%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP159^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 146.45s 121.62s
% Output : Refutation 147.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 298
% Syntax : Number of formulae : 598 ( 210 unt; 0 typ; 0 def)
% Number of atoms : 2251 ( 352 equ; 14 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 8624 ( 114 ~; 11 |; 68 &;7757 @)
% ( 0 <=>; 674 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 214 ( 214 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 41 usr; 8 con; 0-5 aty)
% Number of variables : 2032 ( 78 ^;1924 !; 30 ?;2032 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[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(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_top_decl,type,
order_top:
!>[TA: $tType] : $o ).
thf(bounded_lattice_top_decl,type,
bounded_lattice_top:
!>[TA: $tType] : $o ).
thf(comple187826305attice_decl,type,
comple187826305attice:
!>[TA: $tType] : $o ).
thf(bNF_Ca1785829860lChain_decl,type,
bNF_Ca1785829860lChain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bijective_decl,type,
bijective:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > $o ) ).
thf(fun_of_rel_decl,type,
fun_of_rel:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > TB > TA ) ).
thf(rel_restrict_decl,type,
rel_restrict:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(uncurry_decl,type,
uncurry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > 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(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(refine1687780735RETURN_decl,type,
refine1687780735RETURN:
!>[TA: $tType] : ( TA > ( refine1665802226e_nres @ TA ) ) ).
thf(refine81118332bs_fun_decl,type,
refine81118332bs_fun:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( refine1665802226e_nres @ TB ) > ( 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(refine1073749519nc_fun_decl,type,
refine1073749519nc_fun:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( refine1665802226e_nres @ TA ) > ( refine1665802226e_nres @ TB ) ) ).
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(refine605929679le_RES_decl,type,
refine605929679le_RES:
!>[TA: $tType] : ( ( set @ TA ) > ( refine1665802226e_nres @ TA ) ) ).
thf(refine1672542526he_RES_decl,type,
refine1672542526he_RES:
!>[TA: $tType] : ( ( refine1665802226e_nres @ TA ) > ( set @ TA ) ) ).
thf(domain_decl,type,
domain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TB ) ) ).
thf(id_decl,type,
id:
!>[TA: $tType] : ( set @ ( product_prod @ TA @ TA ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(transitive_rtrancl_decl,type,
transitive_rtrancl:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(transitive_trancl_decl,type,
transitive_trancl:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(r_decl,type,
r: set @ ( product_prod @ a @ b ) ).
thf(x_decl,type,
x: refine1665802226e_nres @ a ).
thf(140,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_rtrancl @ TA @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_rtrancl__subset__rtrancl) ).
thf(645,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_rtrancl @ TA @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(276,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_ord__le__eq__trans) ).
thf(1036,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)],[276]) ).
thf(135,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_rtrancl__image__unfold__right) ).
thf(629,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(271,axiom,
! [TA: $tType] : ( order_top @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__top_29) ).
thf(1024,plain,
! [TA: $tType] : ( order_top @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_DomainE) ).
thf(347,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(229,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Id__SPEC__refine) ).
thf(893,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(70,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( id @ TA ) ) )
= ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_rtrancl__reflcl) ).
thf(468,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( id @ TA ) ) )
= ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_53_ord__eq__le__eq__trans) ).
thf(941,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)],[243]) ).
thf(289,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_r__le__rtrancl) ).
thf(1110,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(75,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(481,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(255,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_le__cases) ).
thf(977,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)],[255]) ).
thf(263,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_equalityD1) ).
thf(994,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)],[263]) ).
thf(176,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_top__set__def) ).
thf(741,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(62,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_UnI1) ).
thf(449,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(32,axiom,
top @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Otop_25) ).
thf(379,plain,
top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(221,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_rtrancl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rtrancl__mono__rightI) ).
thf(878,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_rtrancl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',fact_108_nres__order__simps_I5_J) ).
thf(655,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)],[144]) ).
thf(88,axiom,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_6) ).
thf(511,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(284,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_equalityE) ).
thf(1078,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)],[284]) ).
thf(35,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_ball__Un) ).
thf(384,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(96,axiom,
! [TA: $tType,A: set @ TA] :
( ( refine1672542526he_RES @ TA @ ( refine605929679le_RES @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_the__RES_Osimps) ).
thf(533,plain,
! [TA: $tType,A: set @ TA] :
( ( refine1672542526he_RES @ TA @ ( refine605929679le_RES @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(166,axiom,
! [TA: $tType] : ( top @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_32) ).
thf(715,plain,
! [TA: $tType] : ( top @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(244,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ A @ B ) ) @ ( rel_restrict @ TA @ ( transitive_trancl @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_rel__restrict__trancl__sub) ).
thf(945,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ A @ B ) ) @ ( rel_restrict @ TA @ ( transitive_trancl @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',fact_98_RES__rule) ).
thf(930,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)],[239]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( domain @ TA @ TB @ B ) )
=> ( ( refine81118332bs_fun @ TA @ TB @ B @ ( refine605929679le_RES @ TA @ A ) )
= ( refine605929679le_RES @ TB @ ( image @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_abs__fun__simps_I2_J) ).
thf(670,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( domain @ TA @ TB @ B ) )
=> ( ( refine81118332bs_fun @ TA @ TB @ B @ ( refine605929679le_RES @ TA @ A ) )
= ( refine605929679le_RES @ TB @ ( image @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(178,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ B ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_conc__trans__additional_I5_J) ).
thf(747,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ B ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(234,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ B ) @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_abs__trans__additional_I6_J) ).
thf(913,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ B ) @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(44,axiom,
order_top @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__top_21) ).
thf(404,plain,
order_top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(51,axiom,
! [TA: $tType,A: TA] : ( refine1102455758nofail @ TA @ ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_nofail__simps_I3_J) ).
thf(417,plain,
! [TA: $tType,A: TA] : ( refine1102455758nofail @ TA @ ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rel__restrict__lift) ).
thf(301,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ C @ D ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB ),C: TA > $o] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ( ! [D: TA,E: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Domain_Oinducts) ).
thf(436,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB ),C: TA > $o] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ( ! [D: TA,E: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(225,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1687780735RETURN @ TB @ A ) @ ( refine1073749519nc_fun @ TB @ TA @ C @ ( refine1687780735RETURN @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_RETURN__refine) ).
thf(885,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1687780735RETURN @ TB @ A ) @ ( refine1073749519nc_fun @ TB @ TA @ C @ ( refine1687780735RETURN @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',fact_48_GreatestI2__order) ).
thf(1046,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)],[279]) ).
thf(112,axiom,
order_top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_14) ).
thf(570,plain,
order_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(168,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_eq__iff) ).
thf(719,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)],[168]) ).
thf(190,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_subset__UnE) ).
thf(785,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(20,axiom,
! [TA: $tType] :
( ( (=) @ ( refine1665802226e_nres @ TA ) )
= ( ^ [A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
= ( refine1102455758nofail @ TA @ B ) )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
= ( refine1315500908_inres @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_pw__eq__iff) ).
thf(344,plain,
! [TA: $tType] :
( ( (=) @ ( refine1665802226e_nres @ TA ) )
= ( ^ [A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
= ( refine1102455758nofail @ TA @ B ) )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
= ( refine1315500908_inres @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(240,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Un__mono) ).
thf(934,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_pair__in__Id__conv) ).
thf(587,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_nres__order__simps_I20_J) ).
thf(619,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)],[131]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(559,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(127,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( rel_restrict @ TA @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_rel__restrict__sub) ).
thf(606,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( rel_restrict @ TA @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(50,axiom,
comple187826305attice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_12) ).
thf(416,plain,
comple187826305attice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(291,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: refine1665802226e_nres @ TB,C: set @ ( product_prod @ TB @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ B ) @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_abs__trans__additional_I1_J) ).
thf(1115,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: refine1665802226e_nres @ TB,C: set @ ( product_prod @ TB @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ B ) @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Domain_Ocases) ).
thf(492,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_top__apply) ).
thf(756,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(277,axiom,
! [TA: $tType] :
( ( refine1315500908_inres @ TA )
= ( ^ [A: refine1665802226e_nres @ TA,B: TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_inres__def) ).
thf(1040,plain,
! [TA: $tType] :
( ( refine1315500908_inres @ TA )
= ( ^ [A: refine1665802226e_nres @ TA,B: TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(206,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_Un__subset__iff) ).
thf(834,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',fact_97_if__rule) ).
thf(806,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)],[197]) ).
thf(74,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_15) ).
thf(480,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(173,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_top__conj_I2_J) ).
thf(734,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_subsetI) ).
thf(774,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)],[186]) ).
thf(40,axiom,
bounded_lattice_top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__top_13) ).
thf(396,plain,
bounded_lattice_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: refine1665802226e_nres @ TC,B: set @ ( product_prod @ TC @ TB ),C: refine1665802226e_nres @ TB,D: set @ ( product_prod @ TB @ TA ),E: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ A @ ( refine1073749519nc_fun @ TC @ TB @ B @ C ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( refine1073749519nc_fun @ TB @ TA @ D @ E ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ A @ ( refine1073749519nc_fun @ TC @ TB @ B @ ( refine1073749519nc_fun @ TB @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_conc__trans) ).
thf(660,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: refine1665802226e_nres @ TC,B: set @ ( product_prod @ TC @ TB ),C: refine1665802226e_nres @ TB,D: set @ ( product_prod @ TB @ TA ),E: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ A @ ( refine1073749519nc_fun @ TC @ TB @ B @ C ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ C @ ( refine1073749519nc_fun @ TB @ TA @ D @ E ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TC ) @ A @ ( refine1073749519nc_fun @ TC @ TB @ B @ ( refine1073749519nc_fun @ TB @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(264,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: $o,B: TB > TA,C: TB,D: TA,E: TB,F: TA] :
( ( A
=> ( ord_less_eq @ TA @ ( B @ C ) @ D ) )
=> ( ( ~ A
=> ( ord_less_eq @ TA @ ( B @ E ) @ F ) )
=> ( ord_less_eq @ TA @ ( B @ ( if @ TB @ A @ C @ E ) ) @ ( if @ TA @ A @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_transfer_Otransfer__if) ).
thf(998,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: $o,B: TB > TA,C: TB,D: TA,E: TB,F: TA] :
( ( A
=> ( ord_less_eq @ TA @ ( B @ C ) @ D ) )
=> ( ( ~ A
=> ( ord_less_eq @ TA @ ( B @ E ) @ F ) )
=> ( ord_less_eq @ TA @ ( B @ ( if @ TB @ A @ C @ E ) ) @ ( if @ TA @ A @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(93,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(527,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(126,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_eq__refl) ).
thf(602,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)],[126]) ).
thf(257,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_conc__trans__additional_I6_J) ).
thf(981,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_ord__le__eq__subst) ).
thf(766,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)],[185]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ TA @ D @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_rtrancl__image__advance__rtrancl) ).
thf(397,plain,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ B ) )
=> ( member @ TA @ D @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(156,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_UNIV__I) ).
thf(687,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(282,axiom,
! [TA: $tType,A: TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_nres__inequalities_I3_J) ).
thf(1072,plain,
! [TA: $tType,A: TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_nres__more__simps_I6_J) ).
thf(453,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(33,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( id @ TA ) )
= ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_rtrancl__reflcl__absorb) ).
thf(380,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( id @ TA ) )
= ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_nres__inequalities_I1_J) ).
thf(678,plain,
! [TA: $tType,A: set @ TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(183,axiom,
! [TA: $tType] :
( ( domain @ TA @ TA @ ( id @ TA ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Domain__Id) ).
thf(761,plain,
! [TA: $tType] :
( ( domain @ TA @ TA @ ( id @ TA ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',fact_115_nres__order__simps_I21_J) ).
thf(798,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)],[194]) ).
thf(102,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( id @ TA ) )
=> ( A
= ( id @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_relprop__triggers_I2_J) ).
thf(546,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(192,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_subset__UNIV) ).
thf(793,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(15,axiom,
! [TA: $tType] : ( bijective @ TA @ TA @ ( id @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_bijective__Id) ).
thf(334,plain,
! [TA: $tType] : ( bijective @ TA @ TA @ ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(248,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ A @ B ) @ B )
=> ( ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Image__closed__trancl) ).
thf(957,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ A @ B ) @ B )
=> ( ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TB @ ( refine1073749519nc_fun @ TB @ TA @ A @ B ) )
= ( refine1102455758nofail @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_pw__conc__nofail) ).
thf(825,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TB @ ( refine1073749519nc_fun @ TB @ TA @ A @ B ) )
= ( refine1102455758nofail @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(124,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_order__mono__setup_Orefl) ).
thf(598,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TA )] :
( ~ ( ord_less_eq @ ( set @ TB ) @ A @ ( domain @ TB @ TA @ B ) )
=> ( ( refine81118332bs_fun @ TB @ TA @ B @ ( refine605929679le_RES @ TB @ A ) )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_abs__fun__simps_I3_J) ).
thf(820,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TA )] :
( ~ ( ord_less_eq @ ( set @ TB ) @ A @ ( domain @ TB @ TA @ B ) )
=> ( ( refine81118332bs_fun @ TB @ TA @ B @ ( refine605929679le_RES @ TB @ A ) )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) )
=> ~ ( member @ TA @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_rel__restrict__trancl__notR_I2_J) ).
thf(561,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) )
=> ~ ( member @ TA @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_UnI2) ).
thf(392,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Un__assoc) ).
thf(424,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(46,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( transitive_trancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( id @ TA ) ) )
= ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_trancl__reflcl) ).
thf(407,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( transitive_trancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( id @ TA ) ) )
= ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(171,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 )
= ( ( ( refine1102455758nofail @ TB @ C )
=> ( refine1102455758nofail @ TA @ A ) )
& ! [D: TA] :
( ( ( refine1102455758nofail @ TA @ A )
& ( refine1315500908_inres @ TA @ A @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_pw__bind__le__iff) ).
thf(729,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 )
= ( ( ( refine1102455758nofail @ TB @ C )
=> ( refine1102455758nofail @ TA @ A ) )
& ! [D: TA] :
( ( ( refine1102455758nofail @ TA @ A )
& ( refine1315500908_inres @ TA @ A @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(270,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( A
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) )
=> ~ ! [B: set @ TA] :
( A
!= ( refine605929679le_RES @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_nres__cases) ).
thf(1021,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( A
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) )
=> ~ ! [B: set @ TA] :
( A
!= ( refine605929679le_RES @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(187,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_dual__order_Oantisym) ).
thf(778,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)],[187]) ).
thf(294,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: refine1665802226e_nres @ TC,C: refine1665802226e_nres @ TB,D: set @ ( product_prod @ TB @ TA ),E: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine81118332bs_fun @ TC @ TB @ A @ B ) @ C )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ D @ C ) @ E )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ D @ ( refine81118332bs_fun @ TC @ TB @ A @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_abs__trans) ).
thf(1123,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: refine1665802226e_nres @ TC,C: refine1665802226e_nres @ TB,D: set @ ( product_prod @ TB @ TA ),E: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine81118332bs_fun @ TC @ TB @ A @ B ) @ C )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ D @ C ) @ E )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ D @ ( refine81118332bs_fun @ TC @ TB @ A @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(217,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_top__greatest) ).
thf(862,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: ( TA > TB ) > ( product_prod @ TA @ TA ) > $o,B: TA > TB,C: product_prod @ TA @ TA] :
( ! [D: TA > TB,E: TA,F: TA] : ( A @ D @ ( product_Pair @ TA @ TA @ E @ F ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_pairself_Oinduct) ).
thf(349,plain,
! [TA: $tType,TB: $tType,A: ( TA > TB ) > ( product_prod @ TA @ TA ) > $o,B: TA > TB,C: product_prod @ TA @ TA] :
( ! [D: TA > TB,E: TA,F: TA] : ( A @ D @ ( product_Pair @ TA @ TA @ E @ F ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(274,axiom,
! [TA: $tType] : ( preorder @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_30) ).
thf(1032,plain,
! [TA: $tType] : ( preorder @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_subsetD) ).
thf(625,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)],[133]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_relChain__def) ).
thf(852,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(13,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( image @ TA @ TA @ ( transitive_trancl @ TA @ A ) @ B ) @ B )
= ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_trancl__image__by__rtrancl) ).
thf(329,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( image @ TA @ TA @ ( transitive_trancl @ TA @ A ) @ B ) @ B )
= ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(148,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_rtrancl__mono) ).
thf(665,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( transitive_rtrancl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_Ocomplete__lattice) ).
thf(583,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',fact_26_order__trans) ).
thf(889,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)],[227]) ).
thf(67,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_3) ).
thf(461,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_218_nres__monad1) ).
thf(551,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)],[104]) ).
thf(254,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_top__conj_I1_J) ).
thf(974,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(266,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ~ ( refine1102455758nofail @ TA @ A ) )
= ( A
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_not__nofail__iff) ).
thf(1012,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ~ ( refine1102455758nofail @ TA @ A ) )
= ( A
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(211,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Collect__mono__iff) ).
thf(847,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)],[211]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > TA,C: TB,D: TB] :
( ( member @ ( product_prod @ ( TB > TA ) @ ( TB > TA ) ) @ ( product_Pair @ ( TB > TA ) @ ( TB > TA ) @ A @ B ) @ ( id @ ( TB > TA ) ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( id @ TB ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( A @ C ) @ ( B @ D ) ) @ ( id @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rel__cong) ).
thf(566,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > TA,C: TB,D: TB] :
( ( member @ ( product_prod @ ( TB > TA ) @ ( TB > TA ) ) @ ( product_Pair @ ( TB > TA ) @ ( TB > TA ) @ A @ B ) @ ( id @ ( TB > TA ) ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( id @ TB ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( A @ C ) @ ( B @ D ) ) @ ( id @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(76,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Un__left__absorb) ).
thf(484,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TA > TB ) @ ( product_prod @ TA @ TA )] :
~ ! [B: TA > TB,C: TA,D: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( product_prod @ TA @ TA ) @ B @ ( product_Pair @ TA @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_pairself_Ocases) ).
thf(456,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TA > TB ) @ ( product_prod @ TA @ TA )] :
~ ! [B: TA > TB,C: TA,D: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( product_prod @ TA @ TA ) @ B @ ( product_Pair @ TA @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(209,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= A )
= ( refine1102455758nofail @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_intro__nofail_I2_J) ).
thf(842,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= A )
= ( refine1102455758nofail @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ ( transitive_trancl @ TA @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_rel__restrict__trancl__mem) ).
thf(317,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ ( transitive_trancl @ TA @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(142,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_subset__Un__eq) ).
thf(650,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(268,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/sandbox2/benchmark/theBenchmark.p',fact_19_order__mono__setup_Omono__let) ).
thf(1017,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)],[268]) ).
thf(293,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_UNIV__witness) ).
thf(1121,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(122,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_order_Otrans) ).
thf(593,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)],[122]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_le__funE) ).
thf(783,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)],[189]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ TB @ A @ ( domain @ TB @ TA @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Domain__iff) ).
thf(499,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ TB @ A @ ( domain @ TB @ TA @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',fact_121_RETURN__rule) ).
thf(857,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)],[215]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Un__UNIV__right) ).
thf(697,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(286,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Collect__mono) ).
thf(1089,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)],[286]) ).
thf(71,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ C @ D ) ) )
=> ( ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ C ) )
=> ? [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ C @ D ) ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ D )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ B ) @ ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_trancl__union__outside) ).
thf(471,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ C @ D ) ) )
=> ( ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ C ) )
=> ? [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ C @ D ) ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ D )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ B ) @ ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(78,axiom,
comple187826305attice @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Complete__Lattices_Ocomplete__lattice_19) ).
thf(488,plain,
comple187826305attice @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(18,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ A )
=> ( ( refine605929679le_RES @ TA @ ( refine1672542526he_RES @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_the__RES__inv) ).
thf(339,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)],[18]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
= ( top_top @ ( set @ TA ) ) )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_relprop__UNIV__orient) ).
thf(637,plain,
! [TA: $tType,A: set @ TA] :
( ( A
= ( top_top @ ( set @ TA ) ) )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TA @ TB @ ( sup_sup @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( domain @ TA @ TB @ A ) @ ( domain @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Domain__Un__eq) ).
thf(489,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TA @ TB @ ( sup_sup @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( domain @ TA @ TB @ A ) @ ( domain @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(121,axiom,
! [TA: $tType] :
( ( transitive_rtrancl @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] : ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_trancl @ TA @ A ) @ ( id @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_rtrancl__trancl__reflcl) ).
thf(590,plain,
! [TA: $tType] :
( ( transitive_rtrancl @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] : ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_trancl @ TA @ A ) @ ( id @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(252,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Un__upper1) ).
thf(970,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(103,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( id @ TA ) )
=> ( ( id @ TA )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_relprop__triggers_I3_J) ).
thf(547,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( id @ TA ) )
=> ( ( id @ TA )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(163,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: product_prod @ TA @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_rtrancl @ TA @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_rtrancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_rtrancl__mono__mp) ).
thf(706,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: product_prod @ TA @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_rtrancl @ TA @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_rtrancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(105,axiom,
! [TA: $tType,A: set @ TA] :
( ( refine1315500908_inres @ TA @ ( refine605929679le_RES @ TA @ A ) )
= ( ^ [B: TA] : ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_inres__simps_I2_J) ).
thf(554,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)],[105]) ).
thf(180,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_antisym__conv) ).
thf(753,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)],[180]) ).
thf(283,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_subset__iff) ).
thf(1075,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)],[283]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > TA,C: TB] :
( ( member @ ( product_prod @ ( TB > TA ) @ ( TB > TA ) ) @ ( product_Pair @ ( TB > TA ) @ ( TB > TA ) @ A @ B ) @ ( id @ ( TB > TA ) ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( A @ C ) @ ( B @ C ) ) @ ( id @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_rel__fun__cong) ).
thf(476,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > TA,C: TB] :
( ( member @ ( product_prod @ ( TB > TA ) @ ( TB > TA ) ) @ ( product_Pair @ ( TB > TA ) @ ( TB > TA ) @ A @ B ) @ ( id @ ( TB > TA ) ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( A @ C ) @ ( B @ C ) ) @ ( id @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(141,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_order__class_Oorder_Oantisym) ).
thf(647,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)],[141]) ).
thf(259,axiom,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( transitive_trancl @ TA @ B ) )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ A @ ( transitive_trancl @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_trancl__mono) ).
thf(985,plain,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( transitive_trancl @ TA @ B ) )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ A @ ( transitive_trancl @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TB @ TA ),D: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ C )
=> ( ( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ C )
=> ( D @ A @ B ) )
=> ? [E: TB,F: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ E @ F ) @ C )
& ( D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_bex2I) ).
thf(515,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TB @ TA ),D: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ C )
=> ( ( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ C )
=> ( D @ A @ B ) )
=> ? [E: TB,F: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ E @ F ) @ C )
& ( D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(297,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TB @ TA ),C: TA > $o] :
( ? [D: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1687780735RETURN @ TB @ A ) @ ( refine1073749519nc_fun @ TB @ TA @ B @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_RETURN__SPEC__refine) ).
thf(1131,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TB @ TA ),C: TA > $o] :
( ? [D: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ D ) @ B )
& ( C @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1687780735RETURN @ TB @ A ) @ ( refine1073749519nc_fun @ TB @ TA @ B @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TB,C: refine1665802226e_nres @ TA,D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ A @ B ) @ C )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ C ) @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_abs__trans__additional_I3_J) ).
thf(911,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TB,C: refine1665802226e_nres @ TA,D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ A @ B ) @ C )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ C ) @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(29,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(371,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)],[29]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_le__fun__def) ).
thf(622,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)],[132]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_UNIV__eq__I) ).
thf(837,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(285,axiom,
! [TA: $tType] :
( ( refine1315500908_inres @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) )
= ( ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_inres__simps_I1_J) ).
thf(1086,plain,
! [TA: $tType] :
( ( refine1315500908_inres @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) )
= ( ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(87,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Un__commute) ).
thf(508,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',fact_247_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J) ).
thf(1026,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)],[272]) ).
thf(147,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( domain @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_Domain__rtrancl) ).
thf(662,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( domain @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(237,axiom,
! [TA: $tType] : ( order @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_31) ).
thf(926,plain,
! [TA: $tType] : ( order @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ ( product_prod @ TB @ TA )] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ? [E: TA] :
( ( member @ TA @ E @ B )
& ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ D @ E ) @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine605929679le_RES @ TB @ A ) @ ( refine1073749519nc_fun @ TB @ TA @ C @ ( refine605929679le_RES @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_RES__refine) ).
thf(633,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ ( product_prod @ TB @ TA )] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ? [E: TA] :
( ( member @ TA @ E @ B )
& ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ D @ E ) @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine605929679le_RES @ TB @ A ) @ ( refine1073749519nc_fun @ TB @ TA @ C @ ( refine605929679le_RES @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( A != B )
=> ~ ! [D: TA] :
( ( A != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_converse__rtranclE_H) ).
thf(360,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( A != B )
=> ~ ! [D: TA] :
( ( A != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(232,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( ( refine1102455758nofail @ TA @ B )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ B @ C )
=> ( refine1315500908_inres @ TA @ A @ C ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_pw__leI) ).
thf(906,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( ( refine1102455758nofail @ TA @ B )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ B @ C )
=> ( refine1315500908_inres @ TA @ A @ C ) ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(48,axiom,
bounded_lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice_2) ).
thf(412,plain,
bounded_lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(573,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(157,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Un__upper2) ).
thf(689,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rel__restrict__notR_I1_J) ).
thf(444,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(513,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(56,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
= ( refine1102455758nofail @ TA @ B ) )
=> ( ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
= ( refine1315500908_inres @ TA @ B @ C ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_pw__eqI) ).
thf(430,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
= ( refine1102455758nofail @ TA @ B ) )
=> ( ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
= ( refine1315500908_inres @ TA @ B @ C ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(231,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_linear) ).
thf(904,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)],[231]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( domain @ TA @ TB @ A ) @ ( domain @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Domain__mono) ).
thf(732,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( domain @ TA @ TB @ A ) @ ( domain @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(295,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_order__subst1) ).
thf(1125,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)],[295]) ).
thf(101,axiom,
ord @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_26) ).
thf(545,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType] :
( ( bijective @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB )] :
( ! [B: TA,C: TB,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ A ) )
=> ( C = D ) )
& ! [B: TA,C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ A )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_bijective__def) ).
thf(413,plain,
! [TA: $tType,TB: $tType] :
( ( bijective @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB )] :
( ! [B: TA,C: TB,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ A ) )
=> ( C = D ) )
& ! [B: TA,C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ A )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(220,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_antisym) ).
thf(875,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)],[220]) ).
thf(116,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine463715084e_bind @ TA @ TA @ A @ ( refine1687780735RETURN @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_nres__monad2) ).
thf(577,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine463715084e_bind @ TA @ TA @ A @ ( refine1687780735RETURN @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_order__subst2) ).
thf(711,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)],[165]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',fact_101_SPEC__cons__rule) ).
thf(641,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)],[139]) ).
thf(299,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Un__absorb1) ).
thf(1139,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(241,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( refine1073749519nc_fun @ TA @ TB @ A @ ( top_top @ ( refine1665802226e_nres @ TB ) ) )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_conc__fun__FAIL) ).
thf(936,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( refine1073749519nc_fun @ TA @ TB @ A @ ( top_top @ ( refine1665802226e_nres @ TB ) ) )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(7,axiom,
bounded_lattice_top @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top_20) ).
thf(313,plain,
bounded_lattice_top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_100_SPEC__trans) ).
thf(611,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)],[129]) ).
thf(83,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_16) ).
thf(498,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_4) ).
thf(466,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',fact_161_le__nofailI) ).
thf(947,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)],[245]) ).
thf(99,axiom,
! [TA: $tType,A: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( product_Pair @ TA @ TA @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_IdE) ).
thf(540,plain,
! [TA: $tType,A: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( product_Pair @ TA @ TA @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(205,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_top_Oextremum__unique) ).
thf(831,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(154,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_verit__la__disequality) ).
thf(681,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(292,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ord__eq__le__trans) ).
thf(1117,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)],[292]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TB )] :
( ( refine1102455758nofail @ TB @ ( refine463715084e_bind @ TA @ TB @ A @ B ) )
= ( ( refine1102455758nofail @ TA @ A )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
=> ( refine1102455758nofail @ TB @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_pw__bind__nofail) ).
thf(419,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: TA > ( refine1665802226e_nres @ TB )] :
( ( refine1102455758nofail @ TB @ ( refine463715084e_bind @ TA @ TB @ A @ B ) )
= ( ( refine1102455758nofail @ TA @ A )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
=> ( refine1102455758nofail @ TB @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ B )
=> ( member @ TA @ D @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_rtrancl__image__advance) ).
thf(451,plain,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( member @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ B )
=> ( member @ TA @ D @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(174,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ B ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_conc__trans__additional_I4_J) ).
thf(737,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ B ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ C ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(4,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA,C: set @ TA] :
( ( rel_restrict @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( rel_restrict @ TA @ ( rel_restrict @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_rel__restrict__union) ).
thf(303,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA,C: set @ TA] :
( ( rel_restrict @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( rel_restrict @ TA @ ( rel_restrict @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: set @ ( product_prod @ TB @ TA ),C: refine1665802226e_nres @ TA,D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ C ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ C @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_conc__trans__additional_I3_J) ).
thf(764,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: set @ ( product_prod @ TB @ TA ),C: refine1665802226e_nres @ TA,D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ C ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ C @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(256,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_le__funD) ).
thf(979,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)],[256]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Domain_ODomainI) ).
thf(377,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(261,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: refine1665802226e_nres @ TB,C: set @ ( product_prod @ TB @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine81118332bs_fun @ TB @ TB @ ( id @ TB ) @ A ) @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ B ) @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_abs__trans__additional_I2_J) ).
thf(990,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: refine1665802226e_nres @ TB,C: set @ ( product_prod @ TB @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine81118332bs_fun @ TB @ TB @ ( id @ TB ) @ A ) @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ B ) @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(222,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Un__least) ).
thf(880,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(278,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TA] :
( ( ( refine1073749519nc_fun @ TB @ TA @ A @ B )
= ( top_top @ ( refine1665802226e_nres @ TB ) ) )
= ( B
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_conc__fun__fail__iff_I1_J) ).
thf(1043,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TA] :
( ( ( refine1073749519nc_fun @ TB @ TA @ A @ B )
= ( top_top @ ( refine1665802226e_nres @ TB ) ) )
= ( B
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Domain_Osimps) ).
thf(387,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_bex__Un) ).
thf(494,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(136,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( rel_restrict @ TA @ C @ B ) @ ( rel_restrict @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_rel__restrict__mono2) ).
thf(631,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( rel_restrict @ TA @ C @ B ) @ ( rel_restrict @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(199,axiom,
! [TA: $tType] :
~ ( refine1102455758nofail @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_nofail__simps_I1_J) ).
thf(816,plain,
! [TA: $tType] :
~ ( refine1102455758nofail @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(170,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_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)],[170]) ).
thf(161,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_less_eq @ ( $o > TA ) )
= ( ^ [A: $o > TA,B: $o > TA] :
( ( ord_less_eq @ TA @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_less_eq @ TA @ ( A @ $true ) @ ( B @ $true ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__rel__bool__arg__iff) ).
thf(700,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_less_eq @ ( $o > TA ) )
= ( ^ [A: $o > TA,B: $o > TA] :
( ( ord_less_eq @ TA @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_less_eq @ TA @ ( A @ $true ) @ ( B @ $true ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(230,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( refine1102455758nofail @ TA @ B ) )
=> ( ! [C: TA] :
( ( refine1102455758nofail @ TA @ A )
=> ( ( refine1315500908_inres @ TA @ B @ C )
=> ( refine1315500908_inres @ TA @ A @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_pw__leI_H) ).
thf(895,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( refine1102455758nofail @ TA @ B ) )
=> ( ! [C: TA] :
( ( refine1102455758nofail @ TA @ A )
=> ( ( refine1315500908_inres @ TA @ B @ C )
=> ( refine1315500908_inres @ TA @ A @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(235,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_subset__eq) ).
thf(915,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)],[235]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',fact_43_Greatest__equality) ).
thf(1061,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)],[280]) ).
thf(290,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_top_Oextremum__uniqueI) ).
thf(1112,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(91,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( image @ TA @ TA @ ( transitive_trancl @ TA @ A ) @ B )
= ( image @ TA @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_trancl__Image__unfold__right) ).
thf(521,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( image @ TA @ TA @ ( transitive_trancl @ TA @ A ) @ B )
= ( image @ TA @ TA @ A @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(258,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_trancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_trancl__sub) ).
thf(983,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ ( transitive_trancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( id @ TB ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( C @ A ) @ ( C @ B ) ) @ ( id @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_rel__arg__cong) ).
thf(399,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( id @ TB ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( C @ A ) @ ( C @ B ) ) @ ( id @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_120_RETURN__to__SPEC__rule) ).
thf(695,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)],[159]) ).
thf(224,axiom,
! [TA: $tType] : ( bounded_lattice_top @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice__top_28) ).
thf(883,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(267,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_subset__refl) ).
thf(1015,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(128,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Un__UNIV__left) ).
thf(608,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(109,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Un__absorb) ).
thf(563,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ~ ( member @ TA @ A @ ( domain @ TA @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ ( transitive_rtrancl @ TA @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Not__Domain__rtrancl) ).
thf(505,plain,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ~ ( member @ TA @ A @ ( domain @ TA @ TA @ B ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ ( transitive_rtrancl @ TA @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_le__funI) ).
thf(653,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)],[143]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ! [E: TA] : ( ord_less_eq @ TB @ ( A @ ( B @ E ) ) @ ( C @ E ) )
=> ( ord_less_eq @ TB @ ( A @ ( B @ D ) ) @ ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_transfer_Otransfer__Let) ).
thf(658,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ! [E: TA] : ( ord_less_eq @ TB @ ( A @ ( B @ E ) ) @ ( C @ E ) )
=> ( ord_less_eq @ TB @ ( A @ ( B @ D ) ) @ ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(394,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_UnCI) ).
thf(306,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ C @ D ) @ D )
=> ( ~ ( member @ TA @ B @ D )
=> ~ ( ~ ( member @ TA @ A @ D )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_E__closed__restr__reach__cases) ).
thf(722,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ C @ D ) @ D )
=> ( ~ ( member @ TA @ B @ D )
=> ~ ( ~ ( member @ TA @ A @ D )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(275,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: set @ ( product_prod @ TB @ TA ),C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1073749519nc_fun @ TB @ TA @ A @ C ) @ ( refine1073749519nc_fun @ TB @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_conc__fun__R__mono) ).
thf(1034,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: set @ ( product_prod @ TB @ TA ),C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine1073749519nc_fun @ TB @ TA @ A @ C ) @ ( refine1073749519nc_fun @ TB @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',fact_0_nres__order__simps_I4_J) ).
thf(675,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)],[152]) ).
thf(95,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA] :
( ~ ( refine1102455758nofail @ TA @ A )
=> ( refine1315500908_inres @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_not__nofail__inres) ).
thf(531,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA] :
( ~ ( refine1102455758nofail @ TA @ A )
=> ( refine1315500908_inres @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(193,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Un__absorb2) ).
thf(795,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(30,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( domain @ TA @ TA @ ( transitive_trancl @ TA @ A ) )
= ( domain @ TA @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_trancl__domain) ).
thf(374,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( domain @ TA @ TA @ ( transitive_trancl @ TA @ A ) )
= ( domain @ TA @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(77,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_18) ).
thf(487,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',fact_99_SPEC__rule) ).
thf(812,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)],[198]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_subrelI) ).
thf(749,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(242,axiom,
! [TA: $tType] : ( comple187826305attice @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Complete__Lattices_Ocomplete__lattice_27) ).
thf(939,plain,
! [TA: $tType] : ( comple187826305attice @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(19,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_10) ).
thf(342,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( image @ TA @ TA @ ( transitive_trancl @ TA @ A ) @ B )
= ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ ( image @ TA @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_trancl__Image__unfold__left) ).
thf(355,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ TA] :
( ( image @ TA @ TA @ ( transitive_trancl @ TA @ A ) @ B )
= ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ ( image @ TA @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(202,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Image__mono) ).
thf(823,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(106,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_7) ).
thf(557,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(281,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: set @ ( product_prod @ TB @ TA ),C: refine1665802226e_nres @ TA,D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ C ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ C @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_conc__trans__additional_I1_J) ).
thf(1070,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: set @ ( product_prod @ TB @ TA ),C: refine1665802226e_nres @ TA,D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ C ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ C @ D )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(226,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_subset__trans) ).
thf(887,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)],[226]) ).
thf(247,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_sup__top__left) ).
thf(954,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(175,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_iso__tuple__UNIV__I) ).
thf(739,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(6,axiom,
! [TA: $tType] :
( ( refine406925620_inres @ TA )
= ( ^ [A: refine1665802226e_nres @ TA,B: TA] :
( ( refine1102455758nofail @ TA @ A )
& ( refine1315500908_inres @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_nf__inres__def) ).
thf(310,plain,
! [TA: $tType] :
( ( refine406925620_inres @ TA )
= ( ^ [A: refine1665802226e_nres @ TA,B: TA] :
( ( refine1102455758nofail @ TA @ A )
& ( refine1315500908_inres @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(117,axiom,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA @ ( id @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Image__Id) ).
thf(580,plain,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA @ ( id @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(214,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ C ) )
=> ( ~ ( member @ TA @ A @ D )
=> ( ~ ( member @ TA @ B @ D )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ C @ D ) @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_rel__restrict__tranclI) ).
thf(855,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ C ) )
=> ( ~ ( member @ TA @ A @ D )
=> ( ~ ( member @ TA @ B @ D )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ C @ D ) @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',fact_20_order__mono__setup_Omono__if) ).
thf(673,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)],[151]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',fact_154_nofail__antimono__fun) ).
thf(791,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)],[191]) ).
thf(119,axiom,
! [TA: $tType,A: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_IdI) ).
thf(585,plain,
! [TA: $tType,A: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(167,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_top1I) ).
thf(717,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(85,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ A ) @ B )
= ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_nf__inres__RES) ).
thf(502,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)],[85]) ).
thf(208,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( rel_restrict @ TA @ A @ C ) @ ( rel_restrict @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_rel__restrict__mono) ).
thf(840,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( rel_restrict @ TA @ A @ C ) @ ( rel_restrict @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(463,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(17,axiom,
preorder @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Opreorder_22) ).
thf(338,plain,
preorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(115,axiom,
linorder @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_23) ).
thf(576,plain,
linorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(246,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) )
= ( ^ [A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ B )
=> ( ( refine1102455758nofail @ TA @ A )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
=> ( refine1315500908_inres @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_pw__le__iff) ).
thf(951,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) )
= ( ^ [A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ B )
=> ( ( refine1102455758nofail @ TA @ A )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
=> ( refine1315500908_inres @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( refine81118332bs_fun @ TB @ TA @ A @ ( top_top @ ( refine1665802226e_nres @ TB ) ) )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_abs__fun__simps_I1_J) ).
thf(744,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( refine81118332bs_fun @ TB @ TA @ A @ ( top_top @ ( refine1665802226e_nres @ TB ) ) )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(16,axiom,
! [TA: $tType,A: set @ TA] : ( refine1102455758nofail @ TA @ ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_nofail__simps_I2_J) ).
thf(336,plain,
! [TA: $tType,A: set @ TA] : ( refine1102455758nofail @ TA @ ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',fact_109_less__eq__nres_Osimps_I2_J) ).
thf(703,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)],[162]) ).
thf(130,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_linorder__wlog) ).
thf(613,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)],[130]) ).
thf(125,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ C @ B ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_rtrancl__reachable__induct) ).
thf(600,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ C @ B ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',fact_57_subset__Collect__conv) ).
thf(864,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)],[218]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_BNF__Greatest__Fixpoint_OIdD) ).
thf(314,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(123,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_subset__antisym) ).
thf(595,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)],[123]) ).
thf(82,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(497,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(216,axiom,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
( A
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_nofail__def) ).
thf(859,plain,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
( A
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(61,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Un__left__commute) ).
thf(446,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ ( product_prod @ TA @ TA )] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ ( rel_restrict @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_rel__restrictI) ).
thf(571,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ ( product_prod @ TA @ TA )] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ ( rel_restrict @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(210,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ A ) @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ B ) @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_abs__trans__additional_I4_J) ).
thf(845,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ A ) @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ B ) @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(134,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ A ) @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_abs__trans__additional_I5_J) ).
thf(627,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TA @ TA @ ( id @ TA ) @ A ) @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ C )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(98,axiom,
bounded_lattice @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Obounded__lattice_1) ).
thf(539,plain,
bounded_lattice @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: refine1665802226e_nres @ TA,C: TB] :
( ( refine1315500908_inres @ TB @ ( refine81118332bs_fun @ TA @ TB @ A @ B ) @ C )
= ( ( refine1102455758nofail @ TB @ ( refine81118332bs_fun @ TA @ TB @ A @ B ) )
=> ? [D: TA] :
( ( refine1315500908_inres @ TA @ B @ D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_pw__abs__inres) ).
thf(524,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: refine1665802226e_nres @ TA,C: TB] :
( ( refine1315500908_inres @ TB @ ( refine81118332bs_fun @ TA @ TB @ A @ B ) @ C )
= ( ( refine1102455758nofail @ TB @ ( refine81118332bs_fun @ TA @ TB @ A @ B ) )
=> ? [D: TA] :
( ( refine1315500908_inres @ TA @ B @ D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(182,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: product_prod @ TA @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_trancl @ TA @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_trancl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_trancl__mono__mp) ).
thf(759,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: product_prod @ TA @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_trancl @ TA @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ C @ ( transitive_trancl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(228,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nres__order__simps_I3_J) ).
thf(891,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(28,axiom,
! [TA: $tType,A: TA] :
( ( refine1315500908_inres @ TA @ ( refine1687780735RETURN @ TA @ A ) )
= ( (=) @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_inres__simps_I3_J) ).
thf(368,plain,
! [TA: $tType,A: TA] :
( ( refine1315500908_inres @ TA @ ( refine1687780735RETURN @ TA @ A ) )
= ( (=) @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(288,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( refine1315500908_inres @ TA @ A @ C )
=> ( refine1315500908_inres @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_pwD2) ).
thf(1108,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( refine1315500908_inres @ TA @ A @ C )
=> ( refine1315500908_inres @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(250,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( top_top @ TA ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_meta__le__everything__if__top) ).
thf(963,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( top_top @ TA ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(10,axiom,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
? [B: set @ TA] :
( A
= ( refine605929679le_RES @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_nofail__RES__conv) ).
thf(319,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)],[10]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TB @ ( refine81118332bs_fun @ TA @ TB @ A @ B ) )
= ( ( refine1102455758nofail @ TA @ B )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ B @ C )
=> ( member @ TA @ C @ ( domain @ TA @ TB @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_pw__abs__nofail) ).
thf(351,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TB @ ( refine81118332bs_fun @ TA @ TB @ A @ B ) )
= ( ( refine1102455758nofail @ TA @ B )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ B @ C )
=> ( member @ TA @ C @ ( domain @ TA @ TB @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(37,axiom,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_5) ).
thf(390,plain,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(401,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',fact_160_pwD1) ).
thf(781,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)],[188]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_in__mono) ).
thf(1030,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)],[273]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top) ).
thf(568,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(57,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_nres__more__simps_I4_J) ).
thf(433,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)],[57]) ).
thf(149,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_top__empty__eq) ).
thf(667,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ ( fun_of_rel @ TA @ TB @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_for__in__RI) ).
thf(478,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ ( fun_of_rel @ TA @ TB @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(34,axiom,
order @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_24) ).
thf(383,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',fact_216_bind__FAIL) ).
thf(684,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)],[155]) ).
thf(97,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_nf__inres__SPEC) ).
thf(536,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)],[97]) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',fact_16_Refine__Misc_Oif__mono) ).
thf(1133,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)],[298]) ).
thf(1,conjecture,
ord_less_eq @ ( refine1665802226e_nres @ a ) @ x @ ( refine1073749519nc_fun @ a @ b @ r @ ( top_top @ ( refine1665802226e_nres @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ x @ ( refine1073749519nc_fun @ a @ b @ r @ ( top_top @ ( refine1665802226e_nres @ b ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(300,plain,
~ ( ord_less_eq @ ( refine1665802226e_nres @ a ) @ x @ ( refine1073749519nc_fun @ a @ b @ r @ ( top_top @ ( refine1665802226e_nres @ b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(200,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_dual__order_Otrans) ).
thf(818,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)],[200]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top) ).
thf(405,plain,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(53,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_8) ).
thf(422,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_ord__eq__le__subst) ).
thf(867,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)],[219]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ C @ D ) )
=> ~ ( member @ TA @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_rel__restrict__notR_I2_J) ).
thf(410,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( rel_restrict @ TA @ C @ D ) )
=> ~ ( member @ TA @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(251,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_dual__order_Oeq__iff) ).
thf(967,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)],[251]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_Un__iff) ).
thf(326,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_9) ).
thf(358,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TA] :
( ( ( top_top @ ( refine1665802226e_nres @ TB ) )
= ( refine1073749519nc_fun @ TB @ TA @ A @ B ) )
= ( B
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_conc__fun__fail__iff_I2_J) ).
thf(828,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TA] :
( ( ( top_top @ ( refine1665802226e_nres @ TB ) )
= ( refine1073749519nc_fun @ TB @ TA @ A @ B ) )
= ( B
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(249,axiom,
! [TA: $tType,A: product_unit > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ product_unit @ TA @ ( top_top @ ( refine1665802226e_nres @ product_unit ) ) @ A )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_ibind__strict_I2_J) ).
thf(960,plain,
! [TA: $tType,A: product_unit > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ product_unit @ TA @ ( top_top @ ( refine1665802226e_nres @ product_unit ) ) @ A )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(238,axiom,
! [TA: $tType] : ( ord @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_33) ).
thf(928,plain,
! [TA: $tType] : ( ord @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(236,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] :
( ( refine1102455758nofail @ TB @ B )
=> ( ( refine1315500908_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/sandbox2/benchmark/theBenchmark.p',fact_212_pw__bind__leI) ).
thf(918,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] :
( ( refine1102455758nofail @ TB @ B )
=> ( ( refine1315500908_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)],[236]) ).
thf(195,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_dual__order_Orefl) ).
thf(801,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(287,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_le__cases3) ).
thf(1093,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)],[287]) ).
thf(260,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( transitive_rtrancl @ TA @ B )
= ( transitive_rtrancl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_rtrancl__subset) ).
thf(987,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ B @ ( transitive_rtrancl @ TA @ A ) )
=> ( ( transitive_rtrancl @ TA @ B )
= ( transitive_rtrancl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( uncurry @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_uncurry__apply) ).
thf(427,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( uncurry @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(269,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: refine1665802226e_nres @ TB,C: set @ ( product_prod @ TB @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TB @ ( id @ TB ) @ B ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ B @ ( refine1073749519nc_fun @ TB @ TA @ C @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_conc__trans__additional_I2_J) ).
thf(1019,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TB,B: refine1665802226e_nres @ TB,C: set @ ( product_prod @ TB @ TA ),D: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TB @ ( id @ TB ) @ B ) )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ B @ ( refine1073749519nc_fun @ TB @ TA @ C @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ A @ ( refine1073749519nc_fun @ TB @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(94,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_nres_Oinject) ).
thf(528,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)],[94]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_UnE) ).
thf(459,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(262,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( transitive_rtrancl @ TA @ B ) ) @ ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_rtrancl__Un__subset) ).
thf(992,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] : ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ ( transitive_rtrancl @ TA @ A ) @ ( transitive_rtrancl @ TA @ B ) ) @ ( transitive_rtrancl @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(212,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ C ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_reachable__mono) ).
thf(850,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) @ C ) @ ( image @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',fact_246_bind__cong) ).
thf(1004,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)],[265]) ).
thf(158,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_equalityD2) ).
thf(691,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)],[158]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) )
=> ~ ( member @ TA @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_rel__restrict__trancl__notR_I1_J) ).
thf(442,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_trancl @ TA @ ( rel_restrict @ TA @ C @ D ) ) )
=> ~ ( member @ TA @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(14,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_11) ).
thf(332,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(296,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Id__refine) ).
thf(1129,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine1073749519nc_fun @ TA @ TA @ ( id @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(11,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( id @ TA ) )
=> ( ( id @ TA )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_relprop__id__orient) ).
thf(322,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( id @ TA ) )
=> ( ( id @ TA )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(196,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_set__eq__subset) ).
thf(803,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)],[196]) ).
thf(24,axiom,
top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_17) ).
thf(354,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(543,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(164,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] : ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_eq__UNIV__iff) ).
thf(708,plain,
! [TA: $tType,A: set @ TA] :
( ( A
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] : ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',fact_67_relprop__triggers_I6_J) ).
thf(882,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(253,axiom,
! [TA: $tType] : ( bounded_lattice @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice) ).
thf(972,plain,
! [TA: $tType] : ( bounded_lattice @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1142,plain,
$false,
inference(e,[status(thm)],[645,1036,629,1024,347,893,468,941,1110,481,977,994,741,449,379,878,655,511,1078,384,533,715,945,930,670,747,913,404,417,301,436,885,1046,570,719,785,344,934,587,619,559,606,416,1115,492,756,1040,834,806,480,734,774,396,660,998,527,602,981,766,397,687,1072,453,380,678,761,798,546,793,334,957,825,598,820,561,392,424,407,729,1021,778,1123,862,349,1032,625,852,329,665,583,889,461,551,974,1012,847,566,484,456,842,317,650,1017,1121,593,783,499,857,697,1089,471,488,339,637,489,590,970,547,706,554,753,1075,476,647,985,515,1131,911,371,622,837,1086,508,1026,662,926,633,360,906,412,573,689,444,513,430,904,732,1125,545,413,875,577,711,641,1139,936,313,611,498,466,947,540,831,681,1117,419,451,737,303,764,979,377,990,880,1043,387,494,631,816,726,700,895,915,1061,1112,521,983,399,695,883,1015,608,563,505,653,658,394,306,722,1034,675,531,795,374,487,812,749,939,342,355,823,557,1070,887,954,739,310,580,855,673,791,585,717,502,840,463,338,576,951,744,336,703,613,600,864,314,595,497,859,446,571,845,627,539,524,759,891,368,1108,963,319,351,390,401,781,1030,568,433,667,478,383,684,536,1133,300,818,405,422,867,410,967,326,358,828,960,928,918,801,1093,987,427,1019,528,459,992,850,1004,691,442,332,1129,322,803,354,543,708,882,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP159^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.20 % Computer : n006.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Sep 29 20:03:24 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.65/0.48 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/0.76 % [INFO] Parsing done (278ms).
% 1.54/0.77 % [INFO] Running in sequential loop mode.
% 2.36/0.96 % [INFO] eprover registered as external prover.
% 2.36/0.97 % [INFO] Scanning for conjecture ...
% 2.80/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 298 axioms. Running axiom selection ...
% 3.21/1.14 % [INFO] Axiom selection finished. Selected 297 axioms (removed 1 axioms).
% 3.87/1.36 % [INFO] Problem is higher-order (TPTP THF).
% 3.87/1.38 % [INFO] Type checking passed.
% 3.87/1.38 % [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 ...
% 146.45/121.61 % External prover 'e' found a proof!
% 146.45/121.61 % [INFO] Killing All external provers ...
% 146.45/121.62 % Time passed: 121333ms (effective reasoning time: 120842ms)
% 146.45/121.62 % 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)>
% 146.45/121.62 % Axioms used in derivation (297): tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_30, fact_18_conc__fun__R__mono, fact_138_Domain__iff, fact_70_subset__trans, fact_19_order__mono__setup_Omono__let, fact_38_eq__iff, fact_220_rtrancl__reflcl__absorb, fact_202_pwD2, fact_154_nofail__antimono__fun, fact_86_abs__trans__additional_I6_J, fact_121_RETURN__rule, tcon_Product__Type_Ounit___Orderings_Oord_26, fact_51_le__rel__bool__arg__iff, tcon_HOL_Obool___Lattices_Obounded__lattice_2, tcon_HOL_Obool___Orderings_Opreorder_15, fact_136_nofail__simps_I3_J, fact_63_bijective__Id, fact_233_Un__commute, fact_144_IdE, tcon_Set_Oset___Orderings_Opreorder_8, fact_209_nf__inres__def, fact_77_subset__eq, fact_90_nres__more__simps_I4_J, fact_37_antisym, fact_74_subset__iff, fact_230_Domain__Un__eq, fact_232_Un__left__absorb, fact_205_pw__leI, fact_20_order__mono__setup_Omono__if, fact_92_relprop__UNIV__orient, fact_188_inres__simps_I2_J, fact_162_nofail__RES__conv, fact_113_abs__fun__simps_I3_J, fact_160_pwD1, fact_102_nres__inequalities_I1_J, fact_193_trancl__Image__unfold__left, fact_27_order__class_Oorder_Oantisym, tcon_Set_Oset___Lattices_Obounded__lattice_3, fact_6_conc__trans, fact_0_nres__order__simps_I4_J, fact_13_le__funD, tcon_fun___Orderings_Oord, fact_69_set__eq__subset, fact_95_top__set__def, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_33, fact_199_pw__eqI, fact_80_in__mono, fact_1_conc__fun__fail__iff_I2_J, fact_118_nres__order__simps_I20_J, fact_24_linorder__wlog, fact_50_transfer_Otransfer__if, fact_177_rtrancl__image__unfold__right, fact_167_BNF__Greatest__Fixpoint_OIdD, fact_195_rel__restrict__trancl__notR_I2_J, tcon_HOL_Obool___Lattices_Obounded__lattice__top_13, fact_99_SPEC__rule, fact_176_rtrancl__reachable__induct, tcon_HOL_Obool___Orderings_Olinorder, fact_196_rel__restrict__trancl__notR_I1_J, fact_169_relChain__def, fact_238_UnI2, fact_231_Un__left__commute, fact_163_bijective__def, fact_128_top__conj_I1_J, fact_165_RETURN__refine, fact_126_Image__Id, fact_98_RES__rule, fact_107_abs__trans, fact_53_ord__eq__le__eq__trans, fact_12_top_Oextremum__uniqueI, fact_201_not__nofail__inres, fact_227_Un__absorb2, fact_203_trancl__sub, fact_139_Domain_Ocases, fact_211_trancl__reflcl, fact_75_equalityD2, fact_239_UnI1, fact_112_nf__inres__RES, tcon_fun___Lattices_Obounded__lattice_4, fact_29_ord__eq__le__trans, fact_191_inres__simps_I3_J, fact_87_rel__restrict__mono2, fact_3_conc__fun__FAIL, fact_56_conc__trans__additional_I3_J, fact_64_relprop__id__orient, fact_31_antisym__conv, fact_23_dual__order_Otrans, tcon_Product__Type_Ounit___Lattices_Obounded__lattice__top_20, fact_228_subset__UnE, fact_170_converse__rtranclE_H, fact_130_RETURN__SPEC__refine, fact_178_reachable__mono, fact_215_Un__subset__iff, fact_61_subsetI, fact_240_UnE, fact_73_subset__UNIV, fact_143_subrelI, fact_120_RETURN__to__SPEC__rule, fact_111_nf__inres__SPEC, fact_131_the__RES__inv, fact_105_rel__restrict__mono, fact_88_UNIV__I, fact_71_Collect__mono, fact_129_top__conj_I2_J, fact_15_le__funI, fact_148_rel__restrict__lift, fact_179_Domain__rtrancl, fact_182_rtrancl__subset__rtrancl, tcon_Product__Type_Ounit___Orderings_Oorder_24, fact_85_abs__trans__additional_I5_J, fact_39_ord__le__eq__subst, fact_81_Id__SPEC__refine, fact_42_order__subst1, help_If_1_1_T, fact_34_le__cases, fact_76_equalityD1, fact_21_dual__order_Oantisym, fact_242_ibind__strict_I2_J, fact_213_Un__iff, fact_127_Image__mono, fact_251_pw__bind__le__iff, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Complete__Lattices_Ocomplete__lattice_27, fact_66_relprop__triggers_I3_J, fact_250_trancl__image__by__rtrancl, fact_249_rtrancl__trancl__reflcl, tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_12, fact_212_pw__bind__leI, fact_5_conc__trans__additional_I1_J, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_31, fact_116_nres__more__simps_I6_J, fact_214_UnCI, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__top_29, fact_48_GreatestI2__order, fact_123_Domain__mono, fact_119_nres__inequalities_I3_J, fact_28_ord__le__eq__trans, fact_181_Image__closed__trancl, fact_57_subset__Collect__conv, fact_147_rel__restrictI, fact_122_Domain__Id, fact_52_verit__la__disequality, fact_156_intro__nofail_I2_J, fact_103_nres__cases, fact_78_equalityE, fact_110_iso__tuple__UNIV__I, fact_194_trancl__Image__unfold__right, fact_93_eq__UNIV__iff, fact_246_bind__cong, fact_225_Un__upper2, fact_166_for__in__RI, fact_252_sup__top__left, fact_97_if__rule, fact_241_rel__restrict__union, fact_104_rel__restrict__sub, fact_67_relprop__triggers_I6_J, fact_197_rel__restrict__trancl__mem, fact_159_rel__arg__cong, fact_157_nofail__def, fact_141_Domain_ODomainI, fact_132_pair__in__Id__conv, fact_135_nofail__simps_I1_J, fact_134_nofail__simps_I2_J, tcon_HOL_Obool___Orderings_Oorder_16, fact_9_top__greatest, fact_101_SPEC__cons__rule, fact_7_top__apply, fact_125_abs__fun__simps_I2_J, tcon_Product__Type_Ounit___Orderings_Otop_25, fact_175_rtrancl__image__advance, fact_108_nres__order__simps_I5_J, fact_184_rtrancl__mono, fact_33_order_Otrans, fact_234_Un__absorb, tcon_Product__Type_Ounit___Orderings_Oorder__top_21, fact_89_nres_Oinject, fact_190_inres__simps_I1_J, fact_96_UNIV__eq__I, fact_248_trancl__union__outside, fact_49_transfer_Otransfer__Let, fact_100_SPEC__trans, fact_237_bex__Un, fact_187_pw__abs__nofail, fact_200_pw__eq__iff, fact_155_pw__conc__nofail, fact_243_Un__UNIV__right, help_If_3_1_T, fact_83_abs__trans__additional_I3_J, fact_133_IdI, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice, fact_207_pw__le__iff, help_If_2_1_T, tcon_fun___Lattices_Obounded__lattice__top, fact_40_ord__eq__le__subst, tcon_Set_Oset___Lattices_Obounded__lattice__top_6, tcon_fun___Orderings_Otop, fact_124_top__empty__eq, fact_26_order__trans, fact_91_abs__fun__simps_I1_J, fact_2_conc__fun__fail__iff_I1_J, tcon_Product__Type_Ounit___Orderings_Olinorder_23, tcon_Set_Oset___Orderings_Oorder_9, fact_216_bind__FAIL, fact_109_less__eq__nres_Osimps_I2_J, fact_206_pw__leI_H, fact_145_rel__restrict__notR_I2_J, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_32, fact_41_order__subst2, fact_117_top1I, fact_245_pw__bind__nofail, fact_186_uncurry__apply, fact_62_subset__antisym, fact_158_not__nofail__iff, fact_115_nres__order__simps_I21_J, fact_16_Refine__Misc_Oif__mono, fact_198_rel__restrict__trancl__sub, tcon_fun___Orderings_Opreorder, fact_72_subset__refl, fact_45_Collect__mem__eq, tcon_Product__Type_Ounit___Complete__Lattices_Ocomplete__lattice_19, fact_106_abs__trans__additional_I1_J, fact_247_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J, fact_65_relprop__triggers_I2_J, tcon_fun___Orderings_Oorder__top, fact_79_subsetD, fact_171_rtrancl__mono__rightI, fact_189_trancl__domain, tcon_fun___Complete__Lattices_Ocomplete__lattice, fact_25_dual__order_Orefl, fact_22_dual__order_Oeq__iff, tcon_Set_Oset___Orderings_Oorder__top_7, tcon_Product__Type_Ounit___Orderings_Opreorder_22, fact_58_conc__trans__additional_I6_J, fact_36_linear, tcon_Set_Oset___Orderings_Otop_10, fact_217_nres__monad2, fact_210_pw__abs__inres, fact_17_le__fun__def, fact_244_Un__UNIV__left, fact_164_RES__refine, fact_10_meta__le__everything__if__top, fact_35_eq__refl, fact_185_rel__restrict__tranclI, fact_172_rtrancl__mono__mp, tcon_fun___Orderings_Oorder, fact_183_rtrancl__subset, fact_43_Greatest__equality, fact_174_rtrancl__image__advance__rtrancl, tcon_HOL_Obool___Orderings_Otop_17, fact_150_pairself_Ocases, tcon_Set_Oset___Orderings_Oord_11, fact_151_bex2I, fact_204_trancl__mono__mp, tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_5, fact_168_E__closed__restr__reach__cases, fact_226_Un__absorb1, fact_236_ball__Un, fact_60_conc__trans__additional_I4_J, fact_180_Not__Domain__rtrancl, fact_4_nres__order__simps_I3_J, tcon_HOL_Obool___Orderings_Oord_18, fact_218_nres__monad1, fact_222_Un__mono, fact_153_rel__fun__cong, fact_152_rel__cong, fact_223_Un__least, fact_82_abs__trans__additional_I2_J, fact_142_Domain_Oinducts, tcon_HOL_Obool___Orderings_Oorder__top_14, fact_221_rtrancl__Un__subset, fact_208_inres__def, fact_32_le__cases3, fact_149_pairself_Oinduct, fact_14_le__funE, fact_54_Id__refine, fact_229_subset__Un__eq, fact_55_conc__trans__additional_I2_J, fact_94_UNIV__witness, fact_137_DomainE, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Lattices_Obounded__lattice__top_28, fact_46_Collect__cong, fact_192_trancl__mono, fact_44_mem__Collect__eq, fact_59_conc__trans__additional_I5_J, fact_219_rtrancl__reflcl, fact_84_abs__trans__additional_I4_J, fact_224_Un__upper1, fact_8_order__mono__setup_Orefl, tcon_Product__Type_Ounit___Lattices_Obounded__lattice_1, fact_140_Domain_Osimps, fact_68_Collect__mono__iff, fact_11_top_Oextremum__unique, fact_235_Un__assoc, fact_161_le__nofailI, fact_114_the__RES_Osimps, fact_30_order__class_Oorder_Oeq__iff, fact_146_rel__restrict__notR_I1_J, fact_173_r__le__rtrancl
% 146.45/121.62 % No. of inferences in proof: 598
% 146.45/121.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 121333 ms resp. 120842 ms w/o parsing
% 147.66/121.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 147.66/121.92 % [INFO] Killing All external provers ...
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