osup2, fact_22_sup_Oleft__idem, fact_113_IH, fact_148_option_Odistinct_I1_J, fact_191_add_Oinverse__inverse, fact_143_selectlike__empty, fact_18_insert__iff, fact_183_option_Osimps_I5_J, fact_182_option_Osimps_I4_J, fact_244_Int__iff, tcon_HOL_Obool___Lattices_Osemilattice__sup_18, tcon_Set_Oset___Groups_Ozero_16, fact_178_Vagree__sym, fact_162_option_Oexhaust__sel, fact_80_Uvariation__trans, tcon_Real_Oreal___Lattices_Osemilattice__sup_25, fact_97_not__union__or, tcon_Set_Oset___Lattices_Osemilattice__inf_10, fact_219_stateinterpol__right, tcon_Real_Oreal___Groups_Olinordered__ab__group__add, tcon_Real_Oreal___Groups_Ouminus_29, fact_210_Timeso__undef, fact_37_insert__ident, fact_203_Uvariation__Vagree, fact_228_stateinterpol__FVT, fact_83_insert__is__Un, fact_85_solves__Vagree__trans, fact_220_selectlike__co__selectlike, fact_202_neg__equal__zero, fact_120_variable_Osize__gen_I2_J, fact_169_set__empty__eq, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_99_variable_Odistinct_I1_J, fact_238_inf__idem, fact_231_coincidence__term__cor, fact_152_option_Oinducts, fact_59_Un__left__commute, fact_106_is__singletonI, tcon_fun___Groups_Ouminus, tcon_HOL_Obool___Lattices_Obounded__lattice, fact_65_bex__Un, fact_53_boolean__algebra__cancel_Osup1, fact_123_variable_Osize_I4_J, fact_122_variable_Osize_I3_J, fact_232_Vagree__statediff, fact_160_Differentialo_Ocases, fact_23_sup__idem, tcon_Nat_Onat___Lattices_Osemilattice__sup_3, fact_213_selectlike__equal__cocond, fact_116_usubst__term, fact_171_selectlike__Vagree, fact_9_sup__bot_Oeq__neutr__iff, fact_0_uv, fact_102_bot__empty__eq, fact_19_insertCI, tcon_fun___Lattices_Olattice, fact_54_sup__fun__def, fact_58_inf__sup__aci_I8_J, fact_124_Set_Ois__empty__def
% 52.01/23.13 % No. of inferences in proof: 604
% 52.01/23.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22614 ms resp. 22023 ms w/o parsing
% 52.01/23.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.01/23.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------