%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP154^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 08:06:58 AM UTC 2026
% Result : Theorem 65.99s 51.96s
% Output : Refutation 66.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 301
% Syntax : Number of formulae : 604 ( 133 unt; 0 typ; 0 def)
% Number of atoms : 2803 ( 384 equ; 8 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 10404 ( 226 ~; 28 |; 180 &;8886 @)
% ( 0 <=>;1084 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 140 ( 140 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 9 con; 0-5 aty)
% Number of variables : 2124 ( 62 ^;2028 !; 34 ?;2124 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(inf_decl,type,
inf:
!>[TA: $tType] : $o ).
thf(sup_decl,type,
sup:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(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(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_bot_decl,type,
order_bot:
!>[TA: $tType] : $o ).
thf(semilattice_inf_decl,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(semilattice_sup_decl,type,
semilattice_sup:
!>[TA: $tType] : $o ).
thf(bNF_Ca1785829860lChain_decl,type,
bNF_Ca1785829860lChain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(finite_finite2_decl,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(lattic929149872er_Max_decl,type,
lattic929149872er_Max:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(lattic929674654er_Min_decl,type,
lattic929674654er_Min:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(lattic1704895705min_on_decl,type,
lattic1704895705min_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TB ) ).
thf(lattic2065218050nf_fin_decl,type,
lattic2065218050nf_fin:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(lattic477160up_fin_decl,type,
lattic477160up_fin:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(order_preorder_on_decl,type,
order_preorder_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(order_under_decl,type,
order_under:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > TA > ( set @ TA ) ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(order_Greatest_decl,type,
order_Greatest:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(prefer951318096ood_as_decl,type,
prefer951318096ood_as:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer310429814s_good_decl,type,
prefer310429814s_good:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer1532642881r_than_decl,type,
prefer1532642881r_than:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(prefer199794634erence_decl,type,
prefer199794634erence:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(prefer1997167224erence_decl,type,
prefer1997167224erence:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(prefer1801827867axioms_decl,type,
prefer1801827867axioms:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(id_on_decl,type,
id_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(refl_on_decl,type,
refl_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(total_on_decl,type,
total_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(trans_decl,type,
trans:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(is_empty_decl,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(carrier_decl,type,
carrier: set @ a ).
thf(relation_decl,type,
relation: set @ ( product_prod @ a @ a ) ).
thf(x_decl,type,
x: a ).
thf(y_decl,type,
y: a ).
thf(128,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic929674654er_Min @ TA @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Min__in) ).
thf(645,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic929674654er_Min @ TA @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',fact_111_order__class_Oorder_Oantisym) ).
thf(1036,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)],[255]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_59_subset__antisym) ).
thf(809,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)],[186]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_130_le__funD) ).
thf(1024,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)],[251]) ).
thf(299,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( trans @ TA @ A )
=> ( ( trans @ TA @ B )
=> ( trans @ TA @ ( inf_inf @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_trans__Int) ).
thf(1190,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( trans @ TA @ A )
=> ( ( trans @ TA @ B )
=> ( trans @ TA @ ( inf_inf @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(123,axiom,
! [A: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( prefer1532642881r_than @ a @ A @ carrier @ relation )
!= ( bot_bot @ ( set @ a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_no__better__than__nonepty) ).
thf(628,plain,
! [A: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( prefer1532642881r_than @ a @ A @ carrier @ relation )
!= ( bot_bot @ ( set @ a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(82,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) )
| ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_rational__preference_Ostrict__is__neg__transitive) ).
thf(518,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) )
| ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(225,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Int__absorb1) ).
thf(941,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(295,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Int__absorb2) ).
thf(1179,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',fact_76_subset__trans) ).
thf(1168,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)],[290]) ).
thf(170,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Int__lower1) ).
thf(760,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(244,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_Max_OboundedI) ).
thf(1005,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( B
= ( lattic929674654er_Min @ TA @ A ) )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_eq__Min__iff) ).
thf(741,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( B
= ( lattic929674654er_Min @ TA @ A ) )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(32,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rational__preference_Ototal) ).
thf(379,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(80,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( A = B )
=> ( ( member @ TA @ A @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_Id__on__eqI) ).
thf(511,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( A = B )
=> ( ( member @ TA @ A @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(112,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_16) ).
thf(597,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fact_127_le__fun__def) ).
thf(861,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)],[204]) ).
thf(105,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( inf_inf @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) )
= ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Inf__fin_Oin__idem) ).
thf(582,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( inf_inf @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) )
= ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(171,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( order_Greatest @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_Greatest__equality) ).
thf(762,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( order_Greatest @ TA @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(209,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_empty__subsetI) ).
thf(873,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Pair__inject) ).
thf(449,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(120,axiom,
! [A: a,B: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ~ ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) )
=> ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_at__lst__asgd__not__ge) ).
thf(614,plain,
! [A: a,B: a] :
( ( carrier
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ~ ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) )
=> ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(137,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ B ) @ ( lattic929674654er_Min @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Min_Osubset__imp) ).
thf(677,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ B ) @ ( lattic929674654er_Min @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(94,axiom,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_refl__on__Id__on) ).
thf(550,plain,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(181,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( lattic477160up_fin @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Sup__fin_OcoboundedI) ).
thf(797,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( lattic477160up_fin @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(146,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Max_Obounded__iff) ).
thf(698,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(17,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(340,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(165,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_all__not__in__conv) ).
thf(747,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(217,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_empty__iff) ).
thf(913,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(43,axiom,
inf @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oinf_22) ).
thf(404,plain,
inf @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__set__choice) ).
thf(417,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(258,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ ( prefer1532642881r_than @ TA @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_rational__preference_Oworse__in__no__better) ).
thf(1046,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ ( prefer1532642881r_than @ TA @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(10,axiom,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id_on @ TA @ B ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_Id__onE) ).
thf(320,plain,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id_on @ TA @ B ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(130,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic2065218050nf_fin @ TA @ B ) @ ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_Inf__fin_Osubset__imp) ).
thf(651,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic2065218050nf_fin @ TA @ B ) @ ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( ( inf @ TB )
& ( inf @ TA ) )
=> ( inf @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Oinf_33) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( ( inf @ TB )
& ( inf @ TA ) )
=> ( inf @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',fact_231_Un__subset__iff) ).
thf(724,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)],[156]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rational__preference_Oweak__is__transitive) ).
thf(504,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A )
& ( member @ TA @ E @ A ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(587,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(183,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( lattic929149872er_Max @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Max__ge) ).
thf(802,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( lattic929149872er_Max @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_prod__induct3) ).
thf(357,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(228,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( sup_sup @ TA @ ( lattic477160up_fin @ TA @ B ) @ ( lattic477160up_fin @ TA @ A ) )
= ( lattic477160up_fin @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Sup__fin_Osubset) ).
thf(949,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( sup_sup @ TA @ ( lattic477160up_fin @ TA @ B ) @ ( lattic477160up_fin @ TA @ A ) )
= ( lattic477160up_fin @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_prod__induct4) ).
thf(460,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(234,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( lattic2065218050nf_fin @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ ( lattic2065218050nf_fin @ TA @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Inf__fin_Ounion) ).
thf(969,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( lattic2065218050nf_fin @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ ( lattic2065218050nf_fin @ TA @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(246,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_9) ).
thf(1013,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(11,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_refl__onD1) ).
thf(325,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite) ).
thf(316,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_at__least__as__goodD) ).
thf(492,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(168,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_weak__is__transitive) ).
thf(756,plain,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oord_30) ).
thf(591,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TB )
& ( ord @ TA ) )
=> ( ord @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_subset__emptyI) ).
thf(1109,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(185,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( prefer951318096ood_as @ a @ B @ carrier @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_as__good__as__sameIff) ).
thf(806,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( prefer951318096ood_as @ a @ B @ carrier @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_ssubst__Pair__rhs) ).
thf(353,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(260,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_bot_Oextremum__unique) ).
thf(1051,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(72,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ C @ B ) )
=> ( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ D @ B ) )
=> ( ( order_preorder_on @ TA @ B @ A )
=> ( prefer199794634erence @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_preference_Ointro) ).
thf(485,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ C @ B ) )
=> ( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ TA @ D @ B ) )
=> ( ( order_preorder_on @ TA @ B @ A )
=> ( prefer199794634erence @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(195,axiom,
! [TA: $tType] :
( ( preorder @ 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/sandbox/benchmark/theBenchmark.p',fact_110_order__trans) ).
thf(834,plain,
! [TA: $tType] :
( ( preorder @ 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)],[195]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_78_Collect__mono__iff) ).
thf(634,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)],[125]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_107_dual__order_Otrans) ).
thf(692,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)],[143]) ).
thf(160,axiom,
! [TA: $tType] : ( trans @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_trans__empty) ).
thf(734,plain,
! [TA: $tType] : ( trans @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(206,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ~ ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_rational__preference_Oat__lst__asgd__not__ge) ).
thf(866,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ~ ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__subset) ).
thf(774,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(40,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( prefer951318096ood_as @ TA @ D @ A @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rational__preference_Oas__good__as__sameIff) ).
thf(396,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( prefer951318096ood_as @ TA @ D @ A @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA] : ( trans @ TA @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_trans__Id__on) ).
thf(411,plain,
! [TA: $tType,A: set @ TA] : ( trans @ TA @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(202,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ ( lattic929674654er_Min @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Min_OboundedI) ).
thf(849,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ ( lattic929674654er_Min @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_bot__apply) ).
thf(527,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(266,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_equals0I) ).
thf(1074,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) )
= ( ( A = B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Id__on__iff) ).
thf(439,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) )
= ( ( A = B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(381,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_prod__cases4) ).
thf(366,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic929674654er_Min @ TA @ A ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Min_Obounded__iff) ).
thf(1067,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic929674654er_Min @ TA @ A ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',fact_124_ord__eq__le__subst) ).
thf(1057,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)],[262]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(546,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(179,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( B
= ( lattic929149872er_Max @ TA @ A ) )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_eq__Max__iff) ).
thf(793,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( B
= ( lattic929149872er_Max @ TA @ A ) )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_prod__cases6) ).
thf(334,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(216,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Inf__fin_OboundedE) ).
thf(910,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(271,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ord_less_eq @ TA @ D @ B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ TA @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_GreatestI2__order) ).
thf(1091,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ord_less_eq @ TA @ D @ B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ TA @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(250,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ord_less_eq @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ ( lattic477160up_fin @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Inf__fin__le__Sup__fin) ).
thf(1021,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ord_less_eq @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ ( lattic477160up_fin @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',fact_114_order__class_Oorder_Oeq__iff) ).
thf(952,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)],[229]) ).
thf(293,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 ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_Int__mono) ).
thf(1174,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 ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(598,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(190,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_equalityD1) ).
thf(820,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)],[190]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TB )
& ( order @ TA ) )
=> ( order @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder_29) ).
thf(561,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TB )
& ( order @ TA ) )
=> ( order @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(188,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( prefer1532642881r_than @ TA @ C @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rational__preference_Ono__better__than__nonepty) ).
thf(815,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ C @ A )
=> ( ( prefer1532642881r_than @ TA @ C @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_77_set__eq__subset) ).
thf(729,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)],[158]) ).
thf(277,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__has__maximal) ).
thf(1123,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order_bot @ TB )
& ( order_bot @ TA ) )
=> ( order_bot @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Oorder__bot_25) ).
thf(349,plain,
! [TA: $tType,TB: $tType] :
( ( ( order_bot @ TB )
& ( order_bot @ TA ) )
=> ( order_bot @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(65,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) )
=> ( ( ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rational__preference_Ostrict__not__refl__weak) ).
thf(467,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) )
=> ( ( ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(24,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( inf_inf @ TA @ B @ ( lattic477160up_fin @ TA @ A ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_inf__Sup__absorb) ).
thf(361,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( inf_inf @ TA @ B @ ( lattic477160up_fin @ TA @ A ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(212,axiom,
! [TA: $tType,A: set @ TA,B: TA > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
~ ( B @ C @ C )
=> ( ! [C: TA,D: TA,E: TA] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ C @ D ) ) )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_finite__transitivity__chain) ).
thf(879,plain,
! [TA: $tType,A: set @ TA,B: TA > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
~ ( B @ C @ C )
=> ( ! [C: TA,D: TA,E: TA] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ C @ D ) ) )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(13,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( sup_sup @ TA @ B @ ( lattic477160up_fin @ TA @ A ) )
= ( lattic477160up_fin @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_Sup__fin_Oin__idem) ).
thf(329,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( sup_sup @ TA @ B @ ( lattic477160up_fin @ TA @ A ) )
= ( lattic477160up_fin @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_relChain__def) ).
thf(665,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(198,axiom,
member @ a @ x @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(842,plain,
member @ a @ x @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(272,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Sup__fin_Obounded__iff) ).
thf(1106,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_bot__fun__def) ).
thf(566,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(71,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_19) ).
thf(484,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(139,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_not__outside) ).
thf(682,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',fact_67_in__mono) ).
thf(1195,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)],[301]) ).
thf(104,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_preference_Oindiff__trans) ).
thf(578,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(283,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Pair__mono) ).
thf(1143,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',fact_121_antisym) ).
thf(1111,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)],[274]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fact_122_eq__iff) ).
thf(980,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)],[237]) ).
thf(36,axiom,
lattice @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_17) ).
thf(388,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(281,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: TA,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TB @ ( C @ ( lattic1704895705min_on @ TA @ TB @ C @ A ) ) @ ( C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_arg__min__least) ).
thf(1138,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: TA,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TB @ ( C @ ( lattic1704895705min_on @ TA @ TB @ C @ A ) ) @ ( C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_surj__pair) ).
thf(593,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(207,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_dual__order_Orefl) ).
thf(869,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_58_subsetI) ).
thf(610,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)],[119]) ).
thf(239,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite__has__minimal) ).
thf(989,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(289,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TB,B: TB > TA > $o] :
( ( finite_finite2 @ TB @ A )
=> ( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) )
=> ? [C: TA] :
! [D: TB] :
( ( member @ TB @ D @ A )
=> ? [E: TA] :
( ( ord_less_eq @ TA @ E @ C )
& ( B @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_finite__indexed__bound) ).
thf(1160,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TB,B: TB > TA > $o] :
( ( finite_finite2 @ TB @ A )
=> ( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) )
=> ? [C: TA] :
! [D: TB] :
( ( member @ TB @ D @ A )
=> ? [E: TA] :
( ( ord_less_eq @ TA @ E @ C )
& ( B @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(222,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Inf__fin_Obounded__iff) ).
thf(933,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(554,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(296,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/sandbox/benchmark/theBenchmark.p',fact_73_subset__iff) ).
thf(1182,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)],[296]) ).
thf(126,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( member @ TA @ B @ A )
=> ( ( lattic929149872er_Max @ TA @ A )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_Max__eqI) ).
thf(637,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( member @ TA @ B @ A )
=> ( ( lattic929149872er_Max @ TA @ A )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(248,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_infinite__super) ).
thf(1016,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_125_order__subst2) ).
thf(1039,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)],[256]) ).
thf(149,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Int__greatest) ).
thf(706,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(253,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_strict__trans) ).
thf(1028,plain,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',fact_75_Collect__mono) ).
thf(1082,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)],[268]) ).
thf(122,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_Inf__fin_OboundedI) ).
thf(622,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(275,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite__has__maximal2) ).
thf(1114,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(241,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_ex__in__conv) ).
thf(997,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Un__infinite) ).
thf(701,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_internal__case__prod__conv) ).
thf(515,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(131,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Int__subset__iff) ).
thf(654,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(300,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ~ ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) )
= ( ~ ( finite_finite2 @ TA @ A )
| ~ ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_infinite__Un) ).
thf(1192,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ~ ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) )
= ( ~ ( finite_finite2 @ TA @ A )
| ~ ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(101,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(569,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)],[101]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id_on @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Id__onI) ).
thf(371,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id_on @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(116,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_3) ).
thf(605,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(18,axiom,
! [TA: $tType] :
( ( prefer199794634erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) )
& ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) )
& ( order_preorder_on @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_preference__def) ).
thf(343,plain,
! [TA: $tType] :
( ( prefer199794634erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) )
& ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) )
& ( order_preorder_on @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(79,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_finite__code) ).
thf(508,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_27) ).
thf(541,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)],[90]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',fact_69_equalityE) ).
thf(657,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)],[132]) ).
thf(261,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ( lattic929674654er_Min @ TA @ A )
= B )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_Min__eq__iff) ).
thf(1054,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ( lattic929674654er_Min @ TA @ A )
= B )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(291,axiom,
prefer199794634erence @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_preference__axioms) ).
thf(1170,plain,
prefer199794634erence @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',fact_70_subset__eq) ).
thf(1187,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)],[298]) ).
thf(252,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_8) ).
thf(1026,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(530,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(297,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_linear) ).
thf(1185,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)],[297]) ).
thf(269,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_1) ).
thf(1086,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(224,axiom,
! [A: a,B: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier ) )
=> ( ( ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_strict__not__refl__weak) ).
thf(938,plain,
! [A: a,B: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier ) )
=> ( ( ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(153,axiom,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_preorder__on__empty) ).
thf(718,plain,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_116_le__cases3) ).
thf(888,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)],[213]) ).
thf(280,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/sandbox/benchmark/theBenchmark.p',fact_115_antisym__conv) ).
thf(1135,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)],[280]) ).
thf(166,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_rational__preference_Ono__better__thansubset__rel) ).
thf(750,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(121,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_equalityD2) ).
thf(618,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)],[121]) ).
thf(52,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( total_on @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_rational__preference__axioms_Ointro) ).
thf(430,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( total_on @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(191,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( lattic929149872er_Max @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_Max_OcoboundedI) ).
thf(824,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( lattic929149872er_Max @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_prod_Oinject) ).
thf(375,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(287,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ( lattic929149872er_Max @ TA @ A )
= B )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Max__eq__iff) ).
thf(1154,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ( lattic929149872er_Max @ TA @ A )
= B )
= ( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(144,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_7) ).
thf(694,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_68_subsetD) ).
thf(732,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)],[159]) ).
thf(199,axiom,
finite_finite2 @ a @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(843,plain,
finite_finite2 @ a @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(173,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Min_OcoboundedI) ).
thf(772,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(231,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Un__empty) ).
thf(958,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(413,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(210,axiom,
trans @ a @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_transitivity) ).
thf(875,plain,
trans @ a @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(192,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_pref__in__at__least__as) ).
thf(826,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ A @ ( prefer310429814s_good @ a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(151,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_indiff__trans) ).
thf(711,plain,
! [A: a,B: a,C: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation ) )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( ( inf @ TA )
& ( inf @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( inf_inf @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( product_Pair @ TB @ TA @ ( inf_inf @ TB @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_inf__Pair__Pair) ).
thf(391,plain,
! [TA: $tType,TB: $tType] :
( ( ( inf @ TA )
& ( inf @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( inf_inf @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( product_Pair @ TB @ TA @ ( inf_inf @ TB @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(102,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( prefer310429814s_good @ TA @ C @ A @ B )
= ( prefer310429814s_good @ TA @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rational__preference_Osame__at__least__as__equal) ).
thf(572,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( prefer310429814s_good @ TA @ C @ A @ B )
= ( prefer310429814s_good @ TA @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(6,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_refl__onD) ).
thf(313,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(184,axiom,
! [A: a] :
( ( member @ a @ A @ carrier )
=> ! [B: a] :
( ( member @ a @ B @ carrier )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_compl) ).
thf(804,plain,
! [A: a] :
( ( member @ a @ A @ carrier )
=> ! [B: a] :
( ( member @ a @ B @ carrier )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(227,axiom,
! [TA: $tType] : ( inf @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oinf_11) ).
thf(947,plain,
! [TA: $tType] : ( inf @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(89,axiom,
semilattice_sup @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_12) ).
thf(540,plain,
semilattice_sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(58,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_preference_Onot__outside) ).
thf(445,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(223,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_order__refl) ).
thf(936,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(194,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ B ) @ ( lattic929674654er_Min @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_Min__antimono) ).
thf(831,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ B ) @ ( lattic929674654er_Min @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(177,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__has__minimal2) ).
thf(784,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(245,axiom,
! [A: a,B: a] :
( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) )
| ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nbt__nest) ).
thf(1011,plain,
! [A: a,B: a] :
( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) )
| ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(9,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_rational__preference_Opref__in__at__least__as) ).
thf(318,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ ( prefer310429814s_good @ TA @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) )
| ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) )
| ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(303,plain,
~ ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ x @ carrier @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(259,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ ( lattic929149872er_Max @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Max_Osubset__imp) ).
thf(1048,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ ( lattic929149872er_Max @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(161,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( ( finite_finite2 @ TA @ A )
& ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__Un) ).
thf(736,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( ( finite_finite2 @ TA @ A )
& ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(257,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_bot_Oextremum__uniqueI) ).
thf(1043,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(54,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( sup_sup @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_sup__Inf__absorb) ).
thf(434,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( sup_sup @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_transI) ).
thf(477,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(75,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_total__onI) ).
thf(494,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(169,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_no__better__subset__pref) ).
thf(758,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(95,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_transE) ).
thf(552,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(87,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(535,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(182,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( lattic477160up_fin @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ TA @ ( lattic477160up_fin @ TA @ A ) @ ( lattic477160up_fin @ TA @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Sup__fin_Ounion) ).
thf(799,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( lattic477160up_fin @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ TA @ ( lattic477160up_fin @ TA @ A ) @ ( lattic477160up_fin @ TA @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( ord_less_eq @ TB @ A @ C )
& ( ord_less_eq @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Pair__le) ).
thf(915,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( ord_less_eq @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( ord_less_eq @ TB @ A @ C )
& ( ord_less_eq @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(134,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_empty__Collect__eq) ).
thf(668,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(238,axiom,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) )
| ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_strict__is__neg__transitive) ).
thf(983,plain,
! [A: a,B: a,C: a] :
( ( ( member @ a @ A @ carrier )
& ( member @ a @ B @ carrier )
& ( member @ a @ C @ carrier ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ C ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ A ) @ relation ) )
| ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ C @ B ) @ relation )
& ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ C ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( inf @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oinf) ).
thf(399,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( inf @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_infinite__imp__nonempty) ).
thf(780,plain,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(61,axiom,
! [TA: $tType] :
( ( prefer1997167224erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
& ( prefer1801827867axioms @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_rational__preference__def) ).
thf(455,plain,
! [TA: $tType] :
( ( prefer1997167224erence @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
& ( prefer1801827867axioms @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(247,axiom,
order_preorder_on @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_trans__refl) ).
thf(1015,plain,
order_preorder_on @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TB )
& ( bot @ TA ) )
=> ( bot @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Obot_31) ).
thf(394,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TB )
& ( bot @ TA ) )
=> ( bot @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(99,axiom,
! [TA: $tType] :
( ( trans @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_trans__def) ).
thf(563,plain,
! [TA: $tType] :
( ( trans @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',fact_105_dual__order_Oantisym) ).
thf(1000,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)],[242]) ).
thf(220,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ? [D: TA] :
( ( member @ TA @ D @ A )
& ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ( lattic929149872er_Max @ TA @ A )
= ( lattic929149872er_Max @ TA @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Max__eq__if) ).
thf(922,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ? [D: TA] :
( ( member @ TA @ D @ A )
& ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ( lattic929149872er_Max @ TA @ A )
= ( lattic929149872er_Max @ TA @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(140,axiom,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Id__on__empty) ).
thf(685,plain,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(292,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_bot__set__def) ).
thf(1171,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(294,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( inf_inf @ TA @ ( lattic2065218050nf_fin @ TA @ B ) @ ( lattic2065218050nf_fin @ TA @ A ) )
= ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Inf__fin_Osubset) ).
thf(1176,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( B
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( inf_inf @ TA @ ( lattic2065218050nf_fin @ TA @ B ) @ ( lattic2065218050nf_fin @ TA @ A ) )
= ( lattic2065218050nf_fin @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(118,axiom,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_refl__on__empty) ).
thf(608,plain,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(67,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_15) ).
thf(473,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(155,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_finite__UnI) ).
thf(722,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ ( sup_sup @ ( set @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(136,axiom,
! [TA: $tType] : ( sup @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osup_10) ).
thf(675,plain,
! [TA: $tType] : ( sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_prod__induct6) ).
thf(426,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(589,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(226,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic929674654er_Min @ TA @ A ) )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Min_OboundedE) ).
thf(944,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic929674654er_Min @ TA @ A ) )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Int__lower2) ).
thf(680,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osup) ).
thf(548,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(129,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) )
= ( ord_less_eq @ ( set @ TA ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Un__Int__assoc__eq) ).
thf(648,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) )
= ( ord_less_eq @ ( set @ TA ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(187,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ ( lattic477160up_fin @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_Sup__fin_Osubset__imp) ).
thf(812,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ ( lattic477160up_fin @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(62,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( refl_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_preference_Oreflexivity) ).
thf(458,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( refl_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(196,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Sup__fin_OboundedE) ).
thf(836,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(284,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ ( lattic929149872er_Max @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Max__mono) ).
thf(1145,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( finite_finite2 @ TA @ B )
=> ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ ( lattic929149872er_Max @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(249,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_no__better__thansubset__rel) ).
thf(1018,plain,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( ord_less_eq @ ( set @ a ) @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) @ ( prefer1532642881r_than @ a @ A @ carrier @ relation ) )
=> ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(175,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( finite_finite2 @ TA @ A )
| ( finite_finite2 @ TA @ B ) )
=> ( finite_finite2 @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_finite__Int) ).
thf(776,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( finite_finite2 @ TA @ A )
| ( finite_finite2 @ TA @ B ) )
=> ( finite_finite2 @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(203,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_Sup__fin_OboundedI) ).
thf(855,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ ( lattic477160up_fin @ TA @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(142,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_total__on__empty) ).
thf(690,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',fact_126_order__subst1) ).
thf(1070,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)],[265]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( ( semilattice_sup @ TB )
& ( semilattice_sup @ TA ) )
=> ( semilattice_sup @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Osemilattice__sup_23) ).
thf(327,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)],[12]) ).
thf(162,axiom,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ B @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_worse__in__no__better) ).
thf(739,plain,
! [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
=> ( member @ a @ B @ ( prefer1532642881r_than @ a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( ( semilattice_inf @ TB )
& ( semilattice_inf @ TA ) )
=> ( semilattice_inf @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Osemilattice__inf_24) ).
thf(409,plain,
! [TA: $tType,TB: $tType] :
( ( ( semilattice_inf @ TB )
& ( semilattice_inf @ TA ) )
=> ( semilattice_inf @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_prod__induct7) ).
thf(557,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(243,axiom,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_finite_OemptyI) ).
thf(1003,plain,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(585,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(76,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer199794634erence @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rational__preference_Oaxioms_I1_J) ).
thf(502,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer199794634erence @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_old_Oprod_Orec) ).
thf(470,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(127,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Inf__fin_OcoboundedI) ).
thf(643,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( lattic2065218050nf_fin @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(215,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Set_Ois__empty__def) ).
thf(907,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(164,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_bot__empty__eq) ).
thf(744,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(148,axiom,
! [A: a,B: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( prefer310429814s_good @ a @ A @ carrier @ relation )
= ( prefer310429814s_good @ a @ B @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_same__at__least__as__equal) ).
thf(703,plain,
! [A: a,B: a] :
( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) )
=> ( ( prefer310429814s_good @ a @ A @ carrier @ relation )
= ( prefer310429814s_good @ a @ B @ carrier @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(282,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_6) ).
thf(1141,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(114,axiom,
! [TA: $tType] :
( ( prefer1801827867axioms @ TA )
= ( total_on @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_rational__preference__axioms__def) ).
thf(600,plain,
! [TA: $tType] :
( ( prefer1801827867axioms @ TA )
= ( total_on @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(205,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_2) ).
thf(864,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(157,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_le__cases) ).
thf(727,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)],[157]) ).
thf(211,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Max_OboundedE) ).
thf(876,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic929149872er_Max @ TA @ A ) @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(236,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_4) ).
thf(978,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType] :
( ( ( preorder @ TB )
& ( preorder @ TA ) )
=> ( preorder @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Orderings_Opreorder_26) ).
thf(386,plain,
! [TA: $tType,TB: $tType] :
( ( ( preorder @ TB )
& ( preorder @ TA ) )
=> ( preorder @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_equals0D) ).
thf(845,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(221,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) )
| ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_rational__preference_Onbt__nest) ).
thf(931,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) )
| ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_at__lst__asgd__ge) ).
thf(482,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ TA @ A @ ( prefer310429814s_good @ TA @ B @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_112_ord__le__eq__trans) ).
thf(671,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)],[135]) ).
thf(288,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Collect__empty__eq__bot) ).
thf(1157,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(83,axiom,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_total__on__def) ).
thf(524,plain,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(200,axiom,
prefer1997167224erence @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_rational__preference__axioms) ).
thf(844,plain,
prefer1997167224erence @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(172,axiom,
refl_on @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_reflexivity) ).
thf(771,plain,
refl_on @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_129_le__funE) ).
thf(688,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)],[141]) ).
thf(214,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_eq__refl) ).
thf(903,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_108_linorder__wlog) ).
thf(961,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)],[232]) ).
thf(3,axiom,
semilattice_inf @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_13) ).
thf(304,plain,
semilattice_inf @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( ( lattice @ TB )
& ( lattice @ TA ) )
=> ( lattice @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Olattice_28) ).
thf(351,plain,
! [TA: $tType,TB: $tType] :
( ( ( lattice @ TB )
& ( lattice @ TA ) )
=> ( lattice @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(124,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( refl_on @ TA @ C @ D )
=> ( refl_on @ TA @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_refl__on__Int) ).
thf(632,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( refl_on @ TA @ C @ D )
=> ( refl_on @ TA @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(42,axiom,
! [TA: $tType] :
( ( order_preorder_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( trans @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_preorder__on__def) ).
thf(401,plain,
! [TA: $tType] :
( ( order_preorder_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( trans @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(240,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_emptyE) ).
thf(995,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(31,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_20) ).
thf(378,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(267,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Int__Collect__mono) ).
thf(1077,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_old_Oprod_Oexhaust) ).
thf(383,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rational__preference_OcompleteD) ).
thf(346,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_refl__on__domain) ).
thf(536,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_117_order_Otrans) ).
thf(716,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)],[152]) ).
thf(279,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_Min__le) ).
thf(1133,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(167,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( A != B )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_completeD) ).
thf(752,plain,
! [A: a,B: a] :
( ( member @ a @ A @ carrier )
=> ( ( member @ a @ B @ carrier )
=> ( ( A != B )
=> ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
| ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(59,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_rational__preference_Oaxioms_I2_J) ).
thf(447,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( prefer1801827867axioms @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(7,axiom,
sup @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osup_21) ).
thf(315,plain,
sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rational__preference_Ocompl) ).
thf(432,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(233,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_bot_Oextremum) ).
thf(967,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(189,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( order_under @ TA @ A @ B ) @ ( order_under @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_under__incr) ).
thf(818,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( order_under @ TA @ A @ B ) @ ( order_under @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_old_Oprod_Oinducts) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(285,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_less__by__empty) ).
thf(1148,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_prod__cases) ).
thf(422,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(178,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ A ) @ B )
= ( ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Min__le__iff) ).
thf(790,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ ( lattic929674654er_Min @ TA @ A ) @ B )
= ( ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(29,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_transD) ).
thf(373,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_subset__refl) ).
thf(603,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(4,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_rational__preference_Ostrict__trans) ).
thf(305,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA,E: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) )
=> ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ E ) @ B )
& ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_subrelI) ).
thf(918,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(506,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(55,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( prefer1801827867axioms @ TA @ A @ B )
=> ( prefer1997167224erence @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_rational__preference_Ointro) ).
thf(437,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( ( prefer1801827867axioms @ TA @ A @ B )
=> ( prefer1997167224erence @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_old_Oprod_Oinject) ).
thf(474,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(193,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic929149872er_Max @ TA @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Max__in) ).
thf(828,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic929149872er_Max @ TA @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(145,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rational__preference_Ono__better__subset__pref) ).
thf(696,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( prefer1532642881r_than @ TA @ D @ A @ B ) @ ( prefer1532642881r_than @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(154,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( refl_on @ TA @ C @ D )
=> ( refl_on @ TA @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_refl__on__Un) ).
thf(720,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( refl_on @ TA @ C @ D )
=> ( refl_on @ TA @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(230,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( prefer951318096ood_as @ a @ B @ carrier @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_as__good__asIff) ).
thf(955,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( prefer951318096ood_as @ a @ B @ carrier @ relation ) )
= ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B ) @ relation )
& ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ B @ A ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(180,axiom,
member @ a @ y @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(796,plain,
member @ a @ y @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(48,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( order_preorder_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_preference_Otrans__refl) ).
thf(415,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( order_preorder_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(254,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic929149872er_Max @ TA @ A ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_Max__ge__iff) ).
thf(1033,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ TA @ B @ ( lattic929149872er_Max @ TA @ A ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',fact_123_ord__le__eq__subst) ).
thf(1197,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)],[302]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TA )
& ( sup @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( sup_sup @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( product_Pair @ TB @ TA @ ( sup_sup @ TB @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_sup__Pair__Pair) ).
thf(532,plain,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TA )
& ( sup @ TB ) )
=> ! [A: TB,B: TA,C: TB,D: TA] :
( ( sup_sup @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) )
= ( product_Pair @ TB @ TA @ ( sup_sup @ TB @ A @ C ) @ ( sup_sup @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',fact_128_le__funI) ).
thf(1065,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)],[263]) ).
thf(197,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_subset__empty) ).
thf(839,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_prod__cases3) ).
thf(464,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( bot_bot @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( bot_bot @ TB ) @ ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_bot__prod__def) ).
thf(575,plain,
! [TA: $tType,TB: $tType] :
( ( ( bot @ TA )
& ( bot @ TB ) )
=> ( ( bot_bot @ ( product_prod @ TB @ TA ) )
= ( product_Pair @ TB @ TA @ ( bot_bot @ TB ) @ ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(286,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_5) ).
thf(1152,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(111,axiom,
order_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_14) ).
thf(596,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_prod__cases5) ).
thf(442,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(208,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rev__finite__subset) ).
thf(871,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',fact_106_dual__order_Oeq__iff) ).
thf(1120,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)],[276]) ).
thf(14,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( trans @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_preference_Otransitivity) ).
thf(332,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( prefer199794634erence @ TA @ A @ B )
=> ( trans @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',fact_113_ord__eq__le__trans) ).
thf(1129,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)],[278]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TB )
& ( sup @ TA ) )
=> ( sup @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Lattices_Osup_32) ).
thf(369,plain,
! [TA: $tType,TB: $tType] :
( ( ( sup @ TB )
& ( sup @ TA ) )
=> ( sup @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(117,axiom,
total_on @ a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_total) ).
thf(607,plain,
total_on @ a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_prod__cases7) ).
thf(337,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_prod__induct5) ).
thf(309,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(91,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( prefer951318096ood_as @ TA @ D @ A @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_rational__preference_Oas__good__asIff) ).
thf(543,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( prefer1997167224erence @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( prefer951318096ood_as @ TA @ D @ A @ B ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(25,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_refl__onD2) ).
thf(364,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic1704895705min_on @ TA @ TB @ B @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_arg__min__if__finite_I1_J) ).
thf(708,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( member @ TA @ ( lattic1704895705min_on @ TA @ TB @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(235,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( member @ TA @ B @ A )
=> ( ( lattic929674654er_Min @ TA @ A )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_Min__eqI) ).
thf(972,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( member @ TA @ B @ A )
=> ( ( lattic929674654er_Min @ TA @ A )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(73,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_18) ).
thf(491,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(270,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Collect__empty__eq) ).
thf(1088,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1206,plain,
$false,
inference(e,[status(thm)],[645,1036,809,1024,1190,628,518,941,1179,1168,760,1005,741,379,511,597,861,582,762,873,449,614,677,550,797,698,340,747,913,404,417,1046,320,651,389,724,504,587,802,357,949,460,969,1013,325,316,492,756,591,1109,806,353,1051,485,834,634,692,734,866,774,396,411,849,527,1074,439,381,366,1067,1057,546,793,334,910,1091,1021,952,1174,598,820,561,815,729,1123,349,467,361,879,329,665,842,1106,566,484,682,1195,578,1143,1111,980,388,1138,593,869,610,989,1160,933,554,1182,637,1016,1039,706,1028,1082,622,1114,997,701,515,654,1192,569,371,605,343,508,541,657,1054,1170,1187,1026,530,1185,1086,938,718,888,1135,750,618,430,824,375,1154,694,732,843,772,958,413,875,826,711,391,572,313,804,947,540,445,936,831,784,1011,318,303,1048,736,1043,434,477,494,758,552,535,799,915,668,983,399,780,455,1015,394,563,1000,922,685,1171,1176,608,473,722,675,426,589,944,680,548,648,812,458,836,1145,1018,776,855,690,1070,327,739,409,557,1003,585,502,470,643,907,744,703,1141,600,864,727,876,978,386,845,931,482,671,1157,524,844,771,688,903,961,304,351,632,401,995,378,1077,383,346,536,716,1133,752,447,315,432,967,818,405,1148,422,790,373,603,305,918,506,437,474,828,696,720,955,796,415,1033,1197,532,1065,839,464,575,1152,596,442,871,1120,332,1129,369,607,337,309,543,364,708,972,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP154^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.13 % Computer : n012.cluster.edu
% 0.08/0.13 % Model : x86_64 x86_64
% 0.08/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.13 % Memory : 8046.5625MB
% 0.08/0.13 % OS : Linux 6.8.0-71-generic
% 0.08/0.13 % CPULimit : 300
% 0.08/0.13 % WCLimit : 300
% 0.08/0.13 % DateTime : Tue Sep 29 20:02:18 UTC 2026
% 0.08/0.13 % CPUTime :
% 0.08/0.13 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.55/0.43 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/0.66 % [INFO] Parsing done (222ms).
% 1.15/0.66 % [INFO] Running in sequential loop mode.
% 1.90/0.87 % [INFO] eprover registered as external prover.
% 1.90/0.88 % [INFO] Scanning for conjecture ...
% 2.10/0.97 % [INFO] Found a conjecture (or negated_conjecture) and 301 axioms. Running axiom selection ...
% 2.42/1.05 % [INFO] Axiom selection finished. Selected 300 axioms (removed 1 axioms).
% 3.05/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 3.05/1.26 % [INFO] Type checking passed.
% 3.05/1.26 % [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 ...
% 65.99/51.96 % External prover 'e' found a proof!
% 65.99/51.96 % [INFO] Killing All external provers ...
% 65.99/51.96 % Time passed: 51751ms (effective reasoning time: 51292ms)
% 65.99/51.96 % 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)>
% 65.99/51.96 % Axioms used in derivation (300): fact_123_ord__le__eq__subst, fact_229_Un__empty, fact_244_refl__on__Int, tcon_fun___Orderings_Obot, fact_253_Int__absorb2, fact_252_Int__absorb1, fact_216_Min_Osubset__imp, tcon_Set_Oset___Orderings_Oorder_7, fact_30_rational__preference_OcompleteD, fact_100_total__on__def, fact_55_Collect__empty__eq, fact_4_assms_I1_J, fact_248_Un__Int__assoc__eq, fact_138_prod__cases6, tcon_fun___Lattices_Oinf, fact_132_surj__pair, tcon_Set_Oset___Lattices_Osemilattice__sup_1, tcon_Set_Oset___Lattices_Osemilattice__inf_2, fact_199_Sup__fin_OboundedI, fact_115_antisym__conv, fact_87_finite__has__maximal2, tcon_Product__Type_Oprod___Orderings_Obot_31, tcon_HOL_Obool___Orderings_Opreorder_15, tcon_fun___Finite__Set_Ofinite, fact_142_prod__induct5, fact_75_Collect__mono, fact_162_rational__preference__axioms_Ointro, tcon_Product__Type_Oprod___Lattices_Osup_32, fact_15_not__outside, fact_29_rational__preference_Ototal, fact_221_Min_OcoboundedI, fact_219_Min__le, fact_236_inf__Sup__absorb, fact_52_finite__has__maximal, fact_113_ord__eq__le__trans, fact_171_preference_Otransitivity, fact_84_rational__preference_Oas__good__asIff, fact_98_order__refl, fact_39_rational__preference_Onbt__nest, fact_202_Max_Osubset__imp, fact_189_GreatestI2__order, fact_102_total__on__empty, fact_184_Id__on__eqI, fact_200_Inf__fin_Obounded__iff, fact_218_Min__in, fact_230_Int__subset__iff, fact_125_order__subst2, fact_81_rational__preference_Osame__at__least__as__equal, fact_37_rational__preference_Ono__better__thansubset__rel, fact_76_subset__trans, fact_133_prod__cases, fact_63_ex__in__conv, tcon_HOL_Obool___Orderings_Oord_19, fact_65_equals0D, fact_217_Min_Obounded__iff, tcon_fun___Orderings_Oord, fact_203_Max__mono, fact_41_same__at__least__as__equal, fact_14_completeD, fact_250_Int__lower1, fact_90_infinite__imp__nonempty, fact_0_assms_I3_J, fact_164_rational__preference_Oaxioms_I2_J, fact_80_finite__set__choice, fact_93_infinite__super, fact_92_finite__subset, fact_196_Inf__fin_OboundedE, fact_155_refl__on__domain, fact_140_prod__induct3, tcon_Product__Type_Oprod___Finite__Set_Ofinite_27, fact_38_rational__preference_Ono__better__subset__pref, tcon_HOL_Obool___Orderings_Olinorder, tcon_HOL_Obool___Orderings_Oorder_18, fact_86_Pair__mono, tcon_HOL_Obool___Lattices_Osup_21, fact_91_finite_OemptyI, fact_220_Min__eqI, fact_111_order__class_Oorder_Oantisym, fact_165_Collect__empty__eq__bot, fact_108_linorder__wlog, fact_126_order__subst1, fact_210_Max__eq__iff, fact_205_Max_OcoboundedI, fact_17_weak__is__transitive, fact_191_Inf__fin_Osubset__imp, fact_10_total, fact_178_relChain__def, fact_201_Sup__fin_Obounded__iff, tcon_Product__Type_Oprod___Lattices_Oinf_33, fact_11_worse__in__no__better, fact_134_Pair__inject, fact_240_Sup__fin_Ounion, fact_242_trans__Int, fact_163_rational__preference__axioms__def, fact_22_preference__def, fact_24_preference_Otrans__refl, fact_143_prod__induct6, fact_46_Collect__mem__eq, tcon_Product__Type_Oprod___Orderings_Oord_30, tcon_Product__Type_Oprod___Lattices_Olattice_28, fact_212_eq__Max__iff, fact_179_Id__on__empty, fact_224_eq__Min__iff, tcon_Product__Type_Oprod___Orderings_Opreorder_26, fact_241_Inf__fin_Ounion, fact_2_rational__preference__axioms, fact_31_rational__preference_Ostrict__trans, fact_21_rational__preference_Oaxioms_I1_J, fact_27_preference_Oindiff__trans, fact_185_Id__onE, fact_187_arg__min__least, fact_109_dual__order_Orefl, fact_16_strict__is__neg__transitive, fact_73_subset__iff, fact_71_equalityD1, fact_44_subset__empty, fact_34_rational__preference_Ostrict__is__neg__transitive, tcon_fun___Lattices_Osemilattice__sup, tcon_HOL_Obool___Lattices_Osemilattice__sup_12, fact_206_Max__eq__if, fact_127_le__fun__def, fact_223_Min_OboundedE, fact_110_order__trans, fact_190_arg__min__if__finite_I1_J, fact_175_transI, fact_60_finite__code, fact_246_Un__infinite, fact_129_le__funE, fact_145_old_Oprod_Oexhaust, fact_114_order__class_Oorder_Oeq__iff, tcon_HOL_Obool___Orderings_Oorder__bot_14, fact_69_equalityE, fact_234_inf__Pair__Pair, fact_58_subsetI, fact_173_transD, fact_176_trans__def, fact_77_set__eq__subset, fact_239_Inf__fin_Oin__idem, fact_9_no__better__than__nonepty, tcon_fun___Lattices_Osemilattice__inf, fact_89_bot__prod__def, fact_79_finite, fact_20_strict__not__refl__weak, fact_182_trans__Id__on, fact_215_Min__antimono, fact_62_at__lst__asgd__ge, fact_117_order_Otrans, fact_8_no__better__thansubset__rel, fact_42_pref__in__at__least__as, fact_131_bot__fun__def, fact_3_nbt__nest, fact_45_mem__Collect__eq, fact_105_dual__order_Oantisym, tcon_Set_Oset___Lattices_Oinf_11, fact_169_Set_Ois__empty__def, fact_96_prod_Oinject, fact_49_Pair__le, fact_238_Sup__fin_Oin__idem, fact_74_subset__refl, fact_25_preference_Onot__outside, fact_214_Max_OboundedI, fact_231_Un__subset__iff, fact_152_refl__onD, fact_1_assms_I2_J, fact_186_refl__on__Id__on, fact_139_prod__cases7, tcon_HOL_Obool___Finite__Set_Ofinite_16, fact_204_Max_Obounded__iff, fact_12_reflexivity, fact_194_Sup__fin_OcoboundedI, fact_137_prod__cases5, fact_121_antisym, fact_237_sup__Inf__absorb, fact_158_rational__preference_Ointro, tcon_Product__Type_Oprod___Orderings_Oorder__bot_25, fact_23_preference_Ointro, fact_188_Greatest__equality, fact_227_Inf__fin_Osubset, fact_167_finite__indexed__bound, tcon_HOL_Obool___Lattices_Oinf_22, fact_222_Min_OboundedI, fact_118_le__cases, fact_54_empty__Collect__eq, fact_26_preference_Oreflexivity, fact_249_Int__mono, fact_198_Sup__fin_OboundedE, fact_47_Collect__cong, fact_156_old_Oprod_Orec, fact_180_under__incr, fact_150_bot_Oextremum, fact_28_rational__preference_Ocompl, fact_78_Collect__mono__iff, fact_64_equals0I, tcon_fun___Orderings_Oorder__bot, fact_235_sup__Pair__Pair, fact_209_Max__in, tcon_Set_Oset___Orderings_Opreorder_4, tcon_Set_Oset___Orderings_Oord_8, fact_141_prod__induct4, fact_208_Max__ge, fact_157_rational__preference__def, fact_207_Max__eqI, fact_149_bot_Oextremum__unique, fact_243_refl__on__Un, fact_88_finite__has__minimal2, fact_120_linear, fact_144_prod__induct7, fact_170_internal__case__prod__conv, fact_94_rev__finite__subset, fact_56_all__not__in__conv, fact_146_old_Oprod_Oinducts, fact_174_transE, fact_211_Max__ge__iff, fact_183_Id__on__iff, fact_136_prod__cases4, fact_19_indiff__trans, tcon_Set_Oset___Finite__Set_Ofinite_5, fact_119_eq__refl, fact_251_Int__lower2, fact_57_empty__iff, fact_122_eq__iff, fact_13_compl, fact_112_ord__le__eq__trans, fact_51_as__good__asIff, fact_35_rational__preference_Oworse__in__no__better, fact_130_le__funD, fact_33_rational__preference_Ostrict__not__refl__weak, fact_97_bot__apply, tcon_fun___Orderings_Opreorder, tcon_HOL_Obool___Orderings_Obot_20, fact_5_preference__axioms, fact_99_preorder__on__empty, fact_40_at__lst__asgd__not__ge, fact_160_subset__emptyI, fact_70_subset__eq, fact_197_Inf__fin_OboundedI, fact_59_subset__antisym, fact_225_Min__le__iff, fact_36_rational__preference_Ono__better__than__nonepty, fact_107_dual__order_Otrans, fact_18_strict__trans, fact_148_bot_Oextremum__uniqueI, tcon_HOL_Obool___Lattices_Osemilattice__inf_13, fact_159_finite__transitivity__chain, fact_43_empty__subsetI, fact_7_no__better__subset__pref, fact_66_emptyE, tcon_Set_Oset___Lattices_Osup_10, fact_166_less__by__empty, fact_233_finite__Un, fact_154_refl__onD2, fact_32_rational__preference_Oweak__is__transitive, fact_151_refl__on__empty, tcon_fun___Orderings_Oorder, fact_104_bot__set__def, fact_85_rational__preference_Oat__lst__asgd__not__ge, fact_95_old_Oprod_Oinject, fact_247_infinite__Un, fact_195_Inf__fin_OcoboundedI, fact_101_total__onI, fact_153_refl__onD1, fact_192_Sup__fin_Osubset__imp, tcon_Product__Type_Oprod___Lattices_Osemilattice__sup_23, fact_135_prod__cases3, fact_181_Id__onI, fact_226_Min__eq__iff, fact_128_le__funI, fact_124_ord__eq__le__subst, tcon_Product__Type_Oprod___Orderings_Oorder_29, fact_67_in__mono, fact_50_as__good__as__sameIff, fact_83_rational__preference_Oas__good__as__sameIff, fact_245_finite__UnI, fact_193_Inf__fin__le__Sup__fin, fact_177_preorder__on__def, fact_147_subrelI, fact_6_trans__refl, fact_106_dual__order_Oeq__iff, fact_228_Sup__fin_Osubset, fact_72_equalityD2, fact_168_transitivity, fact_82_rational__preference_Opref__in__at__least__as, fact_172_trans__empty, fact_61_at__least__as__goodD, fact_213_Max_OboundedE, fact_103_bot__empty__eq, fact_53_finite__has__minimal, fact_232_finite__Int, fact_161_ssubst__Pair__rhs, fact_255_Int__Collect__mono, fact_254_Int__greatest, tcon_Product__Type_Oprod___Lattices_Osemilattice__inf_24, fact_116_le__cases3, tcon_Set_Oset___Orderings_Obot_9, tcon_HOL_Obool___Lattices_Olattice_17, tcon_Set_Oset___Orderings_Oorder__bot_3, fact_68_subsetD, tcon_Set_Oset___Lattices_Olattice_6, tcon_fun___Lattices_Olattice, tcon_fun___Lattices_Osup
% 65.99/51.96 % No. of inferences in proof: 604
% 65.99/51.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 51751 ms resp. 51292 ms w/o parsing
% 66.92/52.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.92/52.14 % [INFO] Killing All external provers ...
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