%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP042^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:31 AM UTC 2026
% Result : Theorem 66.89s 35.55s
% Output : Refutation 67.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 346
% Syntax : Number of formulae : 694 ( 216 unt; 0 typ; 0 def)
% Number of atoms : 2496 ( 400 equ; 44 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 9191 ( 70 ~; 13 |; 241 &;8055 @)
% ( 0 <=>; 812 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 592 ( 592 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 18 con; 0-8 aty)
% Number of variables : 2355 ( 215 ^;2095 !; 45 ?;2355 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(real_type,type,
real: $tType ).
thf(sz_type,type,
sz: $tType ).
thf(sf_type,type,
sf: $tType ).
thf(sc_type,type,
sc: $tType ).
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(real_V55928688vector_decl,type,
real_V55928688vector:
!>[TA: $tType] : $o ).
thf(cARD_1_decl,type,
cARD_1:
!>[TA: $tType] : $o ).
thf(ordere890947078_space_decl,type,
ordere890947078_space:
!>[TA: $tType] : $o ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(sup_decl,type,
sup:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(order_top_decl,type,
order_top:
!>[TA: $tType] : $o ).
thf(semilattice_sup_decl,type,
semilattice_sup:
!>[TA: $tType] : $o ).
thf(bounded_lattice_top_decl,type,
bounded_lattice_top:
!>[TA: $tType] : $o ).
thf(topolo2133971006pology_decl,type,
topolo2133971006pology:
!>[TA: $tType] : $o ).
thf(topolo503727757_space_decl,type,
topolo503727757_space:
!>[TA: $tType] : $o ).
thf(bNF_rel_fun_decl,type,
bNF_rel_fun:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC > $o ) > ( TB > TA > $o ) > ( TD > TB ) > ( TC > TA ) > $o ) ).
thf(denotational_Iagree_decl,type,
denotational_Iagree:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( set @ ( sum_sum @ TC @ ( sum_sum @ TB @ TA ) ) ) > $o ) ).
thf(denotational_Vagree_decl,type,
denotational_Vagree:
!>[TA: $tType] : ( ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) > ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) > ( set @ ( sum_sum @ TA @ TA ) ) > $o ) ).
thf(denota593628964ctions_decl,type,
denota593628964ctions:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( denota1663640101rp_ext @ TD @ TC @ TB @ TA ) > TD > ( finite_Cartesian_vec @ real @ TB ) > real ) ).
thf(denota2077489681interp_decl,type,
denota2077489681interp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > $o ) ).
thf(denota126604975rm_sem_decl,type,
denota126604975rm_sem:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( trm @ TC @ TA ) > ( finite_Cartesian_vec @ real @ TA ) > real ) ).
thf(frechet_blin_frechet_decl,type,
frechet_blin_frechet:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( frechet_good_interp @ TC @ TB @ TA ) > ( frechet_strm @ TC @ TA ) > ( finite_Cartesian_vec @ real @ TA ) > ( bounde2145540817linfun @ ( finite_Cartesian_vec @ real @ TA ) @ real ) ) ).
thf(freche457001096interp_decl,type,
freche457001096interp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( frechet_good_interp @ TC @ TB @ TA ) > $o ) ).
thf(frechet_cr_strm_decl,type,
frechet_cr_strm:
!>[TA: $tType,TB: $tType] : ( ( trm @ TB @ TA ) > ( frechet_strm @ TB @ TA ) > $o ) ).
thf(freche227871258interp_decl,type,
freche227871258interp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( frechet_good_interp @ TC @ TB @ TA ) ) ).
thf(freche229654227interp_decl,type,
freche229654227interp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( frechet_good_interp @ TC @ TB @ TA ) > ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) ) ).
thf(frechet_raw_term_decl,type,
frechet_raw_term:
!>[TA: $tType,TB: $tType] : ( ( frechet_strm @ TB @ TA ) > ( trm @ TB @ TA ) ) ).
thf(frechet_simple_term_decl,type,
frechet_simple_term:
!>[TA: $tType,TB: $tType] : ( ( trm @ TB @ TA ) > ( frechet_strm @ TB @ TA ) ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(product_fst_decl,type,
product_fst:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TB ) ).
thf(domainp_decl,type,
domainp:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > TB > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(static_FVT_decl,type,
static_FVT:
!>[TA: $tType,TB: $tType] : ( ( trm @ TB @ TA ) > ( set @ ( sum_sum @ TA @ TA ) ) ) ).
thf(static_SIGT_decl,type,
static_SIGT:
!>[TA: $tType,TB: $tType] : ( ( trm @ TB @ TA ) > ( set @ TB ) ) ).
thf(sum_Inl_decl,type,
sum_Inl:
!>[TA: $tType,TB: $tType] : ( TB > ( sum_sum @ TB @ TA ) ) ).
thf(sum_rec_sum_decl,type,
sum_rec_sum:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TB ) > ( sum_sum @ TC @ TA ) > TB ) ).
thf(dfree_decl,type,
dfree:
!>[TA: $tType,TB: $tType] : ( ( trm @ TB @ TA ) > $o ) ).
thf(times_decl,type,
times:
!>[TA: $tType,TB: $tType] : ( ( trm @ TB @ TA ) > ( trm @ TB @ TA ) > ( trm @ TB @ TA ) ) ).
thf(topolo2071040574ous_on_decl,type,
topolo2071040574ous_on:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > $o ) ).
thf(type_definition_decl,type,
type_definition:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > TB ) > ( set @ TA ) > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(i_decl,type,
i: denota1663640101rp_ext @ a @ c @ b @ product_unit ).
thf(j_decl,type,
j: denota1663640101rp_ext @ a @ c @ b @ product_unit ).
thf(nu_decl,type,
nu: product_prod @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) ).
thf(nu2_decl,type,
nu2: product_prod @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) ).
thf(theta_1_decl,type,
theta_1: trm @ a @ b ).
thf(theta_2_decl,type,
theta_2: trm @ a @ b ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( dfree @ TA @ TB @ ( times @ TA @ TB @ A @ B ) )
= ( ( dfree @ TA @ TB @ A )
& ( dfree @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_dfree__Times__simps) ).
thf(809,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( dfree @ TA @ TB @ ( times @ TA @ TB @ A @ B ) )
= ( ( dfree @ TA @ TB @ A )
& ( dfree @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(330,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_old_Osum_Oinject_I1_J) ).
thf(1190,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).
thf(760,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(219,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( B
= ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_sup_OorderE) ).
thf(893,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( B
= ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(128,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_93_sup_Oassoc) ).
thf(666,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)],[128]) ).
thf(51,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_eq__iff) ).
thf(479,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(300,axiom,
! [TA: $tType,TB: $tType] : ( type_definition @ ( frechet_strm @ TA @ TB ) @ ( trm @ TA @ TB ) @ ( frechet_raw_term @ TA @ TB ) @ ( frechet_simple_term @ TA @ TB ) @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_type__definition__strm) ).
thf(1105,plain,
! [TA: $tType,TB: $tType] : ( type_definition @ ( frechet_strm @ TA @ TB ) @ ( trm @ TA @ TB ) @ ( frechet_raw_term @ TA @ TB ) @ ( frechet_simple_term @ TA @ TB ) @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(110,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_12) ).
thf(628,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(274,axiom,
dfree @ a @ b @ theta_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_dfree__Times_Ohyps_I1_J) ).
thf(1031,plain,
dfree @ a @ b @ theta_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(171,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_equalityD2) ).
thf(777,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(80,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_11) ).
thf(555,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(252,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Un__absorb1) ).
thf(977,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(337,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_UNIV__witness) ).
thf(1211,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(165,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_le__iff__sup) ).
thf(762,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,B: trm @ TA @ TB] :
( ( denota2077489681interp @ TA @ TC @ TB @ A )
=> ( ( dfree @ TA @ TB @ B )
=> ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ TB ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ TB ) ) ) @ ( denota126604975rm_sem @ TA @ TC @ TB @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_sterm__continuous) ).
thf(1005,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,B: trm @ TA @ TB] :
( ( denota2077489681interp @ TA @ TC @ TB @ A )
=> ( ( dfree @ TA @ TB @ B )
=> ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ TB ) @ real @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ TB ) ) ) @ ( denota126604975rm_sem @ TA @ TC @ TB @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,B: trm @ TA @ TB,C: set @ ( finite_Cartesian_vec @ real @ TB )] :
( ( denota2077489681interp @ TA @ TC @ TB @ A )
=> ( ( dfree @ TA @ TB @ B )
=> ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ TB ) @ real @ C @ ( denota126604975rm_sem @ TA @ TC @ TB @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_sterm__continuous_H) ).
thf(730,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,B: trm @ TA @ TB,C: set @ ( finite_Cartesian_vec @ real @ TB )] :
( ( denota2077489681interp @ TA @ TC @ TB @ A )
=> ( ( dfree @ TA @ TB @ B )
=> ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ TB ) @ real @ C @ ( denota126604975rm_sem @ TA @ TC @ TB @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(259,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_sup_Oabsorb2) ).
thf(994,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(288,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ( member @ ( trm @ TA @ TB ) @ B @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ( ( frechet_simple_term @ TA @ TB @ A )
= ( frechet_simple_term @ TA @ TB @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_simple__term__inject) ).
thf(1073,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ( member @ ( trm @ TA @ TB ) @ B @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ( ( frechet_simple_term @ TA @ TB @ A )
= ( frechet_simple_term @ TA @ TB @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(313,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Collect__mono__iff) ).
thf(1142,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(97,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_16) ).
thf(597,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(212,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_14) ).
thf(873,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(336,axiom,
! [TA: $tType,TB: $tType,A: ( frechet_strm @ TA @ TB ) > $o,B: frechet_strm @ TA @ TB] :
( ! [C: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ C @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( A @ ( frechet_simple_term @ TA @ TB @ C ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_simple__term__induct) ).
thf(1205,plain,
! [TA: $tType,TB: $tType,A: ( frechet_strm @ TA @ TB ) > $o,B: frechet_strm @ TA @ TB] :
( ! [C: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ C @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( A @ ( frechet_simple_term @ TA @ TB @ C ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_order__subst1) ).
thf(449,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(214,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( sup_sup @ ( TA > $o ) @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_sup1I2) ).
thf(878,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( sup_sup @ ( TA > $o ) @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bounded_lattice @ TB )
& ( bounded_lattice @ TA ) )
=> ( bounded_lattice @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Obounded__lattice_2) ).
thf(655,plain,
! [TA: $tType,TB: $tType] :
( ( ( bounded_lattice @ TB )
& ( bounded_lattice @ TA ) )
=> ( bounded_lattice @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( ( semilattice_sup @ TB )
& ( semilattice_sup @ TA ) )
=> ( semilattice_sup @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Osemilattice__sup_42) ).
thf(511,plain,
! [TA: $tType,TB: $tType] :
( ( ( semilattice_sup @ TB )
& ( semilattice_sup @ TA ) )
=> ( semilattice_sup @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(290,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > real,C: real,D: TA > TB,E: TA > TB] :
( ( topolo2071040574ous_on @ TA @ TB
@ ( collect @ TA
@ ^ [F: TA] :
( ( member @ TA @ F @ A )
& ( ord_less_eq @ real @ ( B @ F ) @ C ) ) )
@ D )
=> ( ( topolo2071040574ous_on @ TA @ TB
@ ( collect @ TA
@ ^ [F: TA] :
( ( member @ TA @ F @ A )
& ( ord_less_eq @ real @ C @ ( B @ F ) ) ) )
@ E )
=> ( ( topolo2071040574ous_on @ TA @ real @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( ( ( B @ F )
= C )
=> ( ( D @ F )
= ( E @ F ) ) ) )
=> ( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [F: TA] : ( if @ TB @ ( ord_less_eq @ real @ ( B @ F ) @ C ) @ ( D @ F ) @ ( E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_continuous__on__cases__le) ).
thf(1078,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > real,C: real,D: TA > TB,E: TA > TB] :
( ( topolo2071040574ous_on @ TA @ TB
@ ( collect @ TA
@ ^ [F: TA] :
( ( member @ TA @ F @ A )
& ( ord_less_eq @ real @ ( B @ F ) @ C ) ) )
@ D )
=> ( ( topolo2071040574ous_on @ TA @ TB
@ ( collect @ TA
@ ^ [F: TA] :
( ( member @ TA @ F @ A )
& ( ord_less_eq @ real @ C @ ( B @ F ) ) ) )
@ E )
=> ( ( topolo2071040574ous_on @ TA @ real @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( ( ( B @ F )
= C )
=> ( ( D @ F )
= ( E @ F ) ) ) )
=> ( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [F: TA] : ( if @ TB @ ( ord_less_eq @ real @ ( B @ F ) @ C ) @ ( D @ F ) @ ( E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC,B: frechet_good_interp @ TA @ TB @ TC] :
( ( ( freche229654227interp @ TA @ TB @ TC @ A )
= ( freche229654227interp @ TA @ TB @ TC @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_raw__interp__inject) ).
thf(715,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC,B: frechet_good_interp @ TA @ TB @ TC] :
( ( ( freche229654227interp @ TA @ TB @ TC @ A )
= ( freche229654227interp @ TA @ TB @ TC @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(47,axiom,
sup @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osup_30) ).
thf(472,plain,
sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(183,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( sup_sup @ ( TA > $o ) @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_sup1I1) ).
thf(814,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( sup_sup @ ( TA > $o ) @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(913,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(71,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_98_sup__left__commute) ).
thf(538,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)],[71]) ).
thf(320,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,B: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,C: set @ ( sum_sum @ TA @ ( sum_sum @ TC @ TB ) ),D: TA] :
( ( denotational_Iagree @ TA @ TC @ TB @ A @ B @ C )
=> ( ( member @ ( sum_sum @ TA @ ( sum_sum @ TC @ TB ) ) @ ( sum_Inl @ TA @ ( sum_sum @ TC @ TB ) @ D ) @ C )
=> ( ( denota593628964ctions @ TA @ TC @ TB @ product_unit @ A @ D )
= ( denota593628964ctions @ TA @ TC @ TB @ product_unit @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Iagree__Func) ).
thf(1164,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,B: denota1663640101rp_ext @ TA @ TC @ TB @ product_unit,C: set @ ( sum_sum @ TA @ ( sum_sum @ TC @ TB ) ),D: TA] :
( ( denotational_Iagree @ TA @ TC @ TB @ A @ B @ C )
=> ( ( member @ ( sum_sum @ TA @ ( sum_sum @ TC @ TB ) ) @ ( sum_Inl @ TA @ ( sum_sum @ TC @ TB ) @ D ) @ C )
=> ( ( denota593628964ctions @ TA @ TC @ TB @ product_unit @ A @ D )
= ( denota593628964ctions @ TA @ TC @ TB @ product_unit @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(176,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_predicate1D) ).
thf(797,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(342,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(1222,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(234,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_top_Oextremum__uniqueI) ).
thf(930,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(221,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_top_Oextremum__unique) ).
thf(898,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TB] :
( ( type_definition @ TB @ TA @ A @ B @ ( top_top @ ( set @ TA ) ) )
=> ~ ! [D: TA] :
( C
!= ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_type__copy__obj__one__point__absE) ).
thf(709,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TB] :
( ( type_definition @ TB @ TA @ A @ B @ ( top_top @ ( set @ TA ) ) )
=> ~ ! [D: TA] :
( C
!= ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(197,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_le__supI) ).
thf(841,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(250,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( TC > TA ) > ( TC > TB ) > $o ) @ ( bNF_rel_fun @ TC @ TC @ TA @ TB @ ( (=) @ TC ) @ A ) @ ( bNF_rel_fun @ TC @ TC @ TA @ TB @ ( (=) @ TC ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_fun_Orel__mono) ).
thf(973,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( TC > TA ) > ( TC > TB ) > $o ) @ ( bNF_rel_fun @ TC @ TC @ TA @ TB @ ( (=) @ TC ) @ A ) @ ( bNF_rel_fun @ TC @ TC @ TA @ TB @ ( (=) @ TC ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_let__rsp) ).
thf(436,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(344,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_iso__tuple__UNIV__I) ).
thf(1228,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(296,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,C: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) )] :
( ( denotational_Iagree @ TA @ TB @ TC @ A @ B @ C )
=> ( denotational_Iagree @ TA @ TB @ TC @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Iagree__comm) ).
thf(1095,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,C: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) )] :
( ( denotational_Iagree @ TA @ TB @ TC @ A @ B @ C )
=> ( denotational_Iagree @ TA @ TB @ TC @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_apply__rsp_H) ).
thf(404,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(195,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(838,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(178,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_ge__eq__refl) ).
thf(802,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(242,axiom,
top @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Otop_59) ).
thf(949,plain,
top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(229,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_rev__predicate1D) ).
thf(917,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(141,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_106_Un__commute) ).
thf(702,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)],[141]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( ( domainp @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( frechet_good_interp @ TA @ TB @ TC ) @ ( freche457001096interp @ TA @ TB @ TC ) )
= ( denota2077489681interp @ TA @ TB @ TC ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_good__interp_Odomain) ).
thf(751,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( ( domainp @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( frechet_good_interp @ TA @ TB @ TC ) @ ( freche457001096interp @ TA @ TB @ TC ) )
= ( denota2077489681interp @ TA @ TB @ TC ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(73,axiom,
lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_26) ).
thf(542,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_rel__funD) ).
thf(460,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(203,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_108_Un__left__commute) ).
thf(853,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)],[203]) ).
thf(293,axiom,
( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) )
| ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_IA) ).
thf(1087,plain,
( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) )
| ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(26,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_antisym) ).
thf(421,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_top__apply) ).
thf(416,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(304,axiom,
( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_dfree__Times_Oprems_I2_J) ).
thf(1115,plain,
( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(298,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ B @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ( ( freche227871258interp @ TA @ TB @ TC @ A )
= ( freche227871258interp @ TA @ TB @ TC @ B ) )
= ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_good__interp__inject) ).
thf(1100,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ B @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ( ( freche227871258interp @ TA @ TB @ TC @ A )
= ( freche227871258interp @ TA @ TB @ TC @ B ) )
= ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(346,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ ( sum_sum @ TA @ TA ),B: set @ ( sum_sum @ TA @ TA ),C: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),D: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA )] :
( ( ord_less_eq @ ( set @ ( sum_sum @ TA @ TA ) ) @ A @ B )
=> ( ( denotational_Vagree @ TA @ C @ D @ B )
=> ( denotational_Vagree @ TA @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_agree__sub) ).
thf(1232,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ ( sum_sum @ TA @ TA ),B: set @ ( sum_sum @ TA @ TA ),C: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),D: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA )] :
( ( ord_less_eq @ ( set @ ( sum_sum @ TA @ TA ) ) @ A @ B )
=> ( ( denotational_Vagree @ TA @ C @ D @ B )
=> ( denotational_Vagree @ TA @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(267,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_in__mono) ).
thf(1013,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(168,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_sup_Ocobounded2) ).
thf(770,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(49,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_dual__order_Orefl) ).
thf(475,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB] :
( ( frechet_simple_term @ TA @ TB @ ( frechet_raw_term @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_raw__term__inverse) ).
thf(756,plain,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB] :
( ( frechet_simple_term @ TA @ TB @ ( frechet_raw_term @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(173,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_subset__Un__eq) ).
thf(789,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( real_V55928688vector @ TA ) )
=> ( real_V55928688vector @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_4) ).
thf(591,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( real_V55928688vector @ TA ) )
=> ( real_V55928688vector @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( lattice @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_67) ).
thf(646,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( lattice @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(316,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) )] : ( denotational_Iagree @ TA @ TB @ TC @ A @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Iagree__refl) ).
thf(1151,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) )] : ( denotational_Iagree @ TA @ TB @ TC @ A @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Un__upper2) ).
thf(821,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(54,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_96_sup__commute) ).
thf(485,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)],[54]) ).
thf(311,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_103_ball__Un) ).
thf(1136,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)],[311]) ).
thf(192,axiom,
topolo503727757_space @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_20) ).
thf(834,plain,
topolo503727757_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1,conjecture,
( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(348,plain,
~ ( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(88,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( order @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oorder) ).
thf(574,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( order @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(135,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_107_Un__left__absorb) ).
thf(687,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)],[135]) ).
thf(137,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_sup__mono) ).
thf(692,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(245,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___HOL_Otype) ).
thf(956,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(37,axiom,
bounded_lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice_7) ).
thf(453,plain,
bounded_lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ ( product_prod @ TA @ TB ) @ A @ B )
=> ( ord_less_eq @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_fst__mono) ).
thf(396,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ord_less_eq @ ( product_prod @ TA @ TB ) @ A @ B )
=> ( ord_less_eq @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(257,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Un__least) ).
thf(988,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(68,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_95_sup_Ocommute) ).
thf(527,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)],[68]) ).
thf(339,axiom,
finite_finite @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(1215,plain,
finite_finite @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(113,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(634,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(306,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_top__empty__eq) ).
thf(1119,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(170,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_sup_Oabsorb__iff2) ).
thf(774,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(239,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_predicate1I) ).
thf(942,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_subset__UnE) ).
thf(678,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(126,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_69_sup_Oright__idem) ).
thf(661,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)],[126]) ).
thf(317,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_102_bex__Un) ).
thf(1153,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)],[317]) ).
thf(286,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__eq__set__def) ).
thf(1067,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(226,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_sup_Oabsorb__iff1) ).
thf(910,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( sup_sup @ TA @ B @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC] :
( ( freche227871258interp @ TA @ TB @ TC @ ( freche229654227interp @ TA @ TB @ TC @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_raw__interp__inverse) ).
thf(825,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC] :
( ( freche227871258interp @ TA @ TB @ TC @ ( freche229654227interp @ TA @ TB @ TC @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(279,axiom,
finite_finite @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_1) ).
thf(1042,plain,
finite_finite @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA > TF > $o,B: TD > TC > $o,C: TE > TB > $o,D: TA > TD > TE,E: TF > TC > TB] :
( ( bNF_rel_fun @ TA @ TF @ ( TD > TE ) @ ( TC > TB ) @ A @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C ) @ D @ E )
= ( ! [F: TA,G: TF] :
( ( A @ F @ G )
=> ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C @ ( D @ F ) @ ( E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_rel__fun__def__butlast) ).
thf(424,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA > TF > $o,B: TD > TC > $o,C: TE > TB > $o,D: TA > TD > TE,E: TF > TC > TB] :
( ( bNF_rel_fun @ TA @ TF @ ( TD > TE ) @ ( TC > TB ) @ A @ ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C ) @ D @ E )
= ( ! [F: TA,G: TF] :
( ( A @ F @ G )
=> ( bNF_rel_fun @ TD @ TC @ TE @ TB @ B @ C @ ( D @ F ) @ ( E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_9) ).
thf(630,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TB )
& ( cARD_1 @ TA ) )
=> ( linorder @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_65) ).
thf(862,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TB )
& ( cARD_1 @ TA ) )
=> ( linorder @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_45) ).
thf(349,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(200,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Un__UNIV__right) ).
thf(847,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(275,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( static_FVT @ TA @ TB @ ( times @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ ( sum_sum @ TB @ TB ) ) @ ( static_FVT @ TA @ TB @ A ) @ ( static_FVT @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_FVT_Osimps_I5_J) ).
thf(1032,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( static_FVT @ TA @ TB @ ( times @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ ( sum_sum @ TB @ TB ) ) @ ( static_FVT @ TA @ TB @ A ) @ ( static_FVT @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_Domainp_Ocases) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(202,axiom,
ordere890947078_space @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_5) ).
thf(852,plain,
ordere890947078_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(190,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_63_subset__antisym) ).
thf(830,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)],[190]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( ( lattice @ TB )
& ( lattice @ TA ) )
=> ( lattice @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Olattice_46) ).
thf(493,plain,
! [TA: $tType,TB: $tType] :
( ( ( lattice @ TB )
& ( lattice @ TA ) )
=> ( lattice @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(332,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_top__set__def) ).
thf(1195,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(78,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_sup__idem) ).
thf(551,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(308,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_UNIV__eq__I) ).
thf(1128,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_le__funE) ).
thf(519,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(347,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( sup_sup @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_sup__set__def) ).
thf(1234,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( sup_sup @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(615,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(285,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(1064,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)],[285]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_ord__eq__le__subst) ).
thf(388,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( domainp @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Domainp_ODomainI) ).
thf(593,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( domainp @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(210,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( dfree @ TA @ TB @ A )
=> ( ( dfree @ TA @ TB @ B )
=> ( dfree @ TA @ TB @ ( times @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_dfree_Odfree__Times) ).
thf(869,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( dfree @ TA @ TB @ A )
=> ( ( dfree @ TA @ TB @ B )
=> ( dfree @ TA @ TB @ ( times @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_DomainpE) ).
thf(650,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB] :
( ( domainp @ TB @ TA @ A @ B )
=> ~ ! [C: TA] :
~ ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(241,axiom,
topolo2133971006pology @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology) ).
thf(948,plain,
topolo2133971006pology @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(253,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Un__UNIV__left) ).
thf(980,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(17,axiom,
linorder @ sz,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_5) ).
thf(403,plain,
linorder @ sz,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(46,axiom,
semilattice_sup @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osemilattice__sup_32) ).
thf(471,plain,
semilattice_sup @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(216,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_equalityD1) ).
thf(884,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(273,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ~ ! [B: frechet_strm @ TA @ TB] :
( A
!= ( frechet_raw_term @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_raw__term__cases) ).
thf(1028,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ~ ! [B: frechet_strm @ TA @ TB] :
( A
!= ( frechet_raw_term @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(55,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_dual__order_Oantisym) ).
thf(488,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(235,axiom,
! [TA: $tType] :
( ( domainp @ TA @ TA @ ( (=) @ TA ) )
= ( top_top @ ( TA > $o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_Domain__eq__top) ).
thf(933,plain,
! [TA: $tType] :
( ( domainp @ TA @ TA @ ( (=) @ TA ) )
= ( top_top @ ( TA > $o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(79,axiom,
semilattice_sup @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Osemilattice__sup_52) ).
thf(554,plain,
semilattice_sup @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(327,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( sum_sum @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Finite__Set_Ofinite_39) ).
thf(1182,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( sum_sum @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(129,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_order_Otrans) ).
thf(669,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),C: trm @ TC @ TA,D: denota1663640101rp_ext @ TC @ TB @ TA @ product_unit] :
( ( denotational_Vagree @ TA @ A @ B @ ( static_FVT @ TC @ TA @ C ) )
=> ( ( denota126604975rm_sem @ TC @ TB @ TA @ D @ C @ ( product_fst @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) @ A ) )
= ( denota126604975rm_sem @ TC @ TB @ TA @ D @ C @ ( product_fst @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_coincidence__sterm) ).
thf(901,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),C: trm @ TC @ TA,D: denota1663640101rp_ext @ TC @ TB @ TA @ product_unit] :
( ( denotational_Vagree @ TA @ A @ B @ ( static_FVT @ TC @ TA @ C ) )
=> ( ( denota126604975rm_sem @ TC @ TB @ TA @ D @ C @ ( product_fst @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) @ A ) )
= ( denota126604975rm_sem @ TC @ TB @ TA @ D @ C @ ( product_fst @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(249,axiom,
! [A: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,B: trm @ sf @ sz] :
( ( denota2077489681interp @ sf @ sc @ sz @ A )
=> ( ( dfree @ sf @ sz @ B )
=> ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ sz ) @ ( bounde2145540817linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real ) @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ sz ) ) ) @ ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ A ) @ ( frechet_simple_term @ sf @ sz @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_frechet__continuous) ).
thf(970,plain,
! [A: denota1663640101rp_ext @ sf @ sc @ sz @ product_unit,B: trm @ sf @ sz] :
( ( denota2077489681interp @ sf @ sc @ sz @ A )
=> ( ( dfree @ sf @ sz @ B )
=> ( topolo2071040574ous_on @ ( finite_Cartesian_vec @ real @ sz ) @ ( bounde2145540817linfun @ ( finite_Cartesian_vec @ real @ sz ) @ real ) @ ( top_top @ ( set @ ( finite_Cartesian_vec @ real @ sz ) ) ) @ ( frechet_blin_frechet @ sf @ sc @ sz @ ( freche227871258interp @ sf @ sc @ sz @ A ) @ ( frechet_simple_term @ sf @ sz @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(303,axiom,
finite_finite @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_2) ).
thf(1114,plain,
finite_finite @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(260,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_set__eq__subset) ).
thf(997,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(40,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_90_sup__fun__def) ).
thf(457,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)],[40]) ).
thf(85,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_order__class_Oorder_Oeq__iff) ).
thf(569,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(11,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_dual__order_Otrans) ).
thf(371,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(309,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_99_UnE) ).
thf(1131,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)],[309]) ).
thf(122,axiom,
sup @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Osup_61) ).
thf(654,plain,
sup @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(7,axiom,
order_top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_23) ).
thf(360,plain,
order_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TA,D: TB] :
( ( B = C )
& ( A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_Domainp_Osimps) ).
thf(508,plain,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TA,D: TB] :
( ( B = C )
& ( A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(231,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_top1I) ).
thf(921,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(72,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_27) ).
thf(541,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(124,axiom,
ord @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_60) ).
thf(657,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_rev__predicate2D) ).
thf(765,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(322,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_Collect__subset) ).
thf(1170,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB] :
( ! [E: TD,F: TA] :
( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_rel__funI) ).
thf(558,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB] :
( ! [E: TD,F: TA] :
( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(329,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pred__subset__eq) ).
thf(1187,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD > TA > $o,C: TC > TB > $o,D: TC > TB > $o,E: TD > TC,F: TA > TB] :
( ! [G: TD,H: TA] :
( ( A @ G @ H )
=> ( B @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( C @ G @ H )
=> ( D @ G @ H ) )
=> ( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ B @ C @ E @ F )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_rel__fun__mono_H) ).
thf(530,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD > TA > $o,C: TC > TB > $o,D: TC > TB > $o,E: TD > TC,F: TA > TB] :
( ! [G: TD,H: TA] :
( ( A @ G @ H )
=> ( B @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( C @ G @ H )
=> ( D @ G @ H ) )
=> ( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ B @ C @ E @ F )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_predicate2I) ).
thf(926,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(334,axiom,
denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_VAs_I1_J) ).
thf(1202,plain,
denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB )
& ( topolo503727757_space @ TC ) )
=> ! [A: set @ TA,B: TA > ( product_prod @ TB @ TC )] :
( ( topolo2071040574ous_on @ TA @ ( product_prod @ TB @ TC ) @ A @ B )
=> ( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [C: TA] : ( product_fst @ TB @ TC @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_continuous__on__fst) ).
thf(792,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB )
& ( topolo503727757_space @ TC ) )
=> ! [A: set @ TA,B: TA > ( product_prod @ TB @ TC )] :
( ( topolo2071040574ous_on @ TA @ ( product_prod @ TB @ TC ) @ A @ B )
=> ( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [C: TA] : ( product_fst @ TB @ TC @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(292,axiom,
denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_dfree__Times_Oprems_I1_J) ).
thf(1086,plain,
denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(237,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Un__upper1) ).
thf(938,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC > $o,B: TE > TB > $o] : ( bNF_rel_fun @ ( TD > TE > $o ) @ ( TC > TB > $o ) @ ( ( TA > TD ) > ( TA > TE ) > $o ) @ ( ( TA > TC ) > ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TD @ TC @ ( TE > $o ) @ ( TB > $o ) @ A @ ( bNF_rel_fun @ TE @ TB @ $o @ $o @ B @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( TA > TD ) @ ( TA > TC ) @ ( ( TA > TE ) > $o ) @ ( ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TC @ ( (=) @ TA ) @ A ) @ ( bNF_rel_fun @ ( TA > TE ) @ ( TA > TB ) @ $o @ $o @ ( bNF_rel_fun @ TA @ TA @ TE @ TB @ ( (=) @ TA ) @ B ) @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TE @ ( (=) @ TA ) ) @ ( bNF_rel_fun @ TA @ TA @ TC @ TB @ ( (=) @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_fun_Orel__transfer) ).
thf(398,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC > $o,B: TE > TB > $o] : ( bNF_rel_fun @ ( TD > TE > $o ) @ ( TC > TB > $o ) @ ( ( TA > TD ) > ( TA > TE ) > $o ) @ ( ( TA > TC ) > ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TD @ TC @ ( TE > $o ) @ ( TB > $o ) @ A @ ( bNF_rel_fun @ TE @ TB @ $o @ $o @ B @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ ( TA > TD ) @ ( TA > TC ) @ ( ( TA > TE ) > $o ) @ ( ( TA > TB ) > $o ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TC @ ( (=) @ TA ) @ A ) @ ( bNF_rel_fun @ ( TA > TE ) @ ( TA > TB ) @ $o @ $o @ ( bNF_rel_fun @ TA @ TA @ TE @ TB @ ( (=) @ TA ) @ B ) @ ( (=) @ $o ) ) ) @ ( bNF_rel_fun @ TA @ TA @ TD @ TE @ ( (=) @ TA ) ) @ ( bNF_rel_fun @ TA @ TA @ TC @ TB @ ( (=) @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(276,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),C: set @ ( sum_sum @ TA @ TA ),D: set @ ( sum_sum @ TA @ TA )] :
( ( denotational_Vagree @ TA @ A @ B @ C )
=> ( ( denotational_Vagree @ TA @ A @ B @ D )
=> ( denotational_Vagree @ TA @ A @ B @ ( sup_sup @ ( set @ ( sum_sum @ TA @ TA ) ) @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_agree__union) ).
thf(1035,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),C: set @ ( sum_sum @ TA @ TA ),D: set @ ( sum_sum @ TA @ TA )] :
( ( denotational_Vagree @ TA @ A @ B @ C )
=> ( ( denotational_Vagree @ TA @ A @ B @ D )
=> ( denotational_Vagree @ TA @ A @ B @ ( sup_sup @ ( set @ ( sum_sum @ TA @ TA ) ) @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(272,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_101_UnI2) ).
thf(1026,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)],[272]) ).
thf(321,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Inl__inject) ).
thf(1167,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(175,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Un__absorb) ).
thf(794,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(92,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_sup_Oidem) ).
thf(586,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(148,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_114_le__supE) ).
thf(718,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)],[148]) ).
thf(217,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_sup__ge2) ).
thf(888,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(107,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_linorder__wlog) ).
thf(618,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(299,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ ( sum_sum @ TA @ TA ),B: set @ ( sum_sum @ TA @ TA ),C: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),D: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA )] :
( ( ord_less_eq @ ( set @ ( sum_sum @ TA @ TA ) ) @ A @ B )
=> ( ( denotational_Vagree @ TA @ C @ D @ B )
=> ( denotational_Vagree @ TA @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_agree__supset) ).
thf(1103,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ ( sum_sum @ TA @ TA ),B: set @ ( sum_sum @ TA @ TA ),C: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),D: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA )] :
( ( ord_less_eq @ ( set @ ( sum_sum @ TA @ TA ) ) @ A @ B )
=> ( ( denotational_Vagree @ TA @ C @ D @ B )
=> ( denotational_Vagree @ TA @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(341,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_subset__eq) ).
thf(1219,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(204,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_sup_OboundedI) ).
thf(856,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(158,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Un__absorb2) ).
thf(745,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(87,axiom,
ord @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_37) ).
thf(573,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bounded_lattice @ TB )
& ( bounded_lattice @ TA ) )
=> ( bounded_lattice_top @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Obounded__lattice__top_41) ).
thf(601,plain,
! [TA: $tType,TB: $tType] :
( ( ( bounded_lattice @ TB )
& ( bounded_lattice @ TA ) )
=> ( bounded_lattice_top @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(63,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_88_inf__sup__aci_I6_J) ).
thf(513,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)],[63]) ).
thf(29,axiom,
order @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_58) ).
thf(430,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(185,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_subset__UNIV) ).
thf(819,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( product_fst @ TA @ TB @ ( top_top @ ( product_prod @ TA @ TB ) ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_fst__top) ).
thf(732,plain,
! [TA: $tType,TB: $tType] :
( ( ( top @ TA )
& ( top @ TB ) )
=> ( ( product_fst @ TA @ TB @ ( top_top @ ( product_prod @ TA @ TB ) ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( finite_finite @ TA ) )
=> ( ord @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_69) ).
thf(843,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( finite_finite @ TA ) )
=> ( ord @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(169,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: set @ ( sum_sum @ TA @ TA )] : ( denotational_Vagree @ TA @ A @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_agree__refl) ).
thf(772,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: set @ ( sum_sum @ TA @ TA )] : ( denotational_Vagree @ TA @ A @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(157,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),C: set @ ( sum_sum @ TA @ TA )] :
( ( denotational_Vagree @ TA @ A @ B @ C )
=> ( denotational_Vagree @ TA @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_agree__comm) ).
thf(743,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),C: set @ ( sum_sum @ TA @ TA )] :
( ( denotational_Vagree @ TA @ A @ B @ C )
=> ( denotational_Vagree @ TA @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(213,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( sup_sup @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_sup_OorderI) ).
thf(875,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( sup_sup @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( E @ G @ H )
=> ( A @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( B @ G @ H )
=> ( F @ G @ H ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_rel__fun__mono) ).
thf(579,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( E @ G @ H )
=> ( A @ G @ H ) )
=> ( ! [G: TC,H: TB] :
( ( B @ G @ H )
=> ( F @ G @ H ) )
=> ( bNF_rel_fun @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(246,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le__supI2) ).
thf(958,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(75,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_64_sup__apply) ).
thf(545,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)],[75]) ).
thf(22,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_29) ).
thf(413,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TB] :
( ! [C: TB] : ( A @ C @ C )
=> ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_fun_Orel__refl) ).
thf(562,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TB] :
( ! [C: TB] : ( A @ C @ C )
=> ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(223,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_50_sup_Obounded__iff) ).
thf(904,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)],[223]) ).
thf(251,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_sup_Ocobounded1) ).
thf(975,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(264,axiom,
sup @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Osup_38) ).
thf(1007,plain,
sup @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TB] :
( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [C: TA] : B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_continuous__on__const) ).
thf(694,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TB] :
( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [C: TA] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TB )
& ( order @ TA ) )
=> ( order @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder_47) ).
thf(641,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TB )
& ( order @ TA ) )
=> ( order @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(312,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( static_SIGT @ TA @ TB @ ( times @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( static_SIGT @ TA @ TB @ A ) @ ( static_SIGT @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_SIGT_Osimps_I5_J) ).
thf(1139,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB] :
( ( static_SIGT @ TA @ TB @ ( times @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( static_SIGT @ TA @ TB @ A ) @ ( static_SIGT @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_66) ).
thf(936,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( domainp @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_Domainp__refl) ).
thf(572,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(102,axiom,
top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_28) ).
thf(611,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(301,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC] :
~ ! [B: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( A
= ( freche227871258interp @ TA @ TB @ TC @ B ) )
=> ~ ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ B @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_good__interp__cases) ).
thf(1107,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC] :
~ ! [B: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( A
= ( freche227871258interp @ TA @ TB @ TC @ B ) )
=> ~ ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ B @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > TB,C: set @ TA] :
( ( topolo2071040574ous_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ( topolo2071040574ous_on @ TA @ TB @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_continuous__on__subset) ).
thf(713,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > TB,C: set @ TA] :
( ( topolo2071040574ous_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ( topolo2071040574ous_on @ TA @ TB @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(59,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_91_boolean__algebra__cancel_Osup1) ).
thf(498,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)],[59]) ).
thf(44,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_97_sup_Oleft__commute) ).
thf(466,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)],[44]) ).
thf(295,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
| ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Un__def) ).
thf(1092,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
| ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( finite_finite @ TA ) )
=> ( real_V55928688vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1) ).
thf(919,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( finite_finite @ TA ) )
=> ( real_V55928688vector @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType] :
( ( domainp @ ( trm @ TA @ TB ) @ ( frechet_strm @ TA @ TB ) @ ( frechet_cr_strm @ TA @ TB ) )
= ( dfree @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_strm_Odomain) ).
thf(804,plain,
! [TA: $tType,TB: $tType] :
( ( domainp @ ( trm @ TA @ TB ) @ ( frechet_strm @ TA @ TB ) @ ( frechet_cr_strm @ TA @ TB ) )
= ( dfree @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(19,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_86_inf__sup__aci_I8_J) ).
thf(406,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)],[19]) ).
thf(258,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( ~ ( A @ B )
=> ( C @ B ) )
=> ( sup_sup @ ( TA > $o ) @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_sup1CI) ).
thf(990,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( ~ ( A @ B )
=> ( C @ B ) )
=> ( sup_sup @ ( TA > $o ) @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__funD) ).
thf(567,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(155,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( B
= ( sup_sup @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_sup_Oorder__iff) ).
thf(737,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( B
= ( sup_sup @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(307,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: ( frechet_good_interp @ TA @ TB @ TC ) > $o,B: frechet_good_interp @ TA @ TB @ TC] :
( ! [C: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ C @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( A @ ( freche227871258interp @ TA @ TB @ TC @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_good__interp__induct) ).
thf(1122,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: ( frechet_good_interp @ TA @ TB @ TC ) > $o,B: frechet_good_interp @ TA @ TB @ TC] :
( ! [C: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ C @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( A @ ( freche227871258interp @ TA @ TB @ TC @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osup) ).
thf(599,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(324,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_100_UnI1) ).
thf(1175,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)],[324]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ! [A: denota1663640101rp_ext @ a @ TA @ TB @ product_unit,B: denota1663640101rp_ext @ a @ TA @ TB @ product_unit] :
( ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062) ).
thf(1011,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ! [A: denota1663640101rp_ext @ a @ TA @ TB @ product_unit,B: denota1663640101rp_ext @ a @ TA @ TB @ product_unit] :
( ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(25,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_8) ).
thf(419,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(215,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_131_sup_OboundedE) ).
thf(880,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)],[215]) ).
thf(280,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ! [A: denota1663640101rp_ext @ a @ TA @ TB @ product_unit,B: denota1663640101rp_ext @ a @ TA @ TB @ product_unit] :
( ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062) ).
thf(1043,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ! [A: denota1663640101rp_ext @ a @ TA @ TB @ product_unit,B: denota1663640101rp_ext @ a @ TA @ TB @ product_unit] :
( ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denotational_Iagree @ a @ TA @ TB @ A @ B
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ TA @ TB ) )
@ ^ [C: sum_sum @ a @ ( sum_sum @ TA @ TB )] :
? [D: a] :
( ( C
= ( sum_Inl @ a @ ( sum_sum @ TA @ TB ) @ D ) )
& ( member @ a @ D @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(434,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(218,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(890,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(50,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype) ).
thf(477,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(184,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_104_Un__assoc) ).
thf(816,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)],[184]) ).
thf(53,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_17) ).
thf(483,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(325,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_UNIV__def) ).
thf(1177,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(42,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_15) ).
thf(462,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(302,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_UNIV__I) ).
thf(1112,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(205,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_sup_Omono) ).
thf(858,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_ord__le__eq__trans) ).
thf(367,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(177,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_sup__absorb2) ).
thf(799,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: set @ TB,D: TB > TA > $o] :
( ( type_definition @ TA @ TB @ A @ B @ C )
=> ( ( D
= ( ^ [E: TB,F: TA] :
( E
= ( A @ F ) ) ) )
=> ( bNF_rel_fun @ TB @ TA @ TB @ TB @ D @ ( (=) @ TB )
@ ^ [E: TB] : E
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_typedef__rep__transfer) ).
thf(726,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: set @ TB,D: TB > TA > $o] :
( ( type_definition @ TA @ TB @ A @ B @ C )
=> ( ( D
= ( ^ [E: TB,F: TA] :
( E
= ( A @ F ) ) ) )
=> ( bNF_rel_fun @ TB @ TA @ TB @ TB @ D @ ( (=) @ TB )
@ ^ [E: TB] : E
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(109,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_18) ).
thf(626,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(228,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_inf__sup__ord_I3_J) ).
thf(915,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order__subst2) ).
thf(521,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(254,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_sup__top__right) ).
thf(983,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(333,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) > $o] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ! [C: frechet_good_interp @ TA @ TB @ TC] : ( B @ ( freche229654227interp @ TA @ TB @ TC @ C ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_raw__interp__induct) ).
thf(1198,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) > $o] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ! [C: frechet_good_interp @ TA @ TB @ TC] : ( B @ ( freche229654227interp @ TA @ TB @ TC @ C ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(338,axiom,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB] : ( member @ ( trm @ TA @ TB ) @ ( frechet_raw_term @ TA @ TB @ A ) @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_raw__term) ).
thf(1213,plain,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB] : ( member @ ( trm @ TA @ TB ) @ ( frechet_raw_term @ TA @ TB @ A ) @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( TA > TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_fun_Orel__eq) ).
thf(636,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_rel_fun @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( TA > TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(39,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_le__cases) ).
thf(455,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(268,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA )] :
( ( denotational_Vagree @ TA @ A @ B @ ( top_top @ ( set @ ( sum_sum @ TA @ TA ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_agree__UNIV__eq) ).
thf(1015,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ),B: product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA )] :
( ( denotational_Vagree @ TA @ A @ B @ ( top_top @ ( set @ ( sum_sum @ TA @ TA ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(101,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_dual__order_Oeq__iff) ).
thf(608,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(255,axiom,
finite_finite @ sf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_6) ).
thf(986,plain,
finite_finite @ sf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(261,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(1000,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_ord__le__eq__subst) ).
thf(438,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(30,axiom,
order_top @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__top_53) ).
thf(431,plain,
order_top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(125,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_94_sup__assoc) ).
thf(658,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)],[125]) ).
thf(149,axiom,
finite_finite @ sc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_3) ).
thf(722,plain,
finite_finite @ sc,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(76,axiom,
linorder @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_55) ).
thf(548,plain,
linorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oord_49) ).
thf(648,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TB )
& ( finite_finite @ TA ) )
=> ( topolo503727757_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_62) ).
thf(812,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TB )
& ( finite_finite @ TA ) )
=> ( topolo503727757_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(161,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_sup__ge1) ).
thf(754,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(194,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_top__greatest) ).
thf(836,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(282,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_62_subsetI) ).
thf(1049,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)],[282]) ).
thf(48,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_linear) ).
thf(473,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(289,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( type_definition @ ( frechet_good_interp @ TA @ TB @ TC ) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( freche229654227interp @ TA @ TB @ TC ) @ ( freche227871258interp @ TA @ TB @ TC ) @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_type__definition__good__interp) ).
thf(1076,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( type_definition @ ( frechet_good_interp @ TA @ TB @ TC ) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( freche229654227interp @ TA @ TB @ TC ) @ ( freche227871258interp @ TA @ TB @ TC ) @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(335,axiom,
! [TA: $tType] :
( ord_less_eq @ ( set @ ( sum_sum @ a @ TA ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_2 ) ) ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Isubs_I2_J) ).
thf(1203,plain,
! [TA: $tType] :
( ord_less_eq @ ( set @ ( sum_sum @ a @ TA ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_2 ) ) ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order_top @ TB )
& ( order_top @ TA ) )
=> ( order_top @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder__top_43) ).
thf(589,plain,
! [TA: $tType,TB: $tType] :
( ( ( order_top @ TB )
& ( order_top @ TA ) )
=> ( order_top @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(106,axiom,
lattice @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Olattice_57) ).
thf(617,plain,
lattice @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_le__fun__def) ).
thf(516,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(314,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) )
= ( sup_sup @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Collect__disj__eq) ).
thf(1145,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) )
= ( sup_sup @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(269,axiom,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB] :
~ ! [B: trm @ TA @ TB] :
( ( A
= ( frechet_simple_term @ TA @ TB @ B ) )
=> ~ ( member @ ( trm @ TA @ TB ) @ B @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_simple__term__cases) ).
thf(1018,plain,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB] :
~ ! [B: trm @ TA @ TB] :
( ( A
= ( frechet_simple_term @ TA @ TB @ B ) )
=> ~ ( member @ ( trm @ TA @ TB ) @ B @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(248,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TB )
& ( finite_finite @ TA ) )
=> ( order @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_68) ).
thf(968,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TB )
& ( finite_finite @ TA ) )
=> ( order @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_subset__refl) ).
thf(823,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType] :
( ( ( top @ TB )
& ( top @ TA ) )
=> ( top @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Otop_48) ).
thf(525,plain,
! [TA: $tType,TB: $tType] :
( ( ( top @ TB )
& ( top @ TA ) )
=> ( top @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TC > TB,B: TC] :
( ( topolo2071040574ous_on @ TA @ ( TC > TB ) @ ( top_top @ ( set @ TA ) ) @ A )
=> ( topolo2071040574ous_on @ TA @ TB @ ( top_top @ ( set @ TA ) )
@ ^ [C: TA] : ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_continuous__on__product__then__coordinatewise__UNIV) ).
thf(690,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TC > TB,B: TC] :
( ( topolo2071040574ous_on @ TA @ ( TC > TB ) @ ( top_top @ ( set @ TA ) ) @ A )
=> ( topolo2071040574ous_on @ TA @ TB @ ( top_top @ ( set @ TA ) )
@ ^ [C: TA] : ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(271,axiom,
dfree @ a @ b @ theta_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dfree__Times_Ohyps_I2_J) ).
thf(1025,plain,
dfree @ a @ b @ theta_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(287,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ( frechet_raw_term @ TA @ TB @ ( frechet_simple_term @ TA @ TB @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_simple__term__inverse) ).
thf(1070,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ( frechet_raw_term @ TA @ TB @ ( frechet_simple_term @ TA @ TB @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( semilattice_sup @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__sup_63) ).
thf(414,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( semilattice_sup @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(145,axiom,
real_V55928688vector @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_6) ).
thf(712,plain,
real_V55928688vector @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(81,axiom,
order @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_36) ).
thf(557,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(262,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( sup_sup @ ( TA > $o ) @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_sup1E) ).
thf(1003,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( sup_sup @ ( TA > $o ) @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > $o,B: TD > TC > $o,C: TA > TB > $o,D: TA > TB > $o] :
( ( ord_less_eq @ ( TD > TC > $o ) @ A @ B )
=> ( ( ord_less_eq @ ( TA > TB > $o ) @ C @ D )
=> ( ord_less_eq @ ( ( TD > TA ) > ( TC > TB ) > $o ) @ ( bNF_rel_fun @ TD @ TC @ TA @ TB @ B @ C ) @ ( bNF_rel_fun @ TD @ TC @ TA @ TB @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_fun__mono) ).
thf(705,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > $o,B: TD > TC > $o,C: TA > TB > $o,D: TA > TB > $o] :
( ( ord_less_eq @ ( TD > TC > $o ) @ A @ B )
=> ( ( ord_less_eq @ ( TA > TB > $o ) @ C @ D )
=> ( ord_less_eq @ ( ( TD > TA ) > ( TC > TB ) > $o ) @ ( bNF_rel_fun @ TD @ TC @ TA @ TB @ B @ C ) @ ( bNF_rel_fun @ TD @ TC @ TA @ TB @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(318,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ real,B: real,C: real > TA,D: real > TA] :
( ( topolo2071040574ous_on @ real @ TA
@ ( collect @ real
@ ^ [E: real] :
( ( member @ real @ E @ A )
& ( ord_less_eq @ real @ E @ B ) ) )
@ C )
=> ( ( topolo2071040574ous_on @ real @ TA
@ ( collect @ real
@ ^ [E: real] :
( ( member @ real @ E @ A )
& ( ord_less_eq @ real @ B @ E ) ) )
@ D )
=> ( ( ( member @ real @ B @ A )
=> ( ( C @ B )
= ( D @ B ) ) )
=> ( topolo2071040574ous_on @ real @ TA @ A
@ ^ [E: real] : ( if @ TA @ ( ord_less_eq @ real @ E @ B ) @ ( C @ E ) @ ( D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_continuous__on__cases__1) ).
thf(1156,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ real,B: real,C: real > TA,D: real > TA] :
( ( topolo2071040574ous_on @ real @ TA
@ ( collect @ real
@ ^ [E: real] :
( ( member @ real @ E @ A )
& ( ord_less_eq @ real @ E @ B ) ) )
@ C )
=> ( ( topolo2071040574ous_on @ real @ TA
@ ( collect @ real
@ ^ [E: real] :
( ( member @ real @ E @ A )
& ( ord_less_eq @ real @ B @ E ) ) )
@ D )
=> ( ( ( member @ real @ B @ A )
=> ( ( C @ B )
= ( D @ B ) ) )
=> ( topolo2071040574ous_on @ real @ TA @ A
@ ^ [E: real] : ( if @ TA @ ( ord_less_eq @ real @ E @ B ) @ ( C @ E ) @ ( D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(343,axiom,
( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ) )
=> ( ( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) )
=> ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
= ( denota126604975rm_sem @ a @ c @ b @ j @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_IH1) ).
thf(1225,plain,
( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_1 ) )
=> ( ( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) ) ) ) )
=> ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
= ( denota126604975rm_sem @ a @ c @ b @ j @ theta_1 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > TC > TB,C: TC] :
( ( topolo2071040574ous_on @ TA @ ( TC > TB ) @ A @ B )
=> ( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [D: TA] : ( B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_continuous__on__product__then__coordinatewise) ).
thf(707,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > TC > TB,C: TC] :
( ( topolo2071040574ous_on @ TA @ ( TC > TB ) @ A @ B )
=> ( topolo2071040574ous_on @ TA @ TB @ A
@ ^ [D: TA] : ( B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(20,axiom,
linorder @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_34) ).
thf(409,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(345,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_subsetD) ).
thf(1230,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(283,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(1053,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(131,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_51_le__sup__iff) ).
thf(673,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)],[131]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TA > $o] :
( ( domainp @ TA @ TB @ A @ B )
=> ( ! [D: TA,E: TB] :
( ( A @ D @ E )
=> ( C @ D ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Domainp_Oinducts) ).
thf(502,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TA > $o] :
( ( domainp @ TA @ TB @ A @ B )
=> ( ! [D: TA,E: TB] :
( ( A @ D @ E )
=> ( C @ D ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(117,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_antisym__conv) ).
thf(643,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(224,axiom,
finite_finite @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Finite__Set_Ofinite_56) ).
thf(907,plain,
finite_finite @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(278,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_70_UnCI) ).
thf(1038,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)],[278]) ).
thf(91,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(585,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(291,axiom,
denotational_Vagree @ b @ nu @ nu2 @ ( sup_sup @ ( set @ ( sum_sum @ b @ b ) ) @ ( static_FVT @ a @ b @ theta_1 ) @ ( static_FVT @ a @ b @ theta_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_VA) ).
thf(1085,plain,
denotational_Vagree @ b @ nu @ nu2 @ ( sup_sup @ ( set @ ( sum_sum @ b @ b ) ) @ ( static_FVT @ a @ b @ theta_1 ) @ ( static_FVT @ a @ b @ theta_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(89,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_order__class_Oorder_Oantisym) ).
thf(576,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(270,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC] : ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( freche229654227interp @ TA @ TB @ TC @ A ) @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_raw__interp) ).
thf(1023,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: frechet_good_interp @ TA @ TB @ TC] : ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( freche229654227interp @ TA @ TB @ TC @ A ) @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(104,axiom,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_10) ).
thf(613,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB,B: frechet_strm @ TA @ TB] :
( ( ( frechet_raw_term @ TA @ TB @ A )
= ( frechet_raw_term @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_raw__term__inject) ).
thf(864,plain,
! [TA: $tType,TB: $tType,A: frechet_strm @ TA @ TB,B: frechet_strm @ TA @ TB] :
( ( ( frechet_raw_term @ TA @ TB @ A )
= ( frechet_raw_term @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(265,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_subset__iff) ).
thf(1008,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(35,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_68_sup__left__idem) ).
thf(446,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)],[35]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(595,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(103,axiom,
lattice @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Lattices_Olattice_35) ).
thf(612,plain,
lattice @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(199,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Un__mono) ).
thf(845,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(326,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) ),B: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) ),C: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,D: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( ord_less_eq @ ( set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) ) ) @ A @ B )
=> ( ( denotational_Iagree @ TA @ TB @ TC @ C @ D @ B )
=> ( denotational_Iagree @ TA @ TB @ TC @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Iagree__sub) ).
thf(1180,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) ),B: set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) ),C: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,D: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( ord_less_eq @ ( set @ ( sum_sum @ TA @ ( sum_sum @ TB @ TC ) ) ) @ A @ B )
=> ( ( denotational_Iagree @ TA @ TB @ TC @ C @ D @ B )
=> ( denotational_Iagree @ TA @ TB @ TC @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(9,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_92_boolean__algebra__cancel_Osup2) ).
thf(363,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)],[9]) ).
thf(52,axiom,
semilattice_sup @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_22) ).
thf(482,plain,
semilattice_sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_Let__transfer) ).
thf(671,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o] :
( bNF_rel_fun @ TD @ TA @ ( ( TD > TC ) > TC ) @ ( ( TA > TB ) > TB ) @ A @ ( bNF_rel_fun @ ( TD > TC ) @ ( TA > TB ) @ TC @ TB @ ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B ) @ B )
@ ^ [C: TD,D: TD > TC] : ( D @ C )
@ ^ [C: TA,D: TA > TB] : ( D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(58,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_89_inf__sup__aci_I5_J) ).
thf(495,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)],[58]) ).
thf(163,axiom,
finite_finite @ sz,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_4) ).
thf(759,plain,
finite_finite @ sz,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(340,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ( freche229654227interp @ TA @ TB @ TC @ ( freche227871258interp @ TA @ TB @ TC @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_good__interp__inverse) ).
thf(1216,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ( ( freche229654227interp @ TA @ TB @ TC @ ( freche227871258interp @ TA @ TB @ TC @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: TB > $o] :
( ( type_definition @ TA @ TB @ A @ B @ ( top_top @ ( set @ TB ) ) )
=> ( ( ? [D: TB] : ( C @ D ) )
= ( ? [D: TA] : ( C @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_type__copy__ex__RepI) ).
thf(699,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: TB > $o] :
( ( type_definition @ TA @ TB @ A @ B @ ( top_top @ ( set @ TB ) ) )
=> ( ( ? [D: TB] : ( C @ D ) )
= ( ? [D: TA] : ( C @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(240,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space) ).
thf(946,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top) ).
thf(632,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(172,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ D @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ E @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ D )
=> ( ( ord_less_eq @ TA @ F @ D )
=> ( ord_less_eq @ TA @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_sup__unique) ).
thf(781,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ D @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ E @ ( A @ D @ E ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ D )
=> ( ( ord_less_eq @ TA @ F @ D )
=> ( ord_less_eq @ TA @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo2133971006pology @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > TB] : ( topolo2071040574ous_on @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_continuous__on__discrete) ).
thf(896,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo2133971006pology @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: TA > TB] : ( topolo2071040574ous_on @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(159,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_sup__absorb1) ).
thf(748,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( sup @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Lattices_Osup_70) ).
thf(652,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( sup @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(4,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_87_inf__sup__aci_I7_J) ).
thf(351,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)],[4]) ).
thf(331,axiom,
! [TA: $tType] :
( ord_less_eq @ ( set @ ( sum_sum @ a @ TA ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) ) ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Isubs_I1_J) ).
thf(1193,plain,
! [TA: $tType] :
( ord_less_eq @ ( set @ ( sum_sum @ a @ TA ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_1 ) ) ) )
@ ( collect @ ( sum_sum @ a @ TA )
@ ^ [A: sum_sum @ a @ TA] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ TA @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ ( times @ a @ b @ theta_1 @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( ( freche457001096interp @ TA @ TB @ TC )
= ( ^ [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: frechet_good_interp @ TA @ TB @ TC] :
( A
= ( freche229654227interp @ TA @ TB @ TC @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_cr__good__interp__def) ).
thf(684,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( ( freche457001096interp @ TA @ TB @ TC )
= ( ^ [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit,B: frechet_good_interp @ TA @ TB @ TC] :
( A
= ( freche229654227interp @ TA @ TB @ TC @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( ordere890947078_space @ TA ) )
=> ( ordere890947078_space @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space_3) ).
thf(549,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( ordere890947078_space @ TA ) )
=> ( ordere890947078_space @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(70,axiom,
! [TA: $tType] : ( sup @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osup_19) ).
thf(536,plain,
! [TA: $tType] : ( sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(281,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Collect__mono) ).
thf(1045,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(319,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_sum_Oinject_I1_J) ).
thf(1161,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(305,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
( ( sum_rec_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_old_Osum_Osimps_I7_J) ).
thf(1116,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
( ( sum_rec_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(310,axiom,
( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ) )
=> ( ( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) )
=> ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
= ( denota126604975rm_sem @ a @ c @ b @ j @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_IH2) ).
thf(1133,plain,
( ( denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ) )
=> ( ( denotational_Iagree @ a @ c @ b @ i @ j
@ ( collect @ ( sum_sum @ a @ ( sum_sum @ c @ b ) )
@ ^ [A: sum_sum @ a @ ( sum_sum @ c @ b )] :
? [B: a] :
( ( A
= ( sum_Inl @ a @ ( sum_sum @ c @ b ) @ B ) )
& ( member @ a @ B @ ( static_SIGT @ a @ b @ theta_2 ) ) ) ) )
=> ( ( denota126604975rm_sem @ a @ c @ b @ i @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu ) )
= ( denota126604975rm_sem @ a @ c @ b @ j @ theta_2 @ ( product_fst @ ( finite_Cartesian_vec @ real @ b ) @ ( finite_Cartesian_vec @ real @ b ) @ nu2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( real_V55928688vector @ TA ) )
=> ( topolo503727757_space @ ( bounde2145540817linfun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_71) ).
thf(432,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( real_V55928688vector @ TA ) )
=> ( topolo503727757_space @ ( bounde2145540817linfun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(315,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_sup__Un__eq) ).
thf(1148,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType] :
( bNF_rel_fun @ ( trm @ TA @ TB ) @ ( frechet_strm @ TA @ TB ) @ ( trm @ TA @ TB ) @ ( trm @ TA @ TB ) @ ( frechet_cr_strm @ TA @ TB ) @ ( (=) @ ( trm @ TA @ TB ) )
@ ^ [A: trm @ TA @ TB] : A
@ ( frechet_raw_term @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_strm_Orep__transfer) ).
thf(867,plain,
! [TA: $tType,TB: $tType] :
( bNF_rel_fun @ ( trm @ TA @ TB ) @ ( frechet_strm @ TA @ TB ) @ ( trm @ TA @ TB ) @ ( trm @ TA @ TB ) @ ( frechet_cr_strm @ TA @ TB ) @ ( (=) @ ( trm @ TA @ TB ) )
@ ^ [A: trm @ TA @ TB] : A
@ ( frechet_raw_term @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(154,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_sup_OcoboundedI2) ).
thf(735,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(191,axiom,
topolo503727757_space @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_31) ).
thf(833,plain,
topolo503727757_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(21,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_67_sup_Oleft__idem) ).
thf(410,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)],[21]) ).
thf(243,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_refl__ge__eq) ).
thf(950,plain,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(297,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ~ ! [B: frechet_good_interp @ TA @ TB @ TC] :
( A
!= ( freche229654227interp @ TA @ TB @ TC @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_raw__interp__cases) ).
thf(1097,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ! [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] :
( ( member @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ A @ ( collect @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota2077489681interp @ TA @ TB @ TC ) ) )
=> ~ ! [B: frechet_good_interp @ TA @ TB @ TC] :
( A
!= ( freche229654227interp @ TA @ TB @ TC @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(193,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_25) ).
thf(835,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(12,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_le__cases3) ).
thf(373,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > $o,B: TC > TB > $o,C: TA > TC,D: TA > TB,E: TA] :
( ( bNF_rel_fun @ TA @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( B @ ( C @ E ) @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_rel__funD2) ).
thf(603,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > $o,B: TC > TB > $o,C: TA > TC,D: TA > TB,E: TA] :
( ( bNF_rel_fun @ TA @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ E )
=> ( B @ ( C @ E ) @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TA )
& ( sup @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TB @ ( sup_sup @ ( product_prod @ TA @ TB ) @ A @ B ) )
= ( sup_sup @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_fst__sup) ).
thf(400,plain,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TA )
& ( sup @ TB ) )
=> ! [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TB @ ( sup_sup @ ( product_prod @ TA @ TB ) @ A @ B ) )
= ( sup_sup @ TA @ ( product_fst @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TC ) )
=> ! [A: set @ TA,B: TA > TB > TC] :
( ! [C: TB] :
( topolo2071040574ous_on @ TA @ TC @ A
@ ^ [D: TA] : ( B @ D @ C ) )
=> ( topolo2071040574ous_on @ TA @ ( TB > TC ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_continuous__on__coordinatewise__then__product) ).
thf(828,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TC ) )
=> ! [A: set @ TA,B: TA > TB > TC] :
( ! [C: TB] :
( topolo2071040574ous_on @ TA @ TC @ A
@ ^ [D: TA] : ( B @ D @ C ) )
=> ( topolo2071040574ous_on @ TA @ ( TB > TC ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(247,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_equalityE) ).
thf(960,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(139,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Un__subset__iff) ).
thf(696,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(244,axiom,
bounded_lattice @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice) ).
thf(955,plain,
bounded_lattice @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TB )
& ( sup @ TA ) )
=> ( sup @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Osup_50) ).
thf(358,plain,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TB )
& ( sup @ TA ) )
=> ( sup @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(180,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_le__supI1) ).
thf(807,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(323,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_71_Un__iff) ).
thf(1172,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)],[323]) ).
thf(167,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_sup__top__left) ).
thf(767,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(284,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( topolo2071040574ous_on @ TA @ TB @ A @ C )
= ( topolo2071040574ous_on @ TA @ TB @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_continuous__on__cong) ).
thf(1056,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( topolo2071040574ous_on @ TA @ TB @ A @ C )
= ( topolo2071040574ous_on @ TA @ TB @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(664,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(156,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_sup_Oabsorb1) ).
thf(740,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( sup_sup @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(256,axiom,
bounded_lattice_top @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top_51) ).
thf(987,plain,
bounded_lattice_top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top) ).
thf(464,plain,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TB] : ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_Domainp__iff) ).
thf(427,plain,
! [TA: $tType,TB: $tType] :
( ( domainp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: TA] :
? [C: TB] : ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(206,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_sup__least) ).
thf(860,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(225,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_sup_OcoboundedI1) ).
thf(908,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType] :
( ( frechet_cr_strm @ TA @ TB )
= ( ^ [A: trm @ TA @ TB,B: frechet_strm @ TA @ TB] :
( A
= ( frechet_raw_term @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_cr__strm__def) ).
thf(723,plain,
! [TA: $tType,TB: $tType] :
( ( frechet_cr_strm @ TA @ TB )
= ( ^ [A: trm @ TA @ TB,B: frechet_strm @ TA @ TB] :
( A
= ( frechet_raw_term @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subset__trans) ).
thf(850,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(211,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_predicate2D) ).
thf(871,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_rel__funE) ).
thf(624,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD > TC,D: TA > TB,E: TD,F: TA] :
( ( bNF_rel_fun @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( A @ E @ F )
=> ( B @ ( C @ E ) @ ( D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(196,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_inf__sup__ord_I4_J) ).
thf(839,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(5,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ord__eq__le__trans) ).
thf(354,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB,C: trm @ TA @ TB,D: trm @ TA @ TB] :
( ( ( times @ TA @ TB @ A @ B )
= ( times @ TA @ TB @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_trm_Oinject_I5_J) ).
thf(923,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: trm @ TA @ TB,C: trm @ TA @ TB,D: trm @ TA @ TB] :
( ( ( times @ TA @ TB @ A @ B )
= ( times @ TA @ TB @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(328,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_conj__subset__def) ).
thf(1184,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(74,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ord @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oord) ).
thf(543,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ord @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(277,axiom,
denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_VAs_I2_J) ).
thf(1037,plain,
denotational_Vagree @ b @ nu @ nu2 @ ( static_FVT @ a @ b @ theta_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( real_V55928688vector @ TA ) )
=> ( real_V55928688vector @ ( bounde2145540817linfun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector) ).
thf(639,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TB )
& ( real_V55928688vector @ TA ) )
=> ( real_V55928688vector @ ( bounde2145540817linfun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( bNF_rel_fun @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( frechet_good_interp @ TA @ TB @ TC ) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( freche457001096interp @ TA @ TB @ TC ) @ ( (=) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) )
@ ^ [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] : A
@ ( freche229654227interp @ TA @ TB @ TC ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_good__interp_Orep__transfer) ).
thf(676,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB )
& ( finite_finite @ TC ) )
=> ( bNF_rel_fun @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( frechet_good_interp @ TA @ TB @ TC ) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) @ ( freche457001096interp @ TA @ TB @ TC ) @ ( (=) @ ( denota1663640101rp_ext @ TA @ TB @ TC @ product_unit ) )
@ ^ [A: denota1663640101rp_ext @ TA @ TB @ TC @ product_unit] : A
@ ( freche229654227interp @ TA @ TB @ TC ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(38,axiom,
bounded_lattice_top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__top_21) ).
thf(454,plain,
bounded_lattice_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TB )
& ( topolo503727757_space @ TA ) )
=> ( topolo503727757_space @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_40) ).
thf(469,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TB )
& ( topolo503727757_space @ TA ) )
=> ( topolo503727757_space @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(238,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA] :
( topolo2071040574ous_on @ TA @ TA @ A
@ ^ [B: TA] : B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_continuous__on__id) ).
thf(940,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA] :
( topolo2071040574ous_on @ TA @ TA @ A
@ ^ [B: TA] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_le__funI) ).
thf(491,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(294,axiom,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: ( trm @ TA @ TB ) > $o] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ! [C: frechet_strm @ TA @ TB] : ( B @ ( frechet_raw_term @ TA @ TB @ C ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_raw__term__induct) ).
thf(1088,plain,
! [TA: $tType,TB: $tType,A: trm @ TA @ TB,B: ( trm @ TA @ TB ) > $o] :
( ( member @ ( trm @ TA @ TB ) @ A @ ( collect @ ( trm @ TA @ TB ) @ ( dfree @ TA @ TB ) ) )
=> ( ! [C: frechet_strm @ TA @ TB] : ( B @ ( frechet_raw_term @ TA @ TB @ C ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1282,plain,
$false,
inference(e,[status(thm)],[809,1190,760,893,666,479,1105,628,1031,777,555,977,1211,762,1005,730,994,1073,1142,597,873,1205,449,878,655,511,1078,715,472,814,913,538,1164,797,1222,930,898,709,841,973,436,1228,1095,404,838,802,949,917,702,751,542,460,853,1087,421,416,1115,1100,1232,1013,770,475,756,789,591,646,1151,821,485,1136,834,348,574,687,692,956,453,396,988,527,1215,634,1119,774,942,678,661,1153,1067,910,825,1042,424,630,862,349,847,1032,361,852,830,493,1195,551,1128,519,1234,615,1064,388,593,869,650,948,980,403,471,884,1028,488,933,554,1182,669,901,970,1114,997,457,569,371,1131,654,360,508,921,541,657,765,1170,558,1187,530,926,1202,792,1086,938,398,1035,1026,1167,794,586,718,888,618,1103,1219,856,745,573,601,513,430,819,732,843,772,743,875,579,958,545,413,562,904,975,1007,694,641,1139,936,572,611,1107,713,498,466,1092,919,804,406,990,567,737,1122,599,1175,1011,419,880,1043,434,890,477,816,483,1177,462,1112,858,367,799,726,626,915,521,983,1198,1213,636,455,1015,608,986,1000,438,431,658,722,548,648,812,754,836,1049,473,1076,1203,589,617,516,1145,1018,968,823,525,690,1025,1070,414,712,557,1003,705,1156,1225,707,409,1230,1053,673,502,643,907,1038,585,1085,576,1023,613,864,1008,446,595,612,845,1180,363,482,671,495,759,1216,699,946,632,781,896,748,652,351,1193,684,549,536,1045,1161,1116,1133,432,1148,867,735,833,410,950,1097,835,373,603,400,828,960,696,955,358,807,1172,767,1056,664,740,987,464,427,860,908,723,850,871,624,839,354,923,1184,543,1037,639,676,454,469,940,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP042^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n014.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:40:29 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.41/1.24 % [INFO] Parsing done (444ms).
% 2.41/1.26 % [INFO] Running in sequential loop mode.
% 3.29/1.65 % [INFO] eprover registered as external prover.
% 3.29/1.65 % [INFO] Scanning for conjecture ...
% 3.70/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 358 axioms. Running axiom selection ...
% 3.92/2.04 % [INFO] Axiom selection finished. Selected 345 axioms (removed 13 axioms).
% 5.38/2.39 % [INFO] Problem is higher-order (TPTP THF).
% 5.76/2.43 % [INFO] Type checking passed.
% 5.76/2.43 % [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 ...
% 66.89/35.54 % External prover 'e' found a proof!
% 66.89/35.54 % [INFO] Killing All external provers ...
% 66.89/35.54 % Time passed: 35200ms (effective reasoning time: 34270ms)
% 66.89/35.54 % 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)>
% 66.89/35.55 % Axioms used in derivation (345): fact_132_sup_OboundedI, tcon_Product__Type_Oprod___Finite__Set_Ofinite_45, fact_90_sup__fun__def, fact_4_dfree__Times_Ohyps_I1_J, fact_170_linorder__wlog, fact_191_le__funE, tcon_Product__Type_Ounit___Lattices_Obounded__lattice, tcon_Real_Oreal___Topological__Spaces_Otopological__space_31, fact_91_boolean__algebra__cancel_Osup1, fact_205_top_Oextremum__unique, fact_210_UNIV__witness, fact_201_fst__top, fact_85_Collect__mono__iff, fact_204_top_Oextremum__uniqueI, fact_147_subset__UnE, tcon_Set_Oset___Lattices_Olattice_15, fact_252_continuous__on__product__then__coordinatewise, tfree_0, fact_174_ord__le__eq__trans, fact_67_sup_Oleft__idem, tcon_fun___Finite__Set_Ofinite, tfree_5, fact_192_le__funD, fact_209_Un__UNIV__right, tcon_Set_Oset___Orderings_Oorder__top_12, fact_220_continuous__on__cases__1, fact_140_fst__mono, fact_77_subset__eq, fact_101_UnI2, fact_40_agree__union, fact_251_conj__subset__def, tcon_Product__Type_Ounit___Lattices_Olattice_57, fact_120_sup_Omono, tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector_6, fact_39_simple__term__inverse, fact_208_Un__UNIV__left, fact_180_le__cases, fact_138_sup_OcoboundedI1, fact_122_sup__least, fact_29_simple__term__inject, fact_51_le__sup__iff, fact_243_continuous__on__fst, tcon_Bounded__Linear__Function_Oblinfun___Topological__Spaces_Otopological__space_71, fact_158_sup1CI, fact_78_equalityD1, tcon_Product__Type_Ounit___Orderings_Otop_59, fact_211_UNIV__eq__I, fact_64_sup__apply, tcon_HOL_Obool___Topological__Spaces_Otopological__space_20, fact_177_antisym__conv, fact_195_pred__subset__eq, fact_118_le__supI1, tcon_Set_Oset___Lattices_Obounded__lattice__top_10, fact_88_inf__sup__aci_I6_J, fact_72_sup__set__def, fact_94_sup__assoc, tcon_fun___Orderings_Oord, fact_143_Un__upper1, fact_200_sup__top__left, fact_222_top__empty__eq, fact_115_le__supI, fact_9_Iagree__comm, fact_153_strm_Orep__transfer, fact_96_sup__commute, fact_139_sup_OcoboundedI2, tcon_fun___Topological__Spaces_Otopological__space, fact_74_in__mono, fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062, fact_84_set__eq__subset, fact_133_sup_Oorder__iff, tcon_Finite__Cartesian__Product_Ovec___Lattices_Osemilattice__sup_63, fact_61_good__interp__cases, tcon_Product__Type_Oprod___Orderings_Oorder_47, fact_103_ball__Un, fact_12_IH1, fact_157_predicate1I, fact_137_sup_Oabsorb__iff2, tcon_Set_Oset___Finite__Set_Ofinite_14, fact_33_raw__term__induct, fact_188_order__subst1, fact_151_sterm__continuous_H, fact_7_Isubs_I2_J, fact_154_good__interp_Orep__transfer, tcon_HOL_Obool___Orderings_Olinorder, fact_255_rel__fun__def__butlast, fact_176_order__class_Oorder_Oeq__iff, fact_160_predicate1D, tcon_fun___Lattices_Obounded__lattice_9, tcon_Real_Oreal___Orderings_Olinorder_34, fact_155_good__interp_Odomain, fact_31_simple__term__cases, fact_231_rel__fun__mono, tcon_HOL_Obool___Lattices_Obounded__lattice_7, fact_105_Un__absorb, fact_87_inf__sup__aci_I7_J, fact_149_type__definition__good__interp, fact_178_le__cases3, tcon_Set_Oset___Lattices_Obounded__lattice_8, tcon_Product__Type_Oprod___Lattices_Obounded__lattice__top_41, tcon_Finite__Cartesian__Product_Ovec___Lattices_Osup_70, fact_23_agree__sub, tcon_Product__Type_Oprod___Lattices_Osemilattice__sup_42, fact_129_sup__absorb1, fact_95_sup_Ocommute, tfree_3, fact_234_refl__ge__eq, fact_68_sup__left__idem, tcon_Sum__Type_Osum___Finite__Set_Ofinite_39, tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space_3, fact_86_inf__sup__aci_I8_J, fact_214_Domainp_Ocases, fact_113_inf__sup__ord_I3_J, tcon_HOL_Obool___Lattices_Obounded__lattice__top_21, fact_14_IH2, fact_179_order_Otrans, fact_46_Collect__mem__eq, tcon_Set_Oset___Lattices_Osup_19, fact_182_linear, fact_80_subset__iff, fact_107_Un__left__absorb, fact_125_sup_OorderI, tfree_4, fact_62_subsetI, tcon_Product__Type_Oprod___Orderings_Otop_48, fact_162_sup1I2, fact_230_rel__funD, fact_112_inf__sup__ord_I4_J, fact_186_ord__eq__le__subst, tcon_HOL_Obool___Lattices_Olattice_26, fact_92_boolean__algebra__cancel_Osup2, fact_119_le__supI2, tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_5, fact_38_raw__term__inverse, fact_246_continuous__on__id, fact_30_simple__term__induct, fact_5_sum_Oinject_I1_J, fact_56_raw__interp__induct, fact_34_raw__term__cases, fact_217_Domainp_Oinducts, fact_229_top1I, fact_198_predicate2I, help_If_1_1_T, tcon_Set_Oset___Orderings_Otop_17, tcon_Product__Type_Ounit___Lattices_Osemilattice__sup_52, tcon_Bounded__Linear__Function_Oblinfun___Real__Vector__Spaces_Oreal__normed__vector, tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology, tcon_fun___Lattices_Osemilattice__sup, fact_6_old_Osum_Oinject_I1_J, tcon_Product__Type_Ounit___Orderings_Olinorder_55, fact_117_sup__ge2, fact_99_UnE, tcon_HOL_Obool___Orderings_Oorder__top_23, fact_240_Domainp__iff, fact_27_cr__good__interp__def, fact_16_raw__interp__inject, fact_203_rev__predicate2D, fact_114_le__supE, fact_110_Un__def, fact_127_sup_Oabsorb1, fact_15_Iagree__Func, fact_245_continuous__on__discrete, fact_238_rel__funE, fact_79_equalityD2, fact_42_dfree_Odfree__Times, tcon_Set_Oset___Orderings_Oorder_16, fact_168_dual__order_Oeq__iff, fact_235_let__rsp, fact_166_typedef__rep__transfer, fact_237_rel__funD2, fact_167_dual__order_Oantisym, tcon_Real_Oreal___Lattices_Osemilattice__sup_32, fact_142_Un__least, fact_70_UnCI, fact_159_fun__mono, fact_206_top__greatest, tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_4, fact_50_sup_Obounded__iff, tfree_2, fact_25_agree__refl, fact_45_mem__Collect__eq, fact_161_rev__predicate1D, fact_3_dfree__Times_Oprems_I2_J, fact_236_Let__transfer, fact_35_raw__term, fact_202_predicate2D, fact_249_continuous__on__product__then__coordinatewise__UNIV, fact_128_sup_Oabsorb2, fact_242_iso__tuple__UNIV__I, fact_66_sup__idem, tcon_Product__Type_Ounit___Orderings_Oorder_58, fact_165_apply__rsp_H, fact_2_IA, fact_226_fun_Orel__eq, fact_18_coincidence__sterm, tcon_HOL_Obool___Orderings_Oorder_27, fact_152_old_Osum_Osimps_I7_J, fact_190_le__funI, fact_75_subsetD, fact_171_dual__order_Orefl, fact_189_le__fun__def, tcon_Finite__Cartesian__Product_Ovec___Topological__Spaces_Otopological__space_62, fact_145_Un__absorb1, fact_144_Un__upper2, tcon_Product__Type_Ounit___Lattices_Osup_61, tcon_Finite__Cartesian__Product_Ovec___Orderings_Olinorder_65, fact_126_sup__unique, fact_108_Un__left__commute, tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_66, fact_71_Un__iff, fact_47_Collect__cong, fact_11_Inl__inject, fact_53_SIGT_Osimps_I5_J, fact_73_less__eq__set__def, tcon_Real_Oreal___Orderings_Oorder_36, tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space, fact_102_bex__Un, subcl_Orderings_Olinorder___Orderings_Oorder, fact_43_cr__strm__def, help_If_3_1_T, fact_24_agree__comm, fact_21_VAs_I1_J, fact_131_sup_OboundedE, help_If_2_1_T, tcon_fun___Lattices_Obounded__lattice__top, fact_121_sup__mono, tcon_fun___Orderings_Otop, fact_213_DomainpE, fact_247_continuous__on__const, subcl_Orderings_Olinorder___Orderings_Oord, fact_248_continuous__on__subset, fact_17_dfree__Times_Ohyps_I2_J, fact_104_Un__assoc, fact_216_Domainp_ODomainI, fact_57_raw__interp__cases, fact_173_order__class_Oorder_Oantisym, fact_239_Domainp__refl, tcon_Set_Oset___Lattices_Osemilattice__sup_11, fact_82_Collect__mono, tcon_Real_Oreal___Lattices_Osup_38, fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062, fact_76_equalityE, fact_197_UNIV__I, tcon_Real_Oreal___Lattices_Olattice_35, tfree_6, tcon_Finite__Cartesian__Product_Ovec___Orderings_Oorder_68, fact_227_frechet__continuous, tcon_Product__Type_Ounit___Orderings_Oorder__top_53, fact_44_fst__sup, fact_218_fun_Orel__mono, tcon_HOL_Obool___Lattices_Osemilattice__sup_22, fact_49_Un__subset__iff, tcon_Product__Type_Ounit___Orderings_Oord_60, fact_193_sterm__continuous, tcon_fun___Orderings_Oorder__top, fact_124_sup_OorderE, fact_130_sup__absorb2, fact_28_dfree__Times__simps, fact_123_le__iff__sup, tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top_51, fact_164_sup1E, fact_254_type__copy__obj__one__point__absE, tcon_Real_Oreal___Orderings_Oord_37, fact_194_sup__Un__eq, fact_169_dual__order_Otrans, tcon_Finite__Cartesian__Product_Ovec___Real__Vector__Spaces_Oreal__normed__vector_1, tcon_Product__Type_Oprod___Lattices_Obounded__lattice_2, fact_36_trm_Oinject_I5_J, fact_100_UnI1, subcl_Finite__Set_Ofinite___HOL_Otype, fact_106_Un__commute, tfree_1, fact_37_raw__term__inject, fact_225_fun_Orel__refl, tcon_Product__Type_Oprod___Orderings_Oorder__top_43, fact_52_FVT_Osimps_I5_J, fact_228_rel__funI, fact_63_subset__antisym, fact_253_continuous__on__coordinatewise__then__product, fact_41_Iagree__sub, tcon_Product__Type_Oprod___Topological__Spaces_Otopological__space_40, fact_26_agree__supset, tcon_fun___Orderings_Oorder, fact_19_dfree__Times_Oprems_I1_J, fact_20_VAs_I2_J, fact_221_agree__UNIV__eq, fact_187_order__subst2, fact_196_top__apply, fact_148_subset__Un__eq, fact_32_raw__interp__inverse, fact_60_good__interp__induct, tcon_Product__Type_Oprod___Lattices_Osup_50, tcon_Finite__Cartesian__Product_Ovec___Orderings_Oord_69, fact_22_VA, tcon_HOL_Obool___Orderings_Otop_28, fact_81_subset__refl, fact_223_top__set__def, fact_232_rel__fun__mono_H, tcon_Product__Type_Oprod___Lattices_Olattice_46, fact_175_ord__eq__le__trans, tcon_Product__Type_Oprod___Orderings_Oord_49, fact_83_subset__trans, fact_109_Collect__subset, fact_69_sup_Oright__idem, fact_244_continuous__on__cong, fact_136_sup_Oabsorb__iff1, tcon_Finite__Cartesian__Product_Ovec___Lattices_Olattice_67, tcon_Product__Type_Ounit___Finite__Set_Ofinite_56, fact_224_fun_Orel__transfer, fact_65_sup_Oidem, tcon_Set_Oset___Orderings_Oord_18, fact_163_sup1I1, fact_135_sup_Ocobounded2, fact_141_Un__mono, fact_146_Un__absorb2, fact_10_Iagree__refl, fact_183_antisym, fact_207_subset__UNIV, fact_116_sup__ge1, fact_59_good__interp__inject, subcl_Orderings_Olinorder___HOL_Otype, fact_250_type__copy__ex__RepI, fact_111_Collect__disj__eq, fact_8_Isubs_I1_J, fact_134_sup_Ocobounded1, fact_55_good__interp__inverse, fact_199_sup__top__right, fact_58_raw__interp, fact_233_ge__eq__refl, fact_93_sup_Oassoc, tcon_HOL_Obool___Lattices_Osup_30, fact_54_type__definition__strm, fact_156_strm_Odomain, fact_184_eq__iff, fact_241_Domain__eq__top, tcon_HOL_Obool___Finite__Set_Ofinite_25, fact_97_sup_Oleft__commute, fact_219_continuous__on__cases__le, fact_98_sup__left__commute, fact_185_ord__le__eq__subst, fact_212_UNIV__def, tcon_HOL_Obool___Orderings_Oord_29, fact_89_inf__sup__aci_I5_J, tcon_fun___Lattices_Olattice, fact_215_Domainp_Osimps, tcon_fun___Lattices_Osup
% 66.89/35.55 % No. of inferences in proof: 694
% 66.89/35.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 35200 ms resp. 34270 ms w/o parsing
% 67.87/35.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 67.87/35.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------