%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP164^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 08:07:01 AM UTC 2026
% Result : Theorem 52.05s 28.93s
% Output : Refutation 53.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 300
% Syntax : Number of formulae : 602 ( 257 unt; 0 typ; 0 def)
% Number of atoms : 2209 ( 517 equ; 18 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 7265 ( 134 ~; 11 |; 80 &;6450 @)
% ( 0 <=>; 590 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 178 ( 178 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 36 usr; 6 con; 0-4 aty)
% Number of variables : 2121 ( 86 ^;2011 !; 24 ?;2121 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(a_type,type,
a: $tType ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_bot_decl,type,
order_bot:
!>[TA: $tType] : $o ).
thf(order_top_decl,type,
order_top:
!>[TA: $tType] : $o ).
thf(comple187826305attice_decl,type,
comple187826305attice:
!>[TA: $tType] : $o ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(order_Greatest_decl,type,
order_Greatest:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(partial_flat_ord_decl,type,
partial_flat_ord:
!>[TA: $tType] : ( TA > TA > TA > $o ) ).
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(refine1150083786ection_decl,type,
refine1150083786ection:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > TB ) > $o ) ).
thf(domain_decl,type,
domain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TB ) ) ).
thf(single_valued_decl,type,
single_valued:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_decl,type,
f: product_unit > ( refine1665802226e_nres @ a ) ).
thf(20,axiom,
order_top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_10) ).
thf(365,plain,
order_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(296,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_empty__subsetI) ).
thf(1168,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_prod_Oinject) ).
thf(347,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(106,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_dual__order_Oeq__iff) ).
thf(628,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)],[106]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_93_pw__abs__nofail) ).
thf(518,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)],[71]) ).
thf(300,axiom,
bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Obot_25) ).
thf(1179,plain,
bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(158,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_le__cases3) ).
thf(777,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)],[158]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_78_pw__conc__nofail) ).
thf(645,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)],[113]) ).
thf(198,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_doubleton__eq__iff) ).
thf(892,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(292,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_nres__more__simps_I5_J) ).
thf(1158,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(127,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_eq__iff) ).
thf(683,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)],[127]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TA @ TB @ ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C ) )
= ( insert @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Domain__insert) ).
thf(730,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TA @ TB @ ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C ) )
= ( insert @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',fact_22_abs__fun__simps_I1_J) ).
thf(1068,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)],[262]) ).
thf(264,axiom,
! [TA: $tType] : ( refine1102455758nofail @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_nofail__simps_I4_J) ).
thf(1073,plain,
! [TA: $tType] : ( refine1102455758nofail @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(285,axiom,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Domain__empty) ).
thf(1142,plain,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(298,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_subset__singletonD) ).
thf(1173,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( refine1073749519nc_fun @ TA @ TB @ A @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conc__fun__strict) ).
thf(1078,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( refine1073749519nc_fun @ TA @ TB @ A @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(27,axiom,
! [TA: $tType,A: set @ TA] :
( ( refine1672542526he_RES @ TA @ ( refine605929679le_RES @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_the__RES_Osimps) ).
thf(385,plain,
! [TA: $tType,A: set @ TA] :
( ( refine1672542526he_RES @ TA @ ( refine605929679le_RES @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(76,axiom,
top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_14) ).
thf(533,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(83,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_dual__order_Otrans) ).
thf(550,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)],[83]) ).
thf(60,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ord_less_eq @ TA @ D @ B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ TA @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_GreatestI2__order) ).
thf(472,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)],[60]) ).
thf(168,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_order_Otrans) ).
thf(814,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)],[168]) ).
thf(206,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_singleton__insert__inj__eq) ).
thf(913,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(217,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_singletonI) ).
thf(945,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_prod__induct4) ).
thf(340,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(538,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(239,axiom,
! [TA: $tType] :
( ( refine1315500908_inres @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) )
= ( ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_inres__simps_I1_J) ).
thf(1001,plain,
! [TA: $tType] :
( ( refine1315500908_inres @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) )
= ( ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(279,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Collect__empty__eq__bot) ).
thf(1127,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(38,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: TA] :
( ( partial_flat_ord @ TA @ ( top_top @ TA ) @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_flat__ord__compat_I2_J) ).
thf(417,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: TA] :
( ( partial_flat_ord @ TA @ ( top_top @ TA ) @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(90,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_insert__mono) ).
thf(565,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_insert__ident) ).
thf(436,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_all__not__in__conv) ).
thf(1095,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(34,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_nres_Oinject) ).
thf(404,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)],[34]) ).
thf(229,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_nres__order__simps_I1_J) ).
thf(973,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(256,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA > ( refine1665802226e_nres @ TB )] :
( ( refine463715084e_bind @ TA @ TB @ ( refine1687780735RETURN @ TA @ A ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nres__monad1) ).
thf(1046,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)],[256]) ).
thf(92,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine605929679le_RES @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_nres__more__simps_I4_J) ).
thf(570,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)],[92]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_subrelI) ).
thf(719,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)],[141]) ).
thf(134,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_3) ).
thf(702,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_surj__pair) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(55,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_linear) ).
thf(460,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)],[55]) ).
thf(213,axiom,
! [TA: $tType] : ( order @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_30) ).
thf(934,plain,
! [TA: $tType] : ( order @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_prod__induct6) ).
thf(357,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(287,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( single_valued @ TA @ TB @ A )
=> ( refine1150083786ection @ ( refine1665802226e_nres @ TA ) @ ( refine1665802226e_nres @ TB ) @ ( refine81118332bs_fun @ TA @ TB @ A ) @ ( refine1073749519nc_fun @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_ac__galois) ).
thf(1147,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( single_valued @ TA @ TB @ A )
=> ( refine1150083786ection @ ( refine1665802226e_nres @ TA ) @ ( refine1665802226e_nres @ TB ) @ ( refine81118332bs_fun @ TA @ TB @ A ) @ ( refine1073749519nc_fun @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(421,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(227,axiom,
! [TA: $tType] : ( top @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_31) ).
thf(969,plain,
! [TA: $tType] : ( top @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(155,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA] :
( ~ ( refine1102455758nofail @ TA @ A )
=> ( refine1315500908_inres @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_not__nofail__inres) ).
thf(770,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)],[155]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Pair__inject) ).
thf(325,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(448,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(289,axiom,
order_top @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__top_18) ).
thf(1151,plain,
order_top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(245,axiom,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
( A
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_nofail__def) ).
thf(1020,plain,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
( A
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',fact_152_DomainE) ).
thf(806,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)],[165]) ).
thf(226,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_less__eq__nres_Osimps_I2_J) ).
thf(966,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)],[226]) ).
thf(258,axiom,
! [TA: $tType] :
( ( refine1315500908_inres @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_inres__simps_I4_J) ).
thf(1051,plain,
! [TA: $tType] :
( ( refine1315500908_inres @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(253,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_empty__iff) ).
thf(1040,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_prod__induct5) ).
thf(321,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_29_conc__trans__additional_I1_J) ).
thf(981,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)],[232]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA,E: TA,F: $o] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ D @ E )
=> ( partial_flat_ord @ TA @ A @ ( if @ TA @ F @ B @ D ) @ ( if @ TA @ F @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_flat__le__mono__setup_Omono__if) ).
thf(397,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA,E: TA,F: $o] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ D @ E )
=> ( partial_flat_ord @ TA @ A @ ( if @ TA @ F @ B @ D ) @ ( if @ TA @ F @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(109,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ ( collect @ TA @ A ) ) @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_nf__inres__SPEC) ).
thf(634,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)],[109]) ).
thf(129,axiom,
comple187826305attice @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_9) ).
thf(692,plain,
comple187826305attice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(222,axiom,
order_bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__bot_19) ).
thf(956,plain,
order_bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__funE) ).
thf(453,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)],[52]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',fact_153_Domain__iff) ).
thf(774,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)],[157]) ).
thf(238,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_equals0I) ).
thf(998,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(36,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_top__empty__eq) ).
thf(411,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(275,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( top_top @ ( refine1665802226e_nres @ TA ) ) @ A )
= ( A
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nres__order__simps_I4_J) ).
thf(1104,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)],[275]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_insert__subset) ).
thf(507,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_prod__cases) ).
thf(307,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_154_Domain_Ocases) ).
thf(380,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)],[25]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( single_valued @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB )] :
! [B: TA,C: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A )
=> ! [D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ A )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_single__valued__def) ).
thf(366,plain,
! [TA: $tType,TB: $tType] :
( ( single_valued @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB )] :
! [B: TA,C: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A )
=> ! [D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ A )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TA > TB,B: TB > TA,C: TA] :
( ( refine1150083786ection @ TA @ TB @ A @ B )
=> ( ord_less_eq @ TA @ C @ ( B @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_galois__connection_O_092_060gamma_062_092_060alpha_062__infl) ).
thf(534,plain,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TA > TB,B: TB > TA,C: TA] :
( ( refine1150083786ection @ TA @ TB @ A @ B )
=> ( ord_less_eq @ TA @ C @ ( B @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TB,C: refine1665802226e_nres @ TA] :
( ( single_valued @ TB @ TA @ A )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ B @ ( refine1073749519nc_fun @ TB @ TA @ A @ C ) )
= ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_conc__abs__swap) ).
thf(942,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: refine1665802226e_nres @ TB,C: refine1665802226e_nres @ TA] :
( ( single_valued @ TB @ TA @ A )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ B @ ( refine1073749519nc_fun @ TB @ TA @ A @ C ) )
= ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine81118332bs_fun @ TB @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(439,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(162,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_order__trans) ).
thf(798,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)],[162]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',fact_74_pw__bind__leI) ).
thf(1057,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)],[260]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',fact_60_pwD2) ).
thf(1163,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)],[294]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_prod__cases4) ).
thf(334,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(223,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_bot__set__def) ).
thf(957,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1,conjecture,
( ( refine463715084e_bind @ product_unit @ a @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ f )
= ( bot_bot @ ( refine1665802226e_nres @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( refine463715084e_bind @ product_unit @ a @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ f )
!= ( bot_bot @ ( refine1665802226e_nres @ a ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(302,plain,
( ( refine463715084e_bind @ product_unit @ a @ ( bot_bot @ ( refine1665802226e_nres @ product_unit ) ) @ f )
!= ( bot_bot @ ( refine1665802226e_nres @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_nres__order__simps_I22_J) ).
thf(862,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(171,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ D )
=> ( partial_flat_ord @ TA @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_flat__ord_Oorder__trans) ).
thf(820,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ D )
=> ( partial_flat_ord @ TA @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(561,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(254,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ~ ( refine1102455758nofail @ TA @ A ) )
= ( A
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_not__nofail__iff) ).
thf(1042,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ~ ( refine1102455758nofail @ TA @ A ) )
= ( A
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( partial_flat_ord @ ( refine1665802226e_nres @ TA ) @ ( top_top @ ( refine1665802226e_nres @ TA ) ) @ A @ B )
=> ( ! [E: TA] : ( partial_flat_ord @ ( refine1665802226e_nres @ TB ) @ ( top_top @ ( refine1665802226e_nres @ TB ) ) @ ( C @ E ) @ ( D @ E ) )
=> ( partial_flat_ord @ ( refine1665802226e_nres @ TB ) @ ( top_top @ ( refine1665802226e_nres @ TB ) ) @ ( refine463715084e_bind @ TA @ TB @ A @ C ) @ ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I2_J) ).
thf(952,plain,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( partial_flat_ord @ ( refine1665802226e_nres @ TA ) @ ( top_top @ ( refine1665802226e_nres @ TA ) ) @ A @ B )
=> ( ! [E: TA] : ( partial_flat_ord @ ( refine1665802226e_nres @ TB ) @ ( top_top @ ( refine1665802226e_nres @ TB ) ) @ ( C @ E ) @ ( D @ E ) )
=> ( partial_flat_ord @ ( refine1665802226e_nres @ TB ) @ ( top_top @ ( refine1665802226e_nres @ TB ) ) @ ( refine463715084e_bind @ TA @ TB @ A @ C ) @ ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(35,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( C = D )
=> ( partial_flat_ord @ TA @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_flat__ord_Oord__le__eq__trans) ).
thf(407,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( C = D )
=> ( partial_flat_ord @ TA @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_le__funD) ).
thf(693,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)],[130]) ).
thf(250,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Collect__empty__eq) ).
thf(1032,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_old_Oprod_Oinducts) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ( ( refine1150083786ection @ TA @ TB )
= ( ^ [A: TA > TB,B: TB > TA] :
! [C: TA,D: TB] :
( ( ord_less_eq @ TA @ C @ ( B @ D ) )
= ( ord_less_eq @ TB @ ( A @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_galois__connection__def) ).
thf(665,plain,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ( ( refine1150083786ection @ TA @ TB )
= ( ^ [A: TA > TB,B: TB > TA] :
! [C: TA,D: TB] :
( ( ord_less_eq @ TA @ C @ ( B @ D ) )
= ( ord_less_eq @ TB @ ( A @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(175,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_insertI2) ).
thf(830,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',fact_69_pw__le__iff) ).
thf(889,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)],[197]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_order__subst2) ).
thf(493,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)],[63]) ).
thf(248,axiom,
ord @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_24) ).
thf(1027,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(152,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 )
=> ( ( single_valued @ TA @ TB @ B )
=> ( single_valued @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_single__valued__subset) ).
thf(757,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 )
=> ( ( single_valued @ TA @ TB @ B )
=> ( single_valued @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(138,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_subset__insert) ).
thf(710,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(180,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(842,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(242,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: TA] :
( ( partial_flat_ord @ TA @ ( bot_bot @ TA ) @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_flat__ord__compat_I1_J) ).
thf(1012,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: TA] :
( ( partial_flat_ord @ TA @ ( bot_bot @ TA ) @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine605929679le_RES @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_nres__order__simps_I5_J) ).
thf(916,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)],[207]) ).
thf(58,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_UNIV__I) ).
thf(467,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(191,axiom,
preorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Opreorder_20) ).
thf(874,plain,
preorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(115,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_6) ).
thf(650,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_bot__apply) ).
thf(1017,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TB > TA,B: TA > TB,C: TA] :
( ( refine1150083786ection @ TB @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( A @ ( B @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_galois__connection_O_092_060alpha_062_092_060gamma_062__defl) ).
thf(388,plain,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TB > TA,B: TA > TB,C: TA] :
( ( refine1150083786ection @ TB @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( A @ ( B @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(283,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_singleton__iff) ).
thf(1138,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(235,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( partial_flat_ord @ ( refine1665802226e_nres @ TA ) @ ( top_top @ ( refine1665802226e_nres @ TA ) ) @ A @ B )
= ( ( refine1102455758nofail @ TA @ A )
=> ( ( refine1102455758nofail @ TA @ B )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
= ( refine1315500908_inres @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_pw__flat__ge__iff) ).
thf(989,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( partial_flat_ord @ ( refine1665802226e_nres @ TA ) @ ( top_top @ ( refine1665802226e_nres @ TA ) ) @ A @ B )
= ( ( 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)],[235]) ).
thf(185,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] : ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_nres__order__simps_I3_J) ).
thf(857,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)],[185]) ).
thf(132,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(697,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(270,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine463715084e_bind @ TA @ TA @ A @ ( refine1687780735RETURN @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nres__monad2) ).
thf(1089,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine463715084e_bind @ TA @ TA @ A @ ( refine1687780735RETURN @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(249,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ B ) ) )
=> ( ! [D: TA] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_SPEC__cons__rule) ).
thf(1028,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)],[249]) ).
thf(112,axiom,
! [TA: $tType,A: TA] :
( ( (=) @ TA )
= ( ^ [B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ C @ B )
& ( partial_flat_ord @ TA @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_flat__ord_Odual__order_Oeq__iff) ).
thf(642,plain,
! [TA: $tType,A: TA] :
( ( (=) @ TA )
= ( ^ [B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ C @ B )
& ( partial_flat_ord @ TA @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(110,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_4) ).
thf(637,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(98,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: $o,B: TA,C: TA,D: TA,E: TA] :
( ( A
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq @ TA @ D @ E ) )
=> ( ord_less_eq @ TA @ ( if @ TA @ A @ B @ D ) @ ( if @ TA @ A @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Refine__Misc_Oif__mono) ).
thf(590,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)],[98]) ).
thf(126,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ord__eq__le__trans) ).
thf(679,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)],[126]) ).
thf(85,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_ord__le__eq__trans) ).
thf(554,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)],[85]) ).
thf(150,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(753,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA] :
( ( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
= ( refine605929679le_RES @ TA @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_nres__more__simps_I1_J) ).
thf(901,plain,
! [TA: $tType,A: set @ TA] :
( ( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
= ( refine605929679le_RES @ TA @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,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 ) ) )
=> ( single_valued @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_single__valuedI) ).
thf(686,plain,
! [TA: $tType,TB: $tType,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 ) ) )
=> ( single_valued @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(265,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_empty__not__UNIV) ).
thf(1075,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(291,axiom,
! [TA: $tType,A: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_nres__more__simps_I2_J) ).
thf(1155,plain,
! [TA: $tType,A: set @ TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TA > TB,B: TB > TA] :
( ! [C: TB,D: TA] :
( ( ord_less_eq @ TB @ C @ ( A @ D ) )
= ( ord_less_eq @ TA @ ( B @ C ) @ D ) )
=> ( refine1150083786ection @ TB @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_galois__connection_Ointro) ).
thf(547,plain,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TA > TB,B: TB > TA] :
( ! [C: TB,D: TA] :
( ( ord_less_eq @ TB @ C @ ( A @ D ) )
= ( ord_less_eq @ TA @ ( B @ C ) @ D ) )
=> ( refine1150083786ection @ TB @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_63_pw__eqI) ).
thf(515,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)],[70]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: TB,C: TA,D: TA] :
( ( single_valued @ TB @ TA @ A )
=> ( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ D ) @ A )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_single__valuedD) ).
thf(457,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: TB,C: TA,D: TA] :
( ( single_valued @ TB @ TA @ A )
=> ( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ D ) @ A )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(205,axiom,
! [TA: $tType] : ( preorder @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_29) ).
thf(911,plain,
! [TA: $tType] : ( preorder @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_insertCI) ).
thf(371,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_le__funI) ).
thf(503,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)],[65]) ).
thf(159,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_iso__tuple__UNIV__I) ).
thf(792,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(269,axiom,
! [TA: $tType,TB: $tType,A: TB > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ TB @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_bind__SUCCEED) ).
thf(1086,plain,
! [TA: $tType,TB: $tType,A: TB > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ TB @ TA @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) @ A )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_prod__induct3) ).
thf(311,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_Ocomplete__lattice) ).
thf(657,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(259,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_singleton__inject) ).
thf(1054,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(297,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/sandbox/benchmark/theBenchmark.p',fact_19_conc__fun__fail__iff_I1_J) ).
thf(1170,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)],[297]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_83_pw__bind__nofail) ).
thf(1035,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)],[251]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top) ).
thf(674,plain,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(210,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_bot__empty__eq) ).
thf(926,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(86,axiom,
! [TA: $tType,A: TA] : ( refine1102455758nofail @ TA @ ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nofail__simps_I3_J) ).
thf(558,plain,
! [TA: $tType,A: TA] : ( refine1102455758nofail @ TA @ ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(263,axiom,
! [TA: $tType] : ( comple187826305attice @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Complete__Lattices_Ocomplete__lattice_26) ).
thf(1071,plain,
! [TA: $tType] : ( comple187826305attice @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA] : ( refine1102455758nofail @ TA @ ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_nofail__simps_I2_J) ).
thf(794,plain,
! [TA: $tType,A: set @ TA] : ( refine1102455758nofail @ TA @ ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(96,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_order__mono__setup_Orefl) ).
thf(586,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(282,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_subset__empty) ).
thf(1135,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(149,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( refine1102455758nofail @ TA @ A )
=> ( ( refine605929679le_RES @ TA @ ( refine1672542526he_RES @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_the__RES__inv) ).
thf(750,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)],[149]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(513,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(173,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insert__UNIV) ).
thf(824,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_Set_Oset__insert) ).
thf(745,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_ord__le__eq__subst) ).
thf(573,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)],[93]) ).
thf(49,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_eq__refl) ).
thf(444,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)],[49]) ).
thf(145,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_insert__commute) ).
thf(733,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_subsetD) ).
thf(584,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)],[95]) ).
thf(41,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_subsetI) ).
thf(423,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)],[41]) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',fact_64_pw__leI) ).
thf(1007,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)],[241]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: TA] : ( partial_flat_ord @ TA @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_flat__le__mono__setup_Orefl) ).
thf(402,plain,
! [TA: $tType,A: TA,B: TA] : ( partial_flat_ord @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(156,axiom,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1) ).
thf(772,plain,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(192,axiom,
order @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_22) ).
thf(875,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',fact_77_pw__bind__le__iff) ).
thf(1124,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)],[278]) ).
thf(202,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bot__fun__def) ).
thf(904,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(230,axiom,
! [TA: $tType] :
( ( refine1687780735RETURN @ TA )
= ( ^ [A: TA] : ( refine605929679le_RES @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_RETURN__def) ).
thf(975,plain,
! [TA: $tType] :
( ( refine1687780735RETURN @ TA )
= ( ^ [A: TA] : ( refine605929679le_RES @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_20_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)],[214]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_subset__eq) ).
thf(382,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)],[26]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA > TB,D: TA] :
( ! [E: TA] : ( partial_flat_ord @ TB @ A @ ( B @ E ) @ ( C @ E ) )
=> ( partial_flat_ord @ TB @ A @ ( B @ D ) @ ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_flat__le__mono__setup_Omono__let) ).
thf(611,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA > TB,D: TA] :
( ! [E: TA] : ( partial_flat_ord @ TB @ A @ ( B @ E ) @ ( C @ E ) )
=> ( partial_flat_ord @ TB @ A @ ( B @ D ) @ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(139,axiom,
! [TA: $tType,A: TA] :
( ( (=) @ TA )
= ( ^ [B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
& ( partial_flat_ord @ TA @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_flat__ord_Oorder_Oeq__iff) ).
thf(713,plain,
! [TA: $tType,A: TA] :
( ( (=) @ TA )
= ( ^ [B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
& ( partial_flat_ord @ TA @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',fact_65_pw__leI_H) ).
thf(1107,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)],[276]) ).
thf(271,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( A
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) )
=> ~ ! [B: set @ TA] :
( A
!= ( refine605929679le_RES @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_nres__cases) ).
thf(1092,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)],[271]) ).
thf(208,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_singletonD) ).
thf(919,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(135,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_subset__antisym) ).
thf(704,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)],[135]) ).
thf(218,axiom,
! [TA: $tType] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nres__inequalities_I2_J) ).
thf(947,plain,
! [TA: $tType] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_prod__induct7) ).
thf(350,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(80,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_order__class_Oorder_Oeq__iff) ).
thf(540,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)],[80]) ).
thf(39,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_le__cases) ).
thf(419,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_92_pw__abs__inres) ).
thf(736,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)],[146]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_nres__more__simps_I6_J) ).
thf(377,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( refine1687780735RETURN @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_prod__cases3) ).
thf(318,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_ord__eq__le__subst) ).
thf(616,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)],[104]) ).
thf(100,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( order_Greatest @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Greatest__equality) ).
thf(599,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)],[100]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_subset__insertI) ).
thf(451,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(91,axiom,
! [TA: $tType,A: TA] :
( ( (=) @ TA )
= ( ^ [B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
& ( partial_flat_ord @ TA @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_flat__ord_Oeq__iff) ).
thf(567,plain,
! [TA: $tType,A: TA] :
( ( (=) @ TA )
= ( ^ [B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
& ( partial_flat_ord @ TA @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_subset__singleton__iff) ).
thf(880,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ! [D: TA] : ( ord_less_eq @ TB @ ( A @ D ) @ ( B @ D ) )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_order__mono__setup_Omono__let) ).
thf(434,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)],[44]) ).
thf(167,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(811,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)],[167]) ).
thf(107,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).
thf(631,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(552,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(169,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_subset__trans) ).
thf(816,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)],[169]) ).
thf(143,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( A = B )
=> ( ( partial_flat_ord @ TA @ C @ B @ D )
=> ( partial_flat_ord @ TA @ C @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_flat__ord_Oord__eq__le__trans) ).
thf(726,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( A = B )
=> ( ( partial_flat_ord @ TA @ C @ B @ D )
=> ( partial_flat_ord @ TA @ C @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType] : ( single_valued @ TA @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_single__valued__empty) ).
thf(895,plain,
! [TA: $tType,TB: $tType] : ( single_valued @ TA @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(288,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_emptyE) ).
thf(1149,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(122,axiom,
! [TA: $tType,A: TA] :
( ( refine1315500908_inres @ TA @ ( refine1687780735RETURN @ TA @ A ) )
= ( (=) @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_inres__simps_I3_J) ).
thf(668,plain,
! [TA: $tType,A: TA] :
( ( refine1315500908_inres @ TA @ ( refine1687780735RETURN @ TA @ A ) )
= ( (=) @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(56,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_8) ).
thf(462,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',fact_155_Domain_Osimps) ).
thf(848,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)],[182]) ).
thf(133,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_insert__subsetI) ).
thf(700,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
=> ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_flat__ord_Odual__order_Oantisym) ).
thf(521,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_insert__not__empty) ).
thf(983,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(32,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( refine406925620_inres @ TA @ ( refine605929679le_RES @ TA @ A ) @ B )
= ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_nf__inres__RES) ).
thf(399,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)],[32]) ).
thf(174,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_insert__absorb2) ).
thf(827,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ D @ B )
=> ( partial_flat_ord @ TA @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_flat__ord_Odual__order_Otrans) ).
thf(695,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ D @ B )
=> ( partial_flat_ord @ TA @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(189,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ( refine1102455758nofail @ TA @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_le__nofailI) ).
thf(868,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)],[189]) ).
thf(89,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_subset__refl) ).
thf(563,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(183,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_order__class_Oorder_Oantisym) ).
thf(851,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)],[183]) ).
thf(66,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_top1I) ).
thf(505,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(117,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( A = B )
=> ( partial_flat_ord @ TA @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_flat__ord_Oeq__refl) ).
thf(653,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( A = B )
=> ( partial_flat_ord @ TA @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(209,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_less__by__empty) ).
thf(922,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(53,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: $o] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( if @ TA @ E @ A @ C ) @ ( if @ TA @ E @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_order__mono__setup_Omono__if) ).
thf(455,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)],[53]) ).
thf(195,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( partial_flat_ord @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ A @ B )
= ( ? [C: TA] : ( refine1315500908_inres @ TA @ A @ C )
=> ( ( ( refine1102455758nofail @ TA @ A )
= ( refine1102455758nofail @ TA @ B ) )
& ! [C: TA] :
( ( refine1315500908_inres @ TA @ A @ C )
= ( refine1315500908_inres @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_pw__flat__le__iff) ).
thf(883,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( partial_flat_ord @ ( refine1665802226e_nres @ TA ) @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) @ A @ B )
= ( ? [C: TA] : ( refine1315500908_inres @ TA @ A @ C )
=> ( ( ( 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)],[195]) ).
thf(299,axiom,
! [TA: $tType] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
= ( refine605929679le_RES @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_bot__nres__def) ).
thf(1176,plain,
! [TA: $tType] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
= ( refine605929679le_RES @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(101,axiom,
! [TA: $tType] :
( ( refine406925620_inres @ TA )
= ( ^ [A: refine1665802226e_nres @ TA,B: TA] :
( ( refine1102455758nofail @ TA @ A )
& ( refine1315500908_inres @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nf__inres__def) ).
thf(608,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)],[101]) ).
thf(30,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_dual__order_Oantisym) ).
thf(394,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)],[30]) ).
thf(234,axiom,
! [TA: $tType,A: TA] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_nres__inequalities_I5_J) ).
thf(986,plain,
! [TA: $tType,A: TA] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',fact_68_pw__eq__iff) ).
thf(490,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)],[62]) ).
thf(75,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_top__greatest) ).
thf(531,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(120,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_subset__UNIV) ).
thf(663,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(267,axiom,
! [TA: $tType,A: set @ TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine605929679le_RES @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_nres__inequalities_I1_J) ).
thf(1081,plain,
! [TA: $tType,A: set @ TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine605929679le_RES @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(215,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_singleton__insert__inj__eq_H) ).
thf(939,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',fact_120_conc__fun__R__mono) ).
thf(1145,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)],[286]) ).
thf(151,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_top_Oextremum__unique) ).
thf(754,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)],[151]) ).
thf(178,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_equalityD1) ).
thf(836,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)],[178]) ).
thf(257,axiom,
! [TA: $tType] : ( ord @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_32) ).
thf(1049,plain,
! [TA: $tType] : ( ord @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_127_Domain_ODomainI) ).
thf(648,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)],[114]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_insert__eq__iff) ).
thf(487,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(247,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > $o] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ B @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( refine605929679le_RES @ TA @ ( collect @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_SPEC__trans) ).
thf(1025,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)],[247]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_70_conc__trans) ).
thf(872,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)],[190]) ).
thf(136,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(707,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',fact_66_abs__trans) ).
thf(954,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)],[221]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_126_Domain_Oinducts) ).
thf(739,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)],[147]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_nres__more__simps_I3_J) ).
thf(1098,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ( refine605929679le_RES @ TA @ A )
= ( refine1687780735RETURN @ TA @ B ) )
= ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(37,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_flat__ord_Oorder_Oantisym) ).
thf(414,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(228,axiom,
! [TA: $tType] : ( order_top @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__top_27) ).
thf(971,plain,
! [TA: $tType] : ( order_top @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_old_Oprod_Oinject) ).
thf(331,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(47,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_15) ).
thf(441,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(252,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_bot_Oextremum) ).
thf(1038,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(179,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_UNIV__witness) ).
thf(840,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_insert__iff) ).
thf(808,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(280,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine1687780735RETURN @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_nres__order__simps_I20_J) ).
thf(1130,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)],[280]) ).
thf(203,axiom,
top @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Otop_23) ).
thf(907,plain,
top @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(284,axiom,
comple187826305attice @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Complete__Lattices_Ocomplete__lattice_17) ).
thf(1141,plain,
comple187826305attice @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(246,axiom,
! [TA: $tType] : ( order_bot @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_28) ).
thf(1023,plain,
! [TA: $tType] : ( order_bot @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(103,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Collect__mono__iff) ).
thf(613,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)],[103]) ).
thf(231,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_empty__Collect__eq) ).
thf(978,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(186,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( A
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_nres__order__simps_I2_J) ).
thf(859,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ ( bot_bot @ ( refine1665802226e_nres @ TA ) ) )
= ( A
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(64,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_linorder__wlog) ).
thf(497,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)],[64]) ).
thf(193,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_equals0D) ).
thf(876,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
= ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_flat__ord_Oantisym__conv) ).
thf(845,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
= ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(268,axiom,
! [TA: $tType] :
~ ( refine1102455758nofail @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_nofail__simps_I1_J) ).
thf(1084,plain,
! [TA: $tType] :
~ ( refine1102455758nofail @ TA @ ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(301,axiom,
! [TA: $tType,TB: $tType,A: TA > ( refine1665802226e_nres @ TB ),B: TA > ( refine1665802226e_nres @ TB ),C: TA] :
( ( ord_less_eq @ ( TA > ( refine1665802226e_nres @ TB ) ) @ A @ B )
=> ( ( refine1102455758nofail @ TB @ ( B @ C ) )
=> ( refine1102455758nofail @ TB @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_nofail__antimono__fun) ).
thf(1180,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)],[301]) ).
thf(212,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_the__elem__eq) ).
thf(931,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(123,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_top_Oextremum__uniqueI) ).
thf(671,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)],[123]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_equalityE) ).
thf(759,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)],[153]) ).
thf(73,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_equalityD2) ).
thf(524,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)],[73]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_le__fun__def) ).
thf(581,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)],[94]) ).
thf(97,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_2) ).
thf(588,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(225,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( ( domain @ TA @ TB @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Domain__empty__iff) ).
thf(963,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( ( domain @ TA @ TB @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_prod__cases6) ).
thf(304,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(274,axiom,
! [TA: $tType] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_nres__inequalities_I4_J) ).
thf(1101,plain,
! [TA: $tType] :
( ( bot_bot @ ( refine1665802226e_nres @ TA ) )
!= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(116,axiom,
order_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_11) ).
thf(652,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ssubst__Pair__rhs) ).
thf(390,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_subset__insertI2) ).
thf(632,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(237,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= A )
= ( refine1102455758nofail @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_intro__nofail_I2_J) ).
thf(995,plain,
! [TA: $tType,A: refine1665802226e_nres @ TA] :
( ( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= A )
= ( refine1102455758nofail @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(68,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_antisym) ).
thf(510,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)],[68]) ).
thf(211,axiom,
! [TA: $tType] : ( bot @ ( refine1665802226e_nres @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_33) ).
thf(929,plain,
! [TA: $tType] : ( bot @ ( refine1665802226e_nres @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(176,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_16) ).
thf(832,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(78,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_dual__order_Orefl) ).
thf(536,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(255,axiom,
linorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_21) ).
thf(1045,plain,
linorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(140,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_subset__iff) ).
thf(716,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)],[140]) ).
thf(293,axiom,
! [TA: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ( refine1102455758nofail @ TA @ B )
=> ( refine1102455758nofail @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_pwD1) ).
thf(1161,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)],[293]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_UNIV__eq__I) ).
thf(800,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)],[163]) ).
thf(277,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ E ) @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( refine463715084e_bind @ TA @ TB @ A @ C )
= ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_bind__cong) ).
thf(1116,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)],[277]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',fact_28_abs__trans__additional_I1_J) ).
thf(1133,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)],[281]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_prod__cases5) ).
thf(315,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_7) ).
thf(432,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA] :
( ( refine1315500908_inres @ TA @ ( refine605929679le_RES @ TA @ A ) )
= ( ^ [B: TA] : ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_inres__simps_I2_J) ).
thf(833,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)],[177]) ).
thf(219,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_subset__emptyI) ).
thf(950,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(170,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_insertI1) ).
thf(818,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(184,axiom,
! [TA: $tType] :
( ( refine1102455758nofail @ TA )
= ( ^ [A: refine1665802226e_nres @ TA] :
? [B: set @ TA] :
( A
= ( refine605929679le_RES @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_nofail__RES__conv) ).
thf(854,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)],[184]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',fact_18_conc__fun__fail__iff_I2_J) ).
thf(865,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)],[188]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',fact_194_abs__fun__simps_I3_J) ).
thf(960,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)],[224]) ).
thf(261,axiom,
! [TA: $tType,A: TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_nres__inequalities_I3_J) ).
thf(1065,plain,
! [TA: $tType,A: TA] :
( ( top_top @ ( refine1665802226e_nres @ TA ) )
!= ( refine1687780735RETURN @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(295,axiom,
! [TA: $tType,TB: $tType,A: TB > ( refine1665802226e_nres @ TA )] :
( ( refine463715084e_bind @ TB @ TA @ ( top_top @ ( refine1665802226e_nres @ TB ) ) @ A )
= ( top_top @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_bind__FAIL) ).
thf(1165,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)],[295]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: TA] : ( partial_flat_ord @ TA @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_flat__ord_Odual__order_Orefl) ).
thf(796,plain,
! [TA: $tType,A: TA,B: TA] : ( partial_flat_ord @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(196,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ex__in__conv) ).
thf(886,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType,A: refine1665802226e_nres @ TA,B: refine1665802226e_nres @ TA,C: TA > ( refine1665802226e_nres @ TB ),D: TA > ( refine1665802226e_nres @ TB )] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ E ) @ A )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( refine1665802226e_nres @ TB ) @ ( refine463715084e_bind @ TA @ TB @ A @ C ) @ ( refine463715084e_bind @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J) ).
thf(897,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)],[200]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TB > TA,B: TA > TB,C: TB,D: TA] :
( ( refine1150083786ection @ TB @ TA @ A @ B )
=> ( ( ord_less_eq @ TB @ C @ ( B @ D ) )
= ( ord_less_eq @ TA @ ( A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_galois__connection_Ogalois) ).
thf(767,plain,
! [TA: $tType,TB: $tType] :
( ( ( comple187826305attice @ TA )
& ( comple187826305attice @ TB ) )
=> ! [A: TB > TA,B: TA > TB,C: TB,D: TA] :
( ( refine1150083786ection @ TB @ TA @ A @ B )
=> ( ( ord_less_eq @ TB @ C @ ( B @ D ) )
= ( ord_less_eq @ TA @ ( A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(105,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Collect__mono) ).
thf(624,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)],[105]) ).
thf(57,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_insertE) ).
thf(464,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(99,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_set__eq__subset) ).
thf(596,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)],[99]) ).
thf(74,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_antisym__conv) ).
thf(528,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)],[74]) ).
thf(142,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_top__set__def) ).
thf(723,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(172,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_in__mono) ).
thf(822,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)],[172]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',fact_67_inres__def) ).
thf(1004,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)],[240]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ D )
=> ( partial_flat_ord @ TA @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_flat__ord_Oorder_Otrans) ).
thf(442,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ D )
=> ( partial_flat_ord @ TA @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',fact_148_Domain__mono) ).
thf(369,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)],[22]) ).
thf(290,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( ord_less_eq @ ( refine1665802226e_nres @ TA ) @ ( refine1687780735RETURN @ TA @ A ) @ ( refine605929679le_RES @ TA @ B ) )
= ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_nres__order__simps_I21_J) ).
thf(1152,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)],[290]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mk__disjoint__insert) ).
thf(427,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(204,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_bot_Oextremum__uniqueI) ).
thf(908,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( refine81118332bs_fun @ TB @ TA @ A @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_abs__fun__strict) ).
thf(992,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( refine81118332bs_fun @ TB @ TA @ A @ ( bot_bot @ ( refine1665802226e_nres @ TB ) ) )
= ( bot_bot @ ( refine1665802226e_nres @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(164,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(803,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_old_Oprod_Oexhaust) ).
thf(337,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_top__apply) ).
thf(469,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_prod__cases7) ).
thf(354,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_order__subst1) ).
thf(659,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)],[119]) ).
thf(81,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( top_top @ TA ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_meta__le__everything__if__top) ).
thf(543,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)],[81]) ).
thf(87,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_13) ).
thf(560,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(111,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_insert__absorb) ).
thf(639,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_flat__ord_Oantisym) ).
thf(676,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( partial_flat_ord @ TA @ A @ B @ C )
=> ( ( partial_flat_ord @ TA @ A @ C @ B )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(137,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).
thf(708,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(243,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_bot_Oextremum__unique) ).
thf(1014,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1182,plain,
$false,
inference(e,[status(thm)],[365,1168,347,628,518,1179,777,645,892,1158,683,730,1068,1073,1142,1173,1078,385,533,550,472,814,913,945,340,538,1001,1127,417,565,436,1095,404,973,1046,570,719,702,344,460,934,357,1147,421,969,770,325,448,1151,1020,806,966,1051,1040,321,981,397,634,692,956,453,774,998,411,1104,507,307,380,366,534,942,439,798,1057,1163,334,957,302,862,820,561,1042,952,407,693,1032,361,665,830,889,493,1027,757,710,842,1012,916,467,874,650,1017,388,1138,989,857,697,1089,1028,642,637,590,679,554,753,901,686,1075,1155,547,515,457,911,371,503,792,1086,311,657,1054,1170,1035,674,926,558,1071,794,586,1135,750,513,824,745,573,444,733,584,423,1007,402,772,875,1124,904,975,936,382,611,713,1107,1092,919,704,947,350,540,419,736,377,318,616,599,451,567,880,434,811,631,552,816,726,895,1149,668,462,848,700,521,983,399,827,695,868,563,851,505,653,922,455,883,1176,608,394,986,490,531,663,1081,939,1145,754,836,1049,648,487,1025,872,707,954,739,1098,414,971,331,441,1038,840,808,1130,907,1141,1023,613,978,859,497,876,845,1084,1180,931,671,759,524,581,588,963,304,1101,652,390,632,995,510,929,832,536,1045,716,1161,800,1116,1133,315,432,833,950,818,854,865,960,1065,1165,796,886,897,767,624,464,596,528,723,822,1004,442,369,1152,427,908,992,803,337,469,354,659,543,560,639,676,708,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP164^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.24 % Computer : n016.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 20:09:35 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.91/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.38/1.22 % [INFO] Parsing done (423ms).
% 2.38/1.23 % [INFO] Running in sequential loop mode.
% 3.58/1.67 % [INFO] eprover registered as external prover.
% 3.58/1.68 % [INFO] Scanning for conjecture ...
% 3.95/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 300 axioms. Running axiom selection ...
% 4.22/1.90 % [INFO] Axiom selection finished. Selected 299 axioms (removed 1 axioms).
% 5.29/2.16 % [INFO] Problem is higher-order (TPTP THF).
% 5.75/2.18 % [INFO] Type checking passed.
% 5.75/2.19 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 52.05/28.92 % External prover 'e' found a proof!
% 52.05/28.92 % [INFO] Killing All external provers ...
% 52.05/28.92 % Time passed: 28547ms (effective reasoning time: 27682ms)
% 52.05/28.92 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 52.05/28.93 % Axioms used in derivation (299): fact_234_subset__insertI2, fact_24_inres__simps_I3_J, fact_123_Domain__empty, fact_72_nofail__def, fact_41_eq__refl, fact_100_flat__le__mono__setup_Orefl, tcon_fun___Orderings_Obot, fact_114_flat__ord_Oantisym, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder_30, fact_95_pw__flat__ge__iff, fact_89_nf__inres__def, fact_91_pw__flat__le__iff, fact_178_equalityD1, fact_230_insert__UNIV, fact_38_eq__iff, fact_19_conc__fun__fail__iff_I1_J, fact_232_subset__insert, fact_23_nofail__simps_I3_J, fact_66_abs__trans, fact_119_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I2_J, tcon_Product__Type_Ounit___Complete__Lattices_Ocomplete__lattice_17, fact_208_galois__connection_Ointro, fact_65_pw__leI_H, fact_163_empty__Collect__eq, fact_134_prod__cases5, fact_149_single__valuedD, fact_0_bind__SUCCEED, fact_248_insertE, fact_183_Collect__empty__eq__bot, fact_168_bot__set__def, fact_112_flat__ord_Oorder_Otrans, fact_216_SPEC__cons__rule, tcon_HOL_Obool___Orderings_Opreorder_12, fact_64_pw__leI, fact_10_nofail__simps_I4_J, fact_242_insert__eq__iff, fact_253_the__RES_Osimps, fact_152_DomainE, fact_8_inres__simps_I4_J, fact_13_top__apply, fact_29_conc__trans__additional_I1_J, fact_52_ord__le__eq__trans, fact_49_antisym__conv, fact_225_singleton__insert__inj__eq, tcon_HOL_Obool___Orderings_Obot_16, fact_63_pw__eqI, fact_58_top__greatest, fact_43_order_Otrans, fact_75_top_Oextremum__uniqueI, fact_55_dual__order_Orefl, fact_6_conc__fun__strict, fact_120_conc__fun__R__mono, fact_155_Domain_Osimps, fact_229_nres__more__simps_I5_J, fact_5_abs__fun__strict, fact_217_SPEC__trans, tcon_fun___Orderings_Oord, fact_60_pwD2, fact_165_equals0D, fact_212_nres__order__simps_I5_J, fact_51_ord__eq__le__trans, fact_101_flat__ord_Odual__order_Oantisym, fact_32_le__funI, fact_105_flat__ord_Odual__order_Otrans, fact_1_bot__apply, fact_179_subset__eq, fact_16_nofail__simps_I1_J, tcon_Product__Type_Ounit___Orderings_Olinorder_21, fact_31_le__funE, fact_193_ac__galois, tcon_Set_Oset___Orderings_Obot_8, fact_181_subsetD, tcon_HOL_Obool___Orderings_Olinorder, fact_236_insert__not__empty, tcon_Set_Oset___Orderings_Otop_6, tcon_Set_Oset___Orderings_Oorder__top_2, fact_148_Domain__mono, fact_249_subset__singletonD, fact_118_flat__ord__compat_I2_J, tcon_Product__Type_Ounit___Orderings_Oorder_22, fact_42_le__cases, fact_184_less__by__empty, tcon_HOL_Obool___Orderings_Oord_15, fact_54_order__trans, fact_2_bot__fun__def, fact_93_pw__abs__nofail, fact_172_subset__trans, fact_175_subset__UNIV, tcon_HOL_Obool___Orderings_Oorder_13, fact_20_conc__fun__FAIL, fact_127_Domain_ODomainI, fact_235_singleton__inject, fact_240_mk__disjoint__insert, fact_174_subset__refl, fact_67_inres__def, fact_22_abs__fun__simps_I1_J, tcon_Product__Type_Ounit___Orderings_Opreorder_20, fact_215_nofail__RES__conv, fact_195_nres_Oinject, tcon_HOL_Obool___Orderings_Oorder__bot_11, fact_121_order__mono__setup_Omono__let, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__top_27, fact_28_abs__trans__additional_I1_J, fact_141_prod__induct7, fact_11_bind__FAIL, fact_171_set__eq__subset, fact_94_conc__abs__swap, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Opreorder_29, fact_46_Collect__mem__eq, fact_9_nres__order__simps_I2_J, fact_213_less__eq__nres_Osimps_I2_J, tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_9, fact_122_order__mono__setup_Omono__if, fact_103_flat__ord_Odual__order_Oeq__iff, help_If_1_1_T, fact_156_subset__empty, fact_26_nres__order__simps_I3_J, fact_142_old_Oprod_Oexhaust, fact_33_le__fun__def, fact_74_pw__bind__leI, fact_138_prod__induct4, fact_185_subset__emptyI, fact_161_all__not__in__conv, fact_25_intro__nofail_I2_J, fact_82_bot_Oextremum, tcon_Product__Type_Ounit___Orderings_Otop_23, fact_132_prod__cases3, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Otop_31, fact_129_surj__pair, fact_111_flat__ord_Oorder__trans, fact_124_old_Oprod_Oinject, fact_108_flat__ord_Oorder_Oantisym, fact_40_linear, fact_186_UNIV__I, fact_221_insert__iff, fact_207_galois__connection__def, fact_160_empty__iff, fact_189_UNIV__eq__I, fact_57_dual__order_Otrans, fact_250_subset__singleton__iff, fact_209_galois__connection_Ogalois, fact_187_UNIV__witness, fact_96_GreatestI2__order, fact_219_nres__order__simps_I22_J, fact_173_Collect__mono, fact_237_doubleton__eq__iff, fact_4_nres__monad2, fact_18_conc__fun__fail__iff_I2_J, fact_214_bot__nres__def, tcon_Set_Oset___Orderings_Oord_7, tcon_HOL_Obool___Orderings_Otop_14, fact_246_insertI2, fact_164_emptyE, fact_45_mem__Collect__eq, fact_44_le__cases3, fact_224_insert__subset, fact_196_nres__more__simps_I4_J, fact_76_not__nofail__iff, fact_254_the__elem__eq, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oord_32, fact_79_not__nofail__inres, fact_194_abs__fun__simps_I3_J, fact_144_subrelI, fact_205_nres__cases, fact_226_singleton__insert__inj__eq_H, fact_140_prod__induct6, fact_238_singleton__iff, fact_220_insert__absorb2, fact_201_nf__inres__SPEC, fact_243_insert__absorb, fact_130_prod__cases, fact_39_antisym, fact_59_pwD1, fact_150_single__valuedI, fact_35_order__subst2, fact_110_flat__ord_Oantisym__conv, fact_244_insert__ident, fact_34_order__subst1, fact_228_nres__more__simps_I3_J, fact_80_bot_Oextremum__uniqueI, fact_191_ssubst__Pair__rhs, fact_14_nres__more__simps_I6_J, fact_125_prod_Oinject, fact_182_in__mono, fact_136_prod__cases7, fact_197_top1I, fact_12_nres__order__simps_I1_J, fact_109_flat__ord_Oorder_Oeq__iff, fact_202_nres__more__simps_I2_J, tcon_Product__Type_Ounit___Orderings_Oorder__bot_19, fact_117_flat__ord__compat_I1_J, fact_245_Set_Oset__insert, fact_251_insert__subsetI, fact_167_ex__in__conv, fact_143_old_Oprod_Oinducts, fact_47_Collect__cong, help_If_3_1_T, tcon_fun___Orderings_Oorder__bot, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Oorder__bot_28, fact_177_equalityD2, help_If_2_1_T, fact_84_bind__cong, fact_159_subset__antisym, tcon_fun___Orderings_Otop, tcon_Set_Oset___Orderings_Opreorder_4, fact_99_flat__ord_Odual__order_Orefl, fact_36_ord__eq__le__subst, tcon_Product__Type_Ounit___Orderings_Obot_25, fact_68_pw__eq__iff, fact_61_dual__order_Oeq__iff, fact_204_nres__order__simps_I21_J, fact_200_nf__inres__RES, fact_131_Pair__inject, fact_7_nres__inequalities_I5_J, fact_166_equals0I, fact_162_Collect__empty__eq, fact_126_Domain_Oinducts, tcon_Product__Type_Ounit___Orderings_Oord_24, fact_151_single__valued__def, fact_153_Domain__iff, tcon_fun___Orderings_Opreorder, tcon_Set_Oset___Orderings_Oorder_5, fact_252_RETURN__def, fact_206_nres__inequalities_I1_J, fact_88_order__mono__setup_Orefl, fact_203_nres__more__simps_I1_J, fact_145_single__valued__subset, tcon_fun___Orderings_Oorder__top, fact_37_ord__le__eq__subst, fact_192_iso__tuple__UNIV__I, tcon_fun___Complete__Lattices_Ocomplete__lattice, fact_77_pw__bind__le__iff, fact_21_nres__order__simps_I20_J, fact_190_top__empty__eq, fact_106_flat__ord_Oord__le__eq__trans, fact_17_inres__simps_I1_J, fact_98_Refine__Misc_Oif__mono, fact_133_prod__cases4, fact_139_prod__induct5, fact_147_Domain__empty__iff, fact_90_meta__le__everything__if__top, fact_87_nres__inequalities_I4_J, fact_70_conc__trans, fact_146_single__valued__empty, fact_199_inres__simps_I2_J, fact_78_pw__conc__nofail, tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1, fact_180_equalityE, fact_81_bot_Oextremum__unique, fact_188_top__set__def, tcon_fun___Orderings_Oorder, fact_102_flat__le__mono__setup_Omono__let, fact_86_nres__inequalities_I2_J, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Complete__Lattices_Ocomplete__lattice_26, fact_176_subset__iff, fact_128_bot__empty__eq, tcon_Refine__Basic__Mirabelle__tqojlsrkwy_Onres___Orderings_Obot_33, fact_3_nres__monad1, fact_247_insertI1, fact_113_flat__ord_Oeq__refl, fact_107_flat__ord_Oord__eq__le__trans, fact_231_insert__mono, fact_56_linorder__wlog, fact_223_singletonI, fact_83_pw__bind__nofail, fact_170_Collect__mono__iff, fact_154_Domain_Ocases, fact_211_galois__connection_O_092_060gamma_062_092_060alpha_062__infl, fact_135_prod__cases6, fact_97_Greatest__equality, fact_158_subsetI, fact_227_Domain__insert, fact_233_subset__insertI, fact_239_singletonD, fact_137_prod__induct3, fact_169_empty__not__UNIV, fact_53_order__class_Oorder_Oantisym, fact_157_empty__subsetI, fact_71_le__nofailI, fact_69_pw__le__iff, fact_15_nres__order__simps_I4_J, fact_218_the__RES__inv, fact_30_le__funD, fact_104_flat__le__mono__setup_Omono__if, fact_73_top_Oextremum__unique, tcon_Product__Type_Ounit___Orderings_Oorder__top_18, fact_115_flat__ord_Oeq__iff, fact_27_nres__inequalities_I3_J, fact_50_order__class_Oorder_Oeq__iff, fact_241_insert__commute, fact_222_insertCI, fact_210_galois__connection_O_092_060alpha_062_092_060gamma_062__defl, fact_116_nofail__antimono__fun, tcon_HOL_Obool___Orderings_Oorder__top_10, fact_92_pw__abs__inres, fact_85_Refine__Basic__Mirabelle__tqojlsrkwy_Obind__mono_I1_J, fact_198_nofail__simps_I2_J, fact_62_dual__order_Oantisym, tcon_Set_Oset___Orderings_Oorder__bot_3
% 52.05/28.93 % No. of inferences in proof: 602
% 52.05/28.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28547 ms resp. 27682 ms w/o parsing
% 53.37/29.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 53.37/29.18 % [INFO] Killing All external provers ...
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