%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP162^2 : 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 : n004.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 08:07:00 AM UTC 2026
% Result : Theorem 53.36s 31.36s
% Output : Refutation 54.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 311
% Syntax : Number of formulae : 624 ( 189 unt; 0 typ; 0 def)
% Number of atoms : 2043 ( 440 equ; 14 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 7053 ( 94 ~; 5 |; 67 &;6108 @)
% ( 0 <=>; 779 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 306 ( 306 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 6 con; 0-5 aty)
% Number of variables : 2019 ( 167 ^;1848 !; 4 ?;2019 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(a_type,type,
a: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(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(bounded_lattice_bot_decl,type,
bounded_lattice_bot:
!>[TA: $tType] : $o ).
thf(bounde1561333602nf_top_decl,type,
bounde1561333602nf_top:
!>[TA: $tType] : $o ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > 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(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(refine1687780735RETURN_decl,type,
refine1687780735RETURN:
!>[TA: $tType] : ( TA > ( refine1665802226e_nres @ TA ) ) ).
thf(refine463715084e_bind_decl,type,
refine463715084e_bind:
!>[TA: $tType,TB: $tType] : ( ( refine1665802226e_nres @ TB ) > ( TB > ( refine1665802226e_nres @ TA ) ) > ( refine1665802226e_nres @ TA ) ) ).
thf(refine1315500908_inres_decl,type,
refine1315500908_inres:
!>[TA: $tType] : ( ( refine1665802226e_nres @ TA ) > TA > $o ) ).
thf(refine406925620_inres_decl,type,
refine406925620_inres:
!>[TA: $tType] : ( ( refine1665802226e_nres @ TA ) > TA > $o ) ).
thf(refine1102455758nofail_decl,type,
refine1102455758nofail:
!>[TA: $tType] : ( ( refine1665802226e_nres @ TA ) > $o ) ).
thf(refine1767639642_FAILi_decl,type,
refine1767639642_FAILi:
!>[TA: $tType] : ( refine1665802226e_nres @ TA ) ).
thf(refine605929679le_RES_decl,type,
refine605929679le_RES:
!>[TA: $tType] : ( ( set @ TA ) > ( refine1665802226e_nres @ TA ) ) ).
thf(refine1442219249c_nres_decl,type,
refine1442219249c_nres:
!>[TA: $tType,TB: $tType] : ( TB > ( ( set @ TA ) > TB ) > ( refine1665802226e_nres @ TA ) > TB ) ).
thf(refine1672542526he_RES_decl,type,
refine1672542526he_RES:
!>[TA: $tType] : ( ( refine1665802226e_nres @ TA ) > ( set @ TA ) ) ).
thf(powp_decl,type,
powp:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_decl,type,
a2: refine1665802226e_nres @ a ).
thf(p_decl,type,
p: a > $o ).
thf(q_decl,type,
q: a > $o ).
thf(246,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_136_Collect__mono) ).
thf(1024,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)],[246]) ).
thf(26,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_inf1D1) ).
thf(365,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_IntD1) ).
thf(479,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(17,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(347,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(300,axiom,
! [TA: $tType,A: set @ TA] : ( refine1102455758nofail @ TA @ ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_nofail__simps_I2_J) ).
thf(1237,plain,
! [TA: $tType,A: set @ TA] : ( refine1102455758nofail @ TA @ ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(93,axiom,
linorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_30) ).
thf(518,plain,
linorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(258,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_107_Int__subset__iff) ).
thf(1083,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)],[258]) ).
thf(219,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_inf_OboundedI) ).
thf(941,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(177,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_51_antisym) ).
thf(777,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)],[177]) ).
thf(267,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_inf__set__def) ).
thf(1110,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(12,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Int__left__commute) ).
thf(333,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(248,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_146_equalityE) ).
thf(1031,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)],[248]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__bot) ).
thf(481,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(19,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_inf__bot__right) ).
thf(352,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(255,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_147_Int__mono) ).
thf(1073,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)],[255]) ).
thf(32,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_10) ).
thf(379,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( ^ [A: TA,B: TA > ( refine1665802226e_nres @ TB )] : ( B @ A ) )
= ( ^ [A: TA] : ( refine463715084e_bind @ TA @ TB @ ( refine1687780735RETURN @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_let__to__bind__conv) ).
thf(408,plain,
! [TA: $tType,TB: $tType] :
( ( ^ [A: TA,B: TA > ( refine1665802226e_nres @ TB )] : ( B @ A ) )
= ( ^ [A: TA] : ( refine463715084e_bind @ TA @ TB @ ( refine1687780735RETURN @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ E ) @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine463715084e_bind @ TA @ TB @ A @ C ) @ ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J) ).
thf(977,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ E ) @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine463715084e_bind @ TA @ TB @ A @ C ) @ ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(58,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_inf__sup__aci_I2_J) ).
thf(440,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(511,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(35,axiom,
semilattice_inf @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Osemilattice__inf_27) ).
thf(385,plain,
semilattice_inf @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(106,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_inf__bot__left) ).
thf(550,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(221,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mem__Collect__eq) ).
thf(945,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(294,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_subset__refl) ).
thf(1222,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(215,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_33_dual__order_Otrans) ).
thf(930,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)],[215]) ).
thf(206,axiom,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ! [D: refine1665802226e_nres @ TA] : ( A @ D @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [D: set @ TA,E: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine605929679le_RES @ TA @ E ) )
=> ( ! [D: set @ TA] : ( A @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ D ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_less__eq__nres_Oinduct) ).
thf(898,plain,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ! [D: refine1665802226e_nres @ TA] : ( A @ D @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [D: set @ TA,E: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine605929679le_RES @ TA @ E ) )
=> ( ! [D: set @ TA] : ( A @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ D ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(275,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_inf__sup__ord_I2_J) ).
thf(1127,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(179,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ A ) )
= ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_inf__nres_Osimps_I2_J) ).
thf(782,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ A ) )
= ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(7,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_boolean__algebra__cancel_Oinf1) ).
thf(320,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(297,axiom,
! [TA: $tType,TB: $tType,A: $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA,D: TA > ( refine1665802226e_nres @ TB )] :
( ( A
=> ( ( refine463715084e_bind @ TA @ TB @ ( if @ ( refine1665802226e_nres @ TA ) @ A @ B @ C ) @ D )
= ( refine463715084e_bind @ TA @ TB @ B @ D ) ) )
& ( ~ A
=> ( ( refine463715084e_bind @ TA @ TB @ ( if @ ( refine1665802226e_nres @ TA ) @ A @ B @ C ) @ D )
= ( refine463715084e_bind @ TA @ TB @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_If__bind__distrib) ).
thf(1228,plain,
! [TA: $tType,TB: $tType,A: $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA,D: TA > ( refine1665802226e_nres @ TB )] :
( ( A
=> ( ( refine463715084e_bind @ TA @ TB @ ( if @ ( refine1665802226e_nres @ TA ) @ A @ B @ C ) @ D )
= ( refine463715084e_bind @ TA @ TB @ B @ D ) ) )
& ( ~ A
=> ( ( refine463715084e_bind @ TA @ TB @ ( if @ ( refine1665802226e_nres @ TA ) @ A @ B @ C ) @ D )
= ( refine463715084e_bind @ TA @ TB @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(306,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: refine1665802226e_nres @ TB,D: TA > ( refine1665802226e_nres @ TB )] :
( ( A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( D @ B ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( refine463715084e_bind @ TA @ TB @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_le__SPEC__bindI) ).
thf(1254,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: refine1665802226e_nres @ TB,D: TA > ( refine1665802226e_nres @ TB )] :
( ( A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( D @ B ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( refine463715084e_bind @ TA @ TB @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(114,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( refine1102455758nofail @ TA @ B )
=> ( refine1102455758nofail @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_pwD1) ).
thf(570,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( refine1102455758nofail @ TA @ B )
=> ( refine1102455758nofail @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(160,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_le__infE) ).
thf(719,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(180,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 )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_subset__CollectI) ).
thf(785,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 )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(29,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_inf__right__idem) ).
thf(372,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TA,B: ( set @ TB ) > TA] :
( ( refine1442219249c_nres @ TA @ TB @ A @ B @ ( refine1767639642_FAILi @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_nres_Osimps_I6_J) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: TA,B: ( set @ TB ) > TA] :
( ( refine1442219249c_nres @ TA @ TB @ A @ B @ ( refine1767639642_FAILi @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(460,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(210,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_48_le__cases) ).
thf(917,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)],[210]) ).
thf(170,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_inf__RETURN__SPEC_I2_J) ).
thf(751,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(21,axiom,
ord @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_34) ).
thf(357,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(285,axiom,
! [TA: $tType,A: set @ TA,B: refine1665802226e_nres @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ C ) @ B ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_lhs__step__RES) ).
thf(1191,plain,
! [TA: $tType,A: set @ TA,B: refine1665802226e_nres @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ C ) @ B ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(110,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_pred__subset__eq) ).
thf(559,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(131,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_inf__sup__ord_I1_J) ).
thf(638,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(200,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Collect__conj__eq) ).
thf(881,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(269,axiom,
! [TA: $tType] : ( bounded_lattice @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice) ).
thf(1115,plain,
! [TA: $tType] : ( bounded_lattice @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(5,axiom,
semilattice_inf @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_17) ).
thf(316,plain,
semilattice_inf @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,axiom,
order @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_32) ).
thf(421,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(196,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_23_order__subst1) ).
thf(870,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)],[196]) ).
thf(213,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_225_bot_Oextremum__unique) ).
thf(924,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)],[213]) ).
thf(81,axiom,
bounded_lattice_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__bot_16) ).
thf(492,plain,
bounded_lattice_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(59,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_inf__assoc) ).
thf(443,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(31,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_inf__sup__aci_I3_J) ).
thf(376,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(134,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_134_subset__trans) ).
thf(646,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)],[134]) ).
thf(282,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_inf__absorb2) ).
thf(1151,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(186,axiom,
! [TA: $tType] : ( order_bot @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_39) ).
thf(806,plain,
! [TA: $tType] : ( order_bot @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(485,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(278,axiom,
! [TA: $tType] : ( refine1102455758nofail @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_nofail__simps_I4_J) ).
thf(1136,plain,
! [TA: $tType] : ( refine1102455758nofail @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: TB > $o,C: TB > ( refine1665802226e_nres @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine605929679le_RES @ TB @ ( collect @ TB @ B ) ) )
=> ( ! [E: TB] :
( ( B @ E )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( C @ E ) @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_specify__left) ).
thf(634,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: TB > $o,C: TB > ( refine1665802226e_nres @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine605929679le_RES @ TB @ ( collect @ TB @ B ) ) )
=> ( ! [E: TB] :
( ( B @ E )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( C @ E ) @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(225,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nres__more__simps_I4_J) ).
thf(956,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(62,axiom,
order_bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__bot_28) ).
thf(453,plain,
order_bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(271,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_relprop__triggers_I6_J) ).
thf(1119,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(45,axiom,
preorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Opreorder_29) ).
thf(411,plain,
preorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(97,axiom,
! [TA: $tType,A: TA] : ( refine1102455758nofail @ TA @ ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_nofail__simps_I3_J) ).
thf(527,plain,
! [TA: $tType,A: TA] : ( refine1102455758nofail @ TA @ ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(121,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_inf_Oabsorb1) ).
thf(602,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(230,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_22_le__fun__def) ).
thf(981,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)],[230]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA] :
( ( refine1315500908_inres @ TA @ ( refine605929679le_RES @ TA @ A ) )
= ( ^ [B: TA] : ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_inres__simps_I2_J) ).
thf(766,plain,
! [TA: $tType,A: set @ TA] :
( ( refine1315500908_inres @ TA @ ( refine605929679le_RES @ TA @ A ) )
= ( ^ [B: TA] : ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_inf__fun__def) ).
thf(397,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(148,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1767639642_FAILi @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_less__eq__nres_Osimps_I1_J) ).
thf(687,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1767639642_FAILi @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(53,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Int__absorb) ).
thf(428,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(287,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_108_subset__antisym) ).
thf(1201,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)],[287]) ).
thf(265,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ( C = D )
=> ( ord_less_eq @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_ord__eq__le__eq__trans) ).
thf(1104,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ( C = D )
=> ( ord_less_eq @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(302,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_55_order__subst2) ).
thf(1242,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)],[302]) ).
thf(289,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_order__mono__setup_Orefl) ).
thf(1206,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(146,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: $o,B: TA,C: TA,D: TA,E: TA] :
( ( A
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq @ TA @ D @ E ) )
=> ( ord_less_eq @ TA @ ( if @ TA @ A @ B @ D ) @ ( if @ TA @ A @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Refine__Misc_Oif__mono) ).
thf(678,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: $o,B: TA,C: TA,D: TA,E: TA] :
( ( A
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq @ TA @ D @ E ) )
=> ( ord_less_eq @ TA @ ( if @ TA @ A @ B @ D ) @ ( if @ TA @ A @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(98,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Int__commute) ).
thf(529,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(182,axiom,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
? [B: set @ TA] :
( A
= ( refine605929679le_RES @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_nofail__RES__conv) ).
thf(793,plain,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
? [B: set @ TA] :
( A
= ( refine605929679le_RES @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(33,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_19) ).
thf(381,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(184,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_47_order_Otrans) ).
thf(798,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)],[184]) ).
thf(204,axiom,
! [TA: $tType] : ( bounded_lattice_bot @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice__bot_37) ).
thf(894,plain,
! [TA: $tType] : ( bounded_lattice_bot @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(168,axiom,
! [TA: $tType,A: set @ TA] :
( ( refine1767639642_FAILi @ TA )
!= ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_nres_Odistinct_I1_J) ).
thf(746,plain,
! [TA: $tType,A: set @ TA] :
( ( refine1767639642_FAILi @ TA )
!= ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(245,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( refine605929679le_RES @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_inf__nres_Osimps_I3_J) ).
thf(1021,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( refine605929679le_RES @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(250,axiom,
! [TA: $tType] :
( ( refine1687780735RETURN @ TA )
= ( ^ [A: TA] :
( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [B: TA] : ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_RETURN__SPEC__conv) ).
thf(1042,plain,
! [TA: $tType] :
( ( refine1687780735RETURN @ TA )
= ( ^ [A: TA] :
( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [B: TA] : ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Int__left__absorb) ).
thf(349,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(189,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ A @ B )
= C )
=> ( ( ( B
= ( refine1767639642_FAILi @ TA ) )
=> ( C != A ) )
=> ( ( ( A
= ( refine1767639642_FAILi @ TA ) )
=> ! [D: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ D ) )
=> ( C
!= ( refine605929679le_RES @ TA @ D ) ) ) )
=> ~ ! [D: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ D ) )
=> ! [E: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ E ) )
=> ( C
!= ( refine605929679le_RES @ TA @ ( inf_inf @ ( set @ TA ) @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_inf__nres_Oelims) ).
thf(820,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ A @ B )
= C )
=> ( ( ( B
= ( refine1767639642_FAILi @ TA ) )
=> ( C != A ) )
=> ( ( ( A
= ( refine1767639642_FAILi @ TA ) )
=> ! [D: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ D ) )
=> ( C
!= ( refine605929679le_RES @ TA @ D ) ) ) )
=> ~ ! [D: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ D ) )
=> ! [E: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ E ) )
=> ( C
!= ( refine605929679le_RES @ TA @ ( inf_inf @ ( set @ TA ) @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(51,axiom,
bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Obot_35) ).
thf(424,plain,
bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(128,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_36_order__trans) ).
thf(630,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)],[128]) ).
thf(163,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( set @ TA ) > $o ) @ ( powp @ TA @ A ) @ ( powp @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Powp__mono) ).
thf(729,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( set @ TA ) > $o ) @ ( powp @ TA @ A ) @ ( powp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(69,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_IntD2) ).
thf(467,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(112,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_le__infI1) ).
thf(566,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Int__iff) ).
thf(361,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(199,axiom,
! [TA: $tType,A: TA > $o] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_SUCCEED__rule) ).
thf(879,plain,
! [TA: $tType,A: TA > $o] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(56,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( top_top @ TA )
= ( inf_inf @ TA @ A @ B ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_inf__top_Oneutr__eq__iff) ).
thf(435,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( top_top @ TA )
= ( inf_inf @ TA @ A @ B ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(10,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_inf__commute) ).
thf(329,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(141,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_le__inf__iff) ).
thf(665,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(95,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_13) ).
thf(522,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(257,axiom,
! [TA: $tType,A: TA > $o,B: refine1665802226e_nres @ TA] :
( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ C ) @ B ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_lhs__step__SPEC) ).
thf(1079,plain,
! [TA: $tType,A: TA > $o,B: refine1665802226e_nres @ TA] :
( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ C ) @ B ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: refine1665802226e_nres @ TB,B: TB > ( refine1665802226e_nres @ TC ),C: TC > $o,D: TB > ( refine1665802226e_nres @ TA ),E: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ ( refine463715084e_bind @ TB @ TC @ A @ B ) @ ( refine605929679le_RES @ TC @ ( collect @ TC @ C ) ) )
=> ( ! [F: TB] :
( ( refine1102455758nofail @ TB @ A )
=> ( ( refine1315500908_inres @ TB @ A @ F )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ ( B @ F ) @ ( refine605929679le_RES @ TC @ ( collect @ TC @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( D @ F ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ E ) ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ D ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_bind__sim__select__rule) ).
thf(757,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: refine1665802226e_nres @ TB,B: TB > ( refine1665802226e_nres @ TC ),C: TC > $o,D: TB > ( refine1665802226e_nres @ TA ),E: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ ( refine463715084e_bind @ TB @ TC @ A @ B ) @ ( refine605929679le_RES @ TC @ ( collect @ TC @ C ) ) )
=> ( ! [F: TB] :
( ( refine1102455758nofail @ TB @ A )
=> ( ( refine1315500908_inres @ TB @ A @ F )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ ( B @ F ) @ ( refine605929679le_RES @ TC @ ( collect @ TC @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( D @ F ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ E ) ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ D ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(286,axiom,
! [TA: $tType,A: $o,B: refine1665802226e_nres @ TA,C: TA > $o,D: refine1665802226e_nres @ TA] :
( ( A
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) )
=> ( ( ~ A
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ D @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( if @ ( refine1665802226e_nres @ TA ) @ A @ B @ D ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_if__rule) ).
thf(1195,plain,
! [TA: $tType,A: $o,B: refine1665802226e_nres @ TA,C: TA > $o,D: refine1665802226e_nres @ TA] :
( ( A
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) )
=> ( ( ~ A
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ D @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( if @ ( refine1665802226e_nres @ TA ) @ A @ B @ D ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(157,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_133_set__eq__subset) ).
thf(710,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)],[157]) ).
thf(8,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_9) ).
thf(324,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(241,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_inf_Oabsorb__iff1) ).
thf(1012,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(82,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( top_top @ TA )
= ( inf_inf @ TA @ A @ B ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_top__eq__inf__iff) ).
thf(493,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( top_top @ TA )
= ( inf_inf @ TA @ A @ B ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(291,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TB,C: TB > ( refine1665802226e_nres @ TA )] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( refine1102455758nofail @ TB @ B ) )
=> ( ! [D: TB] :
( ( refine406925620_inres @ TB @ B @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( C @ D ) @ A ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_lhs__step__bind) ).
thf(1210,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TB,C: TB > ( refine1665802226e_nres @ TA )] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( refine1102455758nofail @ TB @ B ) )
=> ( ! [D: TB] :
( ( refine406925620_inres @ TB @ B @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( C @ D ) @ A ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_bot__fun__def) ).
thf(519,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(197,axiom,
! [TA: $tType] : ( order @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_42) ).
thf(874,plain,
! [TA: $tType] : ( order @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(243,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_inf__le2) ).
thf(1017,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(42,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_inf1D2) ).
thf(403,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(262,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_nres__order__simps_I21_J) ).
thf(1096,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(279,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: $o] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( if @ TA @ E @ A @ C ) @ ( if @ TA @ E @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_order__mono__setup_Omono__if) ).
thf(1138,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: $o] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( if @ TA @ E @ A @ C ) @ ( if @ TA @ E @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(85,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_inf__top_Oleft__neutral) ).
thf(499,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(233,axiom,
! [TA: $tType] : ( bot @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_45) ).
thf(989,plain,
! [TA: $tType] : ( bot @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(152,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_41_antisym__conv) ).
thf(697,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)],[152]) ).
thf(260,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_140_subset__iff) ).
thf(1089,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)],[260]) ).
thf(298,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Collect__restrict) ).
thf(1234,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(308,axiom,
! [TA: $tType] : ( ord @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_44) ).
thf(1259,plain,
! [TA: $tType] : ( ord @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(6,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_inf__top__left) ).
thf(317,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(136,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( A
!= ( refine1767639642_FAILi @ TA ) )
=> ~ ! [B: set @ TA] :
( A
!= ( refine605929679le_RES @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_nres_Oexhaust) ).
thf(650,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( A
!= ( refine1767639642_FAILi @ TA ) )
=> ~ ! [B: set @ TA] :
( A
!= ( refine605929679le_RES @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(222,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_inf_OcoboundedI2) ).
thf(948,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(71,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_inf__sup__aci_I4_J) ).
thf(471,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(201,axiom,
! [TA: $tType,A: TA] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_nres__inequalities_I5_J) ).
thf(884,plain,
! [TA: $tType,A: TA] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(247,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_subset__Collect__conv) ).
thf(1028,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(108,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_31_dual__order_Oantisym) ).
thf(554,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)],[108]) ).
thf(256,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_inf_OboundedE) ).
thf(1075,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(249,axiom,
! [TA: $tType,A: set @ TA] :
( ( refine1672542526he_RES @ TA @ ( refine605929679le_RES @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_the__RES_Osimps) ).
thf(1039,plain,
! [TA: $tType,A: set @ TA] :
( ( refine1672542526he_RES @ TA @ ( refine605929679le_RES @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(104,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_14) ).
thf(547,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(263,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_inf__absorb1) ).
thf(1099,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(167,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_54_ord__eq__le__subst) ).
thf(738,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)],[167]) ).
thf(277,axiom,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA] :
( ( A @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [C: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_nres_Oinduct) ).
thf(1131,plain,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA] :
( ( A @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [C: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(303,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_18_le__funD) ).
thf(1246,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)],[303]) ).
thf(122,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ A )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_inf_Oabsorb__iff2) ).
thf(605,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(310,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_RES__rule) ).
thf(1263,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(237,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_139_Int__absorb1) ).
thf(997,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)],[237]) ).
thf(253,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_163_GreatestI2__order) ).
thf(1050,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)],[253]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_top__apply) ).
thf(457,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(231,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_use__spec__rule) ).
thf(984,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(209,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: $o,B: TA,C: TA,D: TA] :
( ( A
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq @ TA @ D @ C ) )
=> ( ord_less_eq @ TA @ ( if @ TA @ A @ B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lhs__step__If) ).
thf(911,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: $o,B: TA,C: TA,D: TA] :
( ( A
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq @ TA @ D @ C ) )
=> ( ord_less_eq @ TA @ ( if @ TA @ A @ B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(23,axiom,
bounde1561333602nf_top @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__semilattice__inf__top_25) ).
thf(360,plain,
bounde1561333602nf_top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(102,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( top_top @ TA ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_inf__top_Oeq__neutr__iff) ).
thf(541,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( top_top @ TA ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(144,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_143_Int__lower2) ).
thf(674,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)],[144]) ).
thf(140,axiom,
! [TA: $tType,A: product_unit > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ product_unit @ TA @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_ibind__strict_I1_J) ).
thf(662,plain,
! [TA: $tType,A: product_unit > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ product_unit @ TA @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(259,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( A
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_nres__order__simps_I2_J) ).
thf(1086,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( A
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TB ),C: TB > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine463715084e_bind @ TA @ TB @ A @ B ) @ ( refine605929679le_RES @ TB @ ( collect @ TB @ C ) ) )
= ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( B @ D ) @ ( refine605929679le_RES @ TB @ ( collect @ TB @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_bind__rule__complete) ).
thf(938,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TB ),C: TB > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine463715084e_bind @ TA @ TB @ A @ B ) @ ( refine605929679le_RES @ TB @ ( collect @ TB @ C ) ) )
= ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( B @ D ) @ ( refine605929679le_RES @ TB @ ( collect @ TB @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(46,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_inf__top__right) ).
thf(412,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(305,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_44_Collect__cong) ).
thf(1251,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)],[305]) ).
thf(52,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( top_top @ TA ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_inf__eq__top__iff) ).
thf(425,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( top_top @ TA ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(91,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_inf__Int__eq) ).
thf(513,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(293,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_inf_OorderI) ).
thf(1219,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(312,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_142_equalityD1) ).
thf(1273,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)],[312]) ).
thf(149,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ~ ( B @ D )
=> ~ ( C @ D ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
= ( C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_SPEC__iff) ).
thf(689,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ~ ( B @ D )
=> ~ ( C @ D ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
= ( C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(30,axiom,
order_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_18) ).
thf(375,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(165,axiom,
! [TA: $tType] :
~ ( refine1102455758nofail @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_nofail__simps_I1_J) ).
thf(733,plain,
! [TA: $tType] :
~ ( refine1102455758nofail @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(283,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: $o] :
( ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
= C )
=> ( ( ( B
= ( refine1767639642_FAILi @ TA ) )
=> ~ C )
=> ( ! [D: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ D ) )
=> ! [E: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ E ) )
=> ( C
= ( ~ ( ord_less_eq @ ( set @ TA ) @ D @ E ) ) ) ) )
=> ~ ( ( A
= ( refine1767639642_FAILi @ TA ) )
=> ( ? [D: set @ TA] :
( B
= ( refine605929679le_RES @ TA @ D ) )
=> C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_less__eq__nres_Oelims_I1_J) ).
thf(1154,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: $o] :
( ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
= C )
=> ( ( ( B
= ( refine1767639642_FAILi @ TA ) )
=> ~ C )
=> ( ! [D: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ D ) )
=> ! [E: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ E ) )
=> ( C
= ( ~ ( ord_less_eq @ ( set @ TA ) @ D @ E ) ) ) ) )
=> ~ ( ( A
= ( refine1767639642_FAILi @ TA ) )
=> ( ? [D: set @ TA] :
( B
= ( refine605929679le_RES @ TA @ D ) )
=> C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(151,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ ( inf_inf @ ( refine1665802226e_nres @ TA ) @ A @ B ) )
= ( ( refine1102455758nofail @ TA @ A )
| ( refine1102455758nofail @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_pw__inf__nofail) ).
thf(694,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ ( inf_inf @ ( refine1665802226e_nres @ TA ) @ A @ B ) )
= ( ( refine1102455758nofail @ TA @ A )
| ( refine1102455758nofail @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(274,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_inf__mono) ).
thf(1125,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: TB > ( refine1665802226e_nres @ TA ),C: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TB @ A )
=> ( ! [D: TB] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1687780735RETURN @ TB @ D ) @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_bind__le__nofailI) ).
thf(562,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: TB > ( refine1665802226e_nres @ TA ),C: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TB @ A )
=> ( ! [D: TB] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1687780735RETURN @ TB @ D ) @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(228,axiom,
! [TA: $tType,A: set @ TA] :
~ ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_less__eq__nres_Osimps_I3_J) ).
thf(975,plain,
! [TA: $tType,A: set @ TA] :
~ ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(307,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ A )
=> ( ( refine605929679le_RES @ TA @ ( refine1672542526he_RES @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_the__RES__inv) ).
thf(1256,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ A )
=> ( ( refine605929679le_RES @ TA @ ( refine1672542526he_RES @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(296,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: TB > ( refine1665802226e_nres @ TA ),C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A
@ ( refine605929679le_RES @ TB
@ ( collect @ TB
@ ^ [D: TB] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( B @ D ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ B ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_bind__rule) ).
thf(1226,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: TB > ( refine1665802226e_nres @ TA ),C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A
@ ( refine605929679le_RES @ TB
@ ( collect @ TB
@ ^ [D: TB] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( B @ D ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine463715084e_bind @ TB @ TA @ A @ B ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TC ),C: TC > ( refine1665802226e_nres @ TB )] :
( ( refine463715084e_bind @ TC @ TB @ ( refine463715084e_bind @ TA @ TC @ A @ B ) @ C )
= ( refine463715084e_bind @ TA @ TB @ A
@ ^ [D: TA] : ( refine463715084e_bind @ TC @ TB @ ( B @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_nres__monad3) ).
thf(391,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TC ),C: TC > ( refine1665802226e_nres @ TB )] :
( ( refine463715084e_bind @ TC @ TB @ ( refine463715084e_bind @ TA @ TC @ A @ B ) @ C )
= ( refine463715084e_bind @ TA @ TB @ A
@ ^ [D: TA] : ( refine463715084e_bind @ TC @ TB @ ( B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_inf__left__commute) ).
thf(382,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(115,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_138_Int__absorb2) ).
thf(572,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)],[115]) ).
thf(1,conjecture,
( ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2
@ ( refine605929679le_RES @ a
@ ( collect @ a
@ ^ [A: a] :
( ( p @ A )
& ( q @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2
@ ( refine605929679le_RES @ a
@ ( collect @ a
@ ^ [A: a] :
( ( p @ A )
& ( q @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(313,plain,
~ ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2
@ ( refine605929679le_RES @ a
@ ( collect @ a
@ ^ [A: a] :
( ( p @ A )
& ( q @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(124,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_178_Greatest__equality) ).
thf(611,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)],[124]) ).
thf(158,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_38_ord__le__eq__trans) ).
thf(713,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)],[158]) ).
thf(301,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_inf_Oabsorb2) ).
thf(1239,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(261,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_SPEC__rule) ).
thf(1092,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(211,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_224_bot_Oextremum__uniqueI) ).
thf(919,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)],[211]) ).
thf(295,axiom,
! [TA: $tType] : ( bounde1561333602nf_top @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__semilattice__inf__top_36) ).
thf(1224,plain,
! [TA: $tType] : ( bounde1561333602nf_top @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(207,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_inf__unique) ).
thf(900,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(270,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_inf_OcoboundedI1) ).
thf(1117,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(252,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_144_Int__lower1) ).
thf(1048,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)],[252]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA] :
( ( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
= ( refine605929679le_RES @ TA @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_nres__more__simps_I1_J) ).
thf(1122,plain,
! [TA: $tType,A: set @ TA] :
( ( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
= ( refine605929679le_RES @ TA @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(120,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_52_eq__iff) ).
thf(599,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)],[120]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1561333602nf_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__inf__top) ).
thf(509,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1561333602nf_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(55,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_23) ).
thf(434,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(203,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_39_ord__eq__le__trans) ).
thf(890,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)],[203]) ).
thf(73,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_11) ).
thf(477,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_inf1E) ).
thf(387,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_IntE) ).
thf(535,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(188,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_predicate1I) ).
thf(816,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(162,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_40_order__class_Oorder_Oeq__iff) ).
thf(726,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)],[162]) ).
thf(76,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_3) ).
thf(483,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(153,axiom,
! [TA: $tType,A: TA] :
( ( refine605929679le_RES @ TA @ ( collect @ TA @ ( (=) @ TA @ A ) ) )
= ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_SPEC__eq__is__RETURN_I1_J) ).
thf(700,plain,
! [TA: $tType,A: TA] :
( ( refine605929679le_RES @ TA @ ( collect @ TA @ ( (=) @ TA @ A ) ) )
= ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(127,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_106_subsetI) ).
thf(626,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)],[127]) ).
thf(175,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ B ) @ ( refine1687780735RETURN @ TA @ A ) )
= ( refine1687780735RETURN @ TA @ A ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ B ) @ ( refine1687780735RETURN @ TA @ A ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_inf__RETURN__RES_I2_J) ).
thf(769,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ B ) @ ( refine1687780735RETURN @ TA @ A ) )
= ( refine1687780735RETURN @ TA @ A ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ B ) @ ( refine1687780735RETURN @ TA @ A ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(220,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_predicate1D) ).
thf(943,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(142,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_less__eq__set__def) ).
thf(668,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(191,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_inf__greatest) ).
thf(858,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_bot__apply) ).
thf(367,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_inf__apply) ).
thf(462,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(216,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( top_top @ ( refine1665802226e_nres @ TA ) ) @ A )
= ( A
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_nres__order__simps_I4_J) ).
thf(932,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( top_top @ ( refine1665802226e_nres @ TA ) ) @ A )
= ( A
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(226,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_le__infI) ).
thf(959,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(195,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_le__infD1) ).
thf(868,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(178,axiom,
! [TA: $tType] : ( top @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_43) ).
thf(780,plain,
! [TA: $tType] : ( top @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_4) ).
thf(455,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(242,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ B ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_RETURN__rule) ).
thf(1015,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ B ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Int__Collect) ).
thf(608,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(268,axiom,
! [TA: $tType] : ( preorder @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_40) ).
thf(1113,plain,
! [TA: $tType] : ( preorder @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(238,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_141_equalityD2) ).
thf(1000,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)],[238]) ).
thf(264,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_prop__restrict) ).
thf(1102,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(54,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_inf_Ocommute) ).
thf(431,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TB ),C: refine1665802226e_nres @ TB] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine463715084e_bind @ TA @ TB @ A @ B ) @ C )
= ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( if @ ( refine1665802226e_nres @ TA ) @ ( refine1102455758nofail @ TB @ C )
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( B @ D ) @ C ) ) )
@ ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_bind__le__shift) ).
thf(653,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TB ),C: refine1665802226e_nres @ TB] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine463715084e_bind @ TA @ TB @ A @ B ) @ C )
= ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A
@ ( if @ ( refine1665802226e_nres @ TA ) @ ( refine1102455758nofail @ TB @ C )
@ ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [D: TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( B @ D ) @ C ) ) )
@ ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(212,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_149_in__mono) ).
thf(922,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)],[212]) ).
thf(39,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine463715084e_bind @ TA @ TA @ A @ ( refine1687780735RETURN @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_nres__monad2) ).
thf(394,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine463715084e_bind @ TA @ TA @ A @ ( refine1687780735RETURN @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( refine1665802226e_nres @ TB )] :
( ( refine1102455758nofail @ TB @ ( refine463715084e_bind @ TA @ TB @ ( refine605929679le_RES @ TA @ A ) @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( refine1102455758nofail @ TB @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_pw__RES__bind__choose_I1_J) ).
thf(986,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( refine1665802226e_nres @ TB )] :
( ( refine1102455758nofail @ TB @ ( refine463715084e_bind @ TA @ TB @ ( refine605929679le_RES @ TA @ A ) @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( refine1102455758nofail @ TB @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(87,axiom,
bounded_lattice @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice_1) ).
thf(505,plain,
bounded_lattice @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(438,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(79,axiom,
top @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Otop_33) ).
thf(490,plain,
top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(290,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_nres__order__simps_I1_J) ).
thf(1208,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(214,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( A
= ( inf_inf @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_inf_Oorder__iff) ).
thf(927,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( A
= ( inf_inf @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(169,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_le__infI2) ).
thf(749,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(92,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_8) ).
thf(516,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(20,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_7) ).
thf(355,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(171,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_145_subset__eq) ).
thf(754,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)],[171]) ).
thf(107,axiom,
bounde1561333602nf_top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_15) ).
thf(553,plain,
bounde1561333602nf_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(135,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ ( (=) @ TA @ B ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1687780735RETURN @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_RETURN__to__SPEC__rule) ).
thf(648,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ ( (=) @ TA @ B ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1687780735RETURN @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(78,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_inf__idem) ).
thf(487,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ! [D: TA] : ( ord_less_eq @ TB @ ( A @ D ) @ ( B @ D ) )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_order__mono__setup_Omono__let) ).
thf(557,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ! [D: TA] : ( ord_less_eq @ TB @ ( A @ D ) @ ( B @ D ) )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(132,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_132_Collect__mono__iff) ).
thf(640,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)],[132]) ).
thf(155,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
= ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( C = A )
& ( B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_inf__RETURN__SPEC_I1_J) ).
thf(705,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
= ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( C = A )
& ( B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(202,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_conj__subset__def) ).
thf(887,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(224,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ B ) )
=> ( refine1102455758nofail @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_le__RES__nofailI) ).
thf(954,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ B ) )
=> ( refine1102455758nofail @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(311,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_34_linorder__wlog) ).
thf(1267,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)],[311]) ).
thf(235,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_bot_Oextremum) ).
thf(993,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(117,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_46_le__cases3) ).
thf(580,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)],[117]) ).
thf(190,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_235_subset__empty) ).
thf(855,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)],[190]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_IntI) ).
thf(370,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(159,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_dual__order_Orefl) ).
thf(717,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_nres__more__simps_I6_J) ).
thf(502,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(14,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_inf_Oleft__idem) ).
thf(338,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine463715084e_bind @ TA @ TB @ A @ C )
= ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_bind__cong) ).
thf(808,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine463715084e_bind @ TA @ TB @ A @ C )
= ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(133,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_nf__inres__SPEC) ).
thf(643,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ B )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(103,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_inf__top_Oright__neutral) ).
thf(544,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(336,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(154,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_le__infD2) ).
thf(703,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_subset__Collect__iff) ).
thf(656,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(193,axiom,
ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).
thf(864,plain,
ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(3,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(314,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(60,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_boolean__algebra__cancel_Oinf2) ).
thf(446,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(118,axiom,
ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(595,plain,
ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(234,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_SPEC__trans) ).
thf(991,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(280,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_53_ord__le__eq__subst) ).
thf(1140,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)],[280]) ).
thf(36,axiom,
bounded_lattice @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice_2) ).
thf(386,plain,
bounded_lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(84,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_12) ).
thf(497,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(198,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_inf_OorderE) ).
thf(876,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(465,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(450,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(101,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(539,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(143,axiom,
! [TA: $tType,A: TA] :
( ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [B: TA] : ( B = A ) ) )
= ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_SPEC__eq__is__RETURN_I2_J) ).
thf(671,plain,
! [TA: $tType,A: TA] :
( ( refine605929679le_RES @ TA
@ ( collect @ TA
@ ^ [B: TA] : ( B = A ) ) )
= ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(96,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_inf__sup__aci_I1_J) ).
thf(524,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(292,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_less__eq__nres_Osimps_I2_J) ).
thf(1216,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(284,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_50_linear) ).
thf(1189,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)],[284]) ).
thf(266,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_empty__subsetI) ).
thf(1108,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(227,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ~ ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ! [C: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ C ) )
=> ! [D: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ D ) )
=> ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) )
=> ~ ( ( A
= ( refine1767639642_FAILi @ TA ) )
=> ! [C: set @ TA] :
( B
!= ( refine605929679le_RES @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_less__eq__nres_Oelims_I3_J) ).
thf(961,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ~ ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ! [C: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ C ) )
=> ! [D: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ D ) )
=> ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) )
=> ~ ( ( A
= ( refine1767639642_FAILi @ TA ) )
=> ! [C: set @ TA] :
( B
!= ( refine605929679le_RES @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(205,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_inf_Ocobounded1) ).
thf(896,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(129,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_inf_Ocobounded2) ).
thf(632,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(236,axiom,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ! [D: refine1665802226e_nres @ TA] : ( A @ D @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [D: set @ TA] : ( A @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ D ) )
=> ( ! [D: set @ TA,E: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine605929679le_RES @ TA @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_sup__nres_Oinduct) ).
thf(995,plain,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ! [D: refine1665802226e_nres @ TA] : ( A @ D @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [D: set @ TA] : ( A @ ( refine1767639642_FAILi @ TA ) @ ( refine605929679le_RES @ TA @ D ) )
=> ( ! [D: set @ TA,E: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine605929679le_RES @ TA @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(164,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_19_le__funE) ).
thf(731,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)],[164]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(418,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(113,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_20_le__funI) ).
thf(568,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)],[113]) ).
thf(173,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ( inf_inf @ ( set @ TA ) @ C @ B )
= ( inf_inf @ ( set @ TA ) @ D @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ C @ A )
= ( inf_inf @ ( set @ TA ) @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_inter__eq__subsetI) ).
thf(763,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ( inf_inf @ ( set @ TA ) @ C @ B )
= ( inf_inf @ ( set @ TA ) @ D @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ C @ A )
= ( inf_inf @ ( set @ TA ) @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: TB > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ TB @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_bind__SUCCEED) ).
thf(684,plain,
! [TA: $tType,TB: $tType,A: TB > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ TB @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(105,axiom,
lattice @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Olattice_31) ).
thf(549,plain,
lattice @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType,A: TB > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ TB @ TA @ ( top_top @ ( refine1665802226e_nres @ TB ) ) @ A )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_bind__FAIL) ).
thf(1045,plain,
! [TA: $tType,TB: $tType,A: TB > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ TB @ TA @ ( top_top @ ( refine1665802226e_nres @ TB ) ) @ A )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( refine1687780735RETURN @ TA @ A ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_inf__RETURN__RES_I1_J) ).
thf(800,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( refine1687780735RETURN @ TA @ A ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(125,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_le__nofailI) ).
thf(620,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(4,axiom,
lattice @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_20) ).
thf(315,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(223,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
=> ( ! [D: TA] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_SPEC__cons__rule) ).
thf(950,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
=> ( ! [D: TA] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(43,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_inf_Oidem) ).
thf(405,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(281,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Int__def) ).
thf(1148,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,A: TB,B: ( set @ TA ) > TB,C: set @ TA] :
( ( refine1442219249c_nres @ TB @ TA @ A @ B @ ( refine605929679le_RES @ TA @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nres_Osimps_I7_J) ).
thf(865,plain,
! [TA: $tType,TB: $tType,A: TB,B: ( set @ TA ) > TB,C: set @ TA] :
( ( refine1442219249c_nres @ TB @ TA @ A @ B @ ( refine605929679le_RES @ TA @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(166,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_32_dual__order_Oeq__iff) ).
thf(735,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)],[166]) ).
thf(50,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_inf1I) ).
thf(422,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(304,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_le__iff__inf) ).
thf(1248,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_nres__order__simps_I20_J) ).
thf(790,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(9,axiom,
! [TA: $tType,A: TA] :
( ( refine1315500908_inres @ TA @ ( refine1687780735RETURN @ TA @ A ) )
= ( (=) @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_inres__simps_I3_J) ).
thf(326,plain,
! [TA: $tType,A: TA] :
( ( refine1315500908_inres @ TA @ ( refine1687780735RETURN @ TA @ A ) )
= ( (=) @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_inf_Oassoc) ).
thf(341,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_inf__left__idem) ).
thf(506,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(22,axiom,
! [TA: $tType] : ( bounde1561333602nf_top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_5) ).
thf(358,plain,
! [TA: $tType] : ( bounde1561333602nf_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(72,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Int__assoc) ).
thf(474,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_inf_Oright__idem) ).
thf(400,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(183,axiom,
! [TA: $tType] : ( semilattice_inf @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Osemilattice__inf_38) ).
thf(796,plain,
! [TA: $tType] : ( semilattice_inf @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA > ( refine1665802226e_nres @ TB )] :
( ( refine463715084e_bind @ TA @ TB @ ( refine1687780735RETURN @ TA @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_nres__monad1) ).
thf(415,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA > ( refine1665802226e_nres @ TB )] :
( ( refine463715084e_bind @ TA @ TB @ ( refine1687780735RETURN @ TA @ A ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(99,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_inf_Oleft__commute) ).
thf(532,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(254,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( B
!= ( refine1767639642_FAILi @ TA ) )
=> ~ ! [C: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ C ) )
=> ! [D: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ D ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_less__eq__nres_Oelims_I2_J) ).
thf(1065,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( B
!= ( refine1767639642_FAILi @ TA ) )
=> ~ ! [C: set @ TA] :
( ( A
= ( refine605929679le_RES @ TA @ C ) )
=> ! [D: set @ TA] :
( ( B
= ( refine605929679le_RES @ TA @ D ) )
=> ~ ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(126,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_inf__le1) ).
thf(624,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(299,axiom,
ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( inf_inf @ ( refine1665802226e_nres @ a ) @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ) @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062) ).
thf(1236,plain,
ord_less_eq @ ( refine1665802226e_nres @ a ) @ a2 @ ( inf_inf @ ( refine1665802226e_nres @ a ) @ ( refine605929679le_RES @ a @ ( collect @ a @ p ) ) @ ( refine605929679le_RES @ a @ ( collect @ a @ q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(309,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: refine1665802226e_nres @ TB,D: TA > ( refine1665802226e_nres @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( D @ A ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( refine463715084e_bind @ TA @ TB @ ( refine605929679le_RES @ TA @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_RES__bind__choose) ).
thf(1261,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: refine1665802226e_nres @ TB,D: TA > ( refine1665802226e_nres @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( D @ A ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( refine463715084e_bind @ TA @ TB @ ( refine605929679le_RES @ TA @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(116,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_131_Int__Collect__mono) ).
thf(575,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)],[116]) ).
thf(192,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_49_eq__refl) ).
thf(860,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)],[192]) ).
thf(119,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ A ) @ B )
= ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nf__inres__RES) ).
thf(596,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ A ) @ B )
= ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(244,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_135_Int__greatest) ).
thf(1019,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)],[244]) ).
thf(208,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_nres__order__simps_I5_J) ).
thf(908,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(161,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Collect__mem__eq) ).
thf(723,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(239,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ! [D: TA] :
( ( ord_less_eq @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_inf__leI) ).
thf(1004,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ! [D: TA] :
( ( ord_less_eq @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(150,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_inf_Obounded__iff) ).
thf(691,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(272,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_rev__predicate1D) ).
thf(1120,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(11,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_24) ).
thf(332,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType,A: TA > ( refine1665802226e_nres @ TB ),B: TA > ( refine1665802226e_nres @ TB ),C: TA] :
( ( ord_less_eq @ ( TA > ( refine1665802226e_nres @ TB ) ) @ A @ B )
=> ( ( refine1102455758nofail @ TB @ ( B @ C ) )
=> ( refine1102455758nofail @ TB @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_nofail__antimono__fun) ).
thf(1129,plain,
! [TA: $tType,TB: $tType,A: TA > ( refine1665802226e_nres @ TB ),B: TA > ( refine1665802226e_nres @ TB ),C: TA] :
( ( ord_less_eq @ ( TA > ( refine1665802226e_nres @ TB ) ) @ A @ B )
=> ( ( refine1102455758nofail @ TB @ ( B @ C ) )
=> ( refine1102455758nofail @ TB @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(70,axiom,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__bot_6) ).
thf(469,plain,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(139,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1767639642_FAILi @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_inf__nres_Osimps_I1_J) ).
thf(659,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( inf_inf @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1767639642_FAILi @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Collect__subset) ).
thf(775,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(145,axiom,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ! [D: refine1665802226e_nres @ TA] : ( A @ ( refine1767639642_FAILi @ TA ) @ D )
=> ( ! [D: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [D: set @ TA,E: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine605929679le_RES @ TA @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_less__nres_Oinduct) ).
thf(676,plain,
! [TA: $tType,A: ( refine1665802226e_nres @ TA ) > ( refine1665802226e_nres @ TA ) > $o,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ! [D: refine1665802226e_nres @ TA] : ( A @ ( refine1767639642_FAILi @ TA ) @ D )
=> ( ! [D: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine1767639642_FAILi @ TA ) )
=> ( ! [D: set @ TA,E: set @ TA] : ( A @ ( refine605929679le_RES @ TA @ D ) @ ( refine605929679le_RES @ TA @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(80,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(491,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(288,axiom,
! [TA: $tType] : ( lattice @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Olattice_41) ).
thf(1204,plain,
! [TA: $tType] : ( lattice @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(25,axiom,
top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_22) ).
thf(364,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(156,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_148_subsetD) ).
thf(708,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)],[156]) ).
thf(217,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nres_Oinject) ).
thf(935,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(240,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_37_order__class_Oorder_Oantisym) ).
thf(1009,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)],[240]) ).
thf(83,axiom,
bounded_lattice_bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice__bot_26) ).
thf(496,plain,
bounded_lattice_bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(63,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_21) ).
thf(454,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1277,plain,
$false,
inference(e,[status(thm)],[1024,365,479,347,1237,518,1083,941,777,1110,333,1031,481,352,1073,379,408,977,440,511,385,550,945,1222,930,898,1127,782,320,1228,1254,570,719,785,372,344,460,917,751,357,1191,559,638,881,1115,316,421,870,924,492,443,376,646,1151,806,485,1136,634,956,453,1119,411,527,602,981,766,397,687,428,1201,1104,1242,1206,678,529,793,381,798,894,746,1021,1042,349,820,424,630,729,467,566,361,879,435,329,665,522,1079,757,1195,710,324,1012,493,1210,519,874,1017,403,1096,1138,499,989,697,1089,1234,1259,317,650,948,471,884,1028,554,1075,1039,547,1099,738,1131,1246,605,1263,997,1050,457,984,911,360,541,674,662,1086,938,412,1251,425,513,1219,1273,689,375,733,1154,694,1125,562,975,1256,1226,391,382,572,313,611,713,1239,1092,919,1224,900,1117,1048,1122,599,509,434,890,477,387,535,816,726,483,700,626,769,943,668,858,367,462,932,959,868,780,455,1015,608,1113,1000,1102,431,653,922,394,986,505,438,490,1208,927,749,516,355,754,553,648,487,557,640,705,887,954,1267,993,580,855,370,717,502,338,808,643,544,336,703,656,864,314,446,595,991,1140,386,497,876,465,450,539,671,524,1216,1189,1108,961,896,632,995,731,418,568,763,684,549,1045,800,620,315,950,405,1148,865,735,422,1248,790,326,341,506,358,474,400,796,415,532,1065,624,1236,1261,575,860,596,1019,908,723,1004,691,1120,332,1129,469,659,775,676,491,1204,364,708,935,1009,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP162^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.11/0.21 % Computer : n004.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 20:04:07 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.98/1.15 % [INFO] Parsing done (362ms).
% 1.98/1.16 % [INFO] Running in sequential loop mode.
% 3.50/1.63 % [INFO] eprover registered as external prover.
% 3.50/1.64 % [INFO] Scanning for conjecture ...
% 3.93/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 311 axioms. Running axiom selection ...
% 4.21/1.95 % [INFO] Axiom selection finished. Selected 310 axioms (removed 1 axioms).
% 5.76/2.30 % [INFO] Problem is higher-order (TPTP THF).
% 5.76/2.35 % [INFO] Type checking passed.
% 5.76/2.36 % [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 ...
% 53.36/31.35 % External prover 'e' found a proof!
% 53.36/31.35 % [INFO] Killing All external provers ...
% 53.36/31.36 % Time passed: 30999ms (effective reasoning time: 30188ms)
% 53.36/31.36 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 53.36/31.36 % Axioms used in derivation (310): fact_169_less__nres_Oinduct, fact_196_le__RES__nofailI, tcon_fun___Orderings_Obot, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Olattice_41, fact_235_subset__empty, fact_234_top__apply, fact_140_subset__iff, fact_108_subset__antisym, tcon_Set_Oset___Orderings_Obot_14, fact_35_dual__order_Orefl, fact_26_inf__leI, fact_110_less__eq__set__def, fact_222_ibind__strict_I1_J, fact_122_Int__Collect, fact_152_subset__CollectI, tcon_HOL_Obool___Lattices_Obounded__lattice_2, fact_53_ord__le__eq__subst, fact_153_Collect__restrict, fact_14_the__RES_Osimps, fact_129_predicate1D, fact_37_order__class_Oorder_Oantisym, fact_75_inf__sup__aci_I1_J, tcon_HOL_Obool___Orderings_Oorder_21, fact_17_nres_Osimps_I7_J, fact_67_inf_Oleft__commute, fact_227_nres__order__simps_I1_J, fact_12_SPEC__cons__rule, fact_69_inf_Ocommute, fact_127_Int__left__absorb, fact_115_predicate1I, fact_119_Int__def, fact_76_inf__sup__aci_I2_J, fact_243_inf__top_Oneutr__eq__iff, fact_246_nres__order__simps_I4_J, fact_145_subset__eq, fact_111_pred__subset__eq, fact_28_nres__order__simps_I5_J, fact_170_less__eq__nres_Oinduct, fact_157_inf1D2, fact_215_bind__cong, fact_223_bot__fun__def, tcon_HOL_Obool___Orderings_Opreorder_19, fact_85_inf__mono, fact_233_bind__sim__select__rule, tcon_HOL_Obool___Orderings_Otop_22, fact_62_inf__left__idem, fact_95_inf__absorb2, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_44, fact_142_equalityD1, fact_240_top__eq__inf__iff, fact_105_inf_OcoboundedI2, fact_130_rev__predicate1D, tcon_Set_Oset___Lattices_Obounded__lattice_3, tcon_Product__Type_Ounit___Orderings_Otop_33, fact_176_less__eq__nres_Oelims_I2_J, fact_156_inf1D1, fact_70_inf__assoc, fact_138_Int__absorb2, tcon_fun___Orderings_Oord, tcon_Set_Oset___Lattices_Obounded__lattice__bot_6, fact_208_inf__bot__left, fact_219_le__SPEC__bindI, fact_248_inres__simps_I3_J, fact_241_inf__top_Oeq__neutr__iff, fact_116_IntE, fact_78_inf__sup__aci_I4_J, fact_117_IntD1, fact_192_SPEC__eq__is__RETURN_I1_J, tcon_HOL_Obool___Orderings_Olinorder, fact_184_nres__order__simps_I20_J, fact_179_the__RES__inv, fact_29_order__mono__setup_Omono__let, fact_121_Int__absorb, fact_249_nofail__simps_I1_J, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Osemilattice__inf_38, fact_7_SPEC__iff, fact_149_in__mono, fact_187_inf__RETURN__SPEC_I2_J, fact_57_le__inf__iff, fact_89_inf_OorderI, fact_210_nres__monad1, fact_207_inf__bot__right, fact_32_dual__order_Oeq__iff, fact_86_le__infI1, fact_107_Int__subset__iff, fact_245_inres__simps_I2_J, tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_5, fact_106_subsetI, tcon_fun___Lattices_Obounded__lattice_4, fact_25_le__infD1, fact_191_nofail__RES__conv, fact_230_bind__rule, fact_139_Int__absorb1, fact_197_RETURN__rule, fact_148_subsetD, fact_146_equalityE, fact_181_inf__RETURN__SPEC_I1_J, fact_100_inf_Ocobounded1, fact_27_less__eq__nres_Osimps_I2_J, fact_21_Refine__Misc_Oif__mono, tcon_Product__Type_Ounit___Orderings_Oorder__bot_28, fact_224_bot_Oextremum__uniqueI, fact_141_equalityD2, fact_231_bind__le__nofailI, fact_11_use__spec__rule, fact_77_inf__sup__aci_I3_J, tcon_Set_Oset___Orderings_Opreorder_9, fact_44_Collect__cong, fact_216_pw__RES__bind__choose_I1_J, fact_102_inf_Oabsorb__iff1, fact_193_RETURN__SPEC__conv, fact_120_Int__assoc, fact_205_nres__monad3, fact_242_inf__top_Oleft__neutral, fact_82_inf__le2, fact_200_lhs__step__SPEC, fact_182_nres__more__simps_I6_J, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_45, fact_34_linorder__wlog, fact_71_inf_Oassoc, help_If_1_1_T, fact_180_relprop__triggers_I6_J, fact_195_pw__inf__nofail, tcon_Product__Type_Ounit___Orderings_Obot_35, fact_101_inf_Ocobounded2, tcon_Product__Type_Ounit___Lattices_Obounded__semilattice__inf__top_25, tcon_Set_Oset___Lattices_Olattice_10, tcon_Set_Oset___Orderings_Oorder_11, fact_83_le__infE, fact_59_inf_Oidem, fact_159_subset__Collect__conv, fact_103_inf_Oabsorb__iff2, tcon_Set_Oset___Orderings_Otop_12, fact_20_le__funI, fact_31_dual__order_Oantisym, fact_167_nres_Oexhaust, fact_226_bot_Oextremum, fact_201_lhs__step__bind, fact_163_GreatestI2__order, fact_118_IntD2, fact_204_bot__apply, fact_15_nf__inres__RES, fact_50_linear, fact_74_inf__fun__def, tcon_Product__Type_Ounit___Orderings_Opreorder_29, fact_38_ord__le__eq__trans, fact_24_le__infD2, fact_58_inf__apply, fact_194_SPEC__eq__is__RETURN_I2_J, tcon_fun___Lattices_Osemilattice__inf, tcon_Set_Oset___Orderings_Oorder__bot_8, fact_52_eq__iff, fact_40_order__class_Oorder_Oeq__iff, fact_92_inf_Oabsorb1, fact_177_less__eq__nres_Oelims_I3_J, fact_132_Collect__mono__iff, tcon_HOL_Obool___Orderings_Obot_24, fact_94_inf__absorb1, fact_48_le__cases, fact_214_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J, fact_43_Collect__mem__eq, fact_23_order__subst1, tcon_HOL_Obool___Lattices_Obounded__lattice__bot_16, fact_164_inf__nres_Osimps_I1_J, fact_13_order__mono__setup_Orefl, fact_60_inf__idem, tcon_fun___Lattices_Obounded__lattice__bot, tcon_HOL_Obool___Lattices_Olattice_20, fact_54_ord__eq__le__subst, tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_15, fact_172_nres_Osimps_I6_J, fact_143_Int__lower2, fact_16_nf__inres__SPEC, fact_220_RES__bind__choose, fact_166_nres_Oinduct, fact_213_nofail__simps_I4_J, fact_135_Int__greatest, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_42, fact_41_antisym__conv, fact_147_Int__mono, tcon_Set_Oset___Orderings_Oord_13, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__semilattice__inf__top_36, fact_84_le__infI, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_39, help_If_3_1_T, tcon_fun___Orderings_Oorder__bot, fact_96_inf_OboundedE, help_If_2_1_T, fact_1_nres_Oinject, fact_19_le__funE, fact_228_bind__rule__complete, fact_125_inf__Int__eq, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice, fact_39_ord__eq__le__trans, fact_202_inf__RETURN__RES_I2_J, fact_137_subset__refl, fact_150_inter__eq__subsetI, fact_90_inf__unique, fact_93_inf_Oabsorb2, fact_5_if__rule, tcon_fun___Orderings_Otop, fact_239_inf__eq__top__iff, fact_133_set__eq__subset, fact_112_conj__subset__def, fact_136_Collect__mono, fact_2_assms_I2_J, fact_229_specify__left, fact_61_inf_Oleft__idem, fact_55_order__subst2, fact_88_inf_OorderE, fact_158_ord__eq__le__eq__trans, tcon_Set_Oset___Lattices_Osemilattice__inf_7, fact_188_pwD1, fact_183_nofail__simps_I2_J, fact_9_SPEC__trans, fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062, fact_238_inf__top__right, fact_237_inf__top__left, fact_247_bind__FAIL, fact_104_inf_OcoboundedI1, fact_126_Collect__conj__eq, tcon_fun___Orderings_Opreorder, fact_3_assms_I1_J, fact_151_subset__Collect__iff, fact_173_less__eq__nres_Osimps_I3_J, fact_217_let__to__bind__conv, fact_203_inf__RETURN__RES_I1_J, fact_18_le__funD, fact_114_Int__iff, fact_73_boolean__algebra__cancel_Oinf1, fact_91_le__iff__inf, fact_113_IntI, fact_162_inf__nres_Oelims, fact_56_inf_Obounded__iff, fact_46_le__cases3, fact_155_inf1E, fact_186_nres__order__simps_I21_J, fact_175_less__eq__nres_Oelims_I1_J, fact_33_dual__order_Otrans, tcon_HOL_Obool___Lattices_Osemilattice__inf_17, fact_250_nres__more__simps_I1_J, fact_165_nres_Odistinct_I1_J, fact_212_bind__SUCCEED, fact_160_prop__restrict, tcon_Product__Type_Ounit___Lattices_Olattice_31, fact_68_inf__commute, fact_232_bind__le__shift, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice__bot_37, fact_206_If__bind__distrib, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_40, tcon_fun___Orderings_Oorder, fact_30_order__mono__setup_Omono__if, fact_144_Int__lower1, tcon_Product__Type_Ounit___Orderings_Oorder_32, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_43, fact_236_empty__subsetI, tcon_Product__Type_Ounit___Orderings_Oord_34, fact_109_Collect__subset, fact_49_eq__refl, fact_36_order__trans, fact_168_sup__nres_Oinduct, fact_199_RETURN__to__SPEC__rule, fact_134_subset__trans, fact_185_nofail__simps_I3_J, fact_87_le__infI2, fact_128_Int__left__commute, fact_221_SUCCEED__rule, tcon_Product__Type_Ounit___Lattices_Osemilattice__inf_27, tcon_Product__Type_Ounit___Lattices_Obounded__lattice__bot_26, tcon_fun___Lattices_Obounded__semilattice__inf__top, fact_42_mem__Collect__eq, fact_64_inf__right__idem, fact_123_Int__commute, fact_190_nofail__antimono__fun, fact_218_nres__inequalities_I5_J, tcon_Product__Type_Ounit___Orderings_Olinorder_30, fact_0_nres__more__simps_I4_J, fact_209_nres__monad2, tcon_HOL_Obool___Orderings_Oord_23, fact_161_Powp__mono, fact_80_inf__sup__ord_I1_J, fact_97_inf_OboundedI, fact_51_antisym, fact_131_Int__Collect__mono, fact_178_Greatest__equality, fact_198_lhs__step__RES, fact_99_inf_Oorder__iff, fact_65_inf__nres_Osimps_I3_J, fact_124_inf__set__def, fact_72_boolean__algebra__cancel_Oinf2, fact_174_inf__nres_Osimps_I2_J, fact_225_bot_Oextremum__unique, fact_6_RES__rule, fact_22_le__fun__def, fact_8_SPEC__rule, fact_79_inf__sup__ord_I2_J, fact_189_le__nofailI, fact_98_inf__greatest, fact_47_order_Otrans, fact_171_less__eq__nres_Osimps_I1_J, fact_63_inf_Oright__idem, fact_66_inf__left__commute, fact_10_lhs__step__If, fact_244_inf__top_Oright__neutral, tcon_Product__Type_Ounit___Lattices_Obounded__lattice_1, fact_211_nres__order__simps_I2_J, tcon_HOL_Obool___Orderings_Oorder__bot_18, fact_81_inf__le1, tcon_fun___Lattices_Olattice, fact_154_inf1I
% 53.36/31.36 % No. of inferences in proof: 624
% 53.36/31.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 30999 ms resp. 30188 ms w/o parsing
% 54.59/31.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 54.59/31.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------