TSTP Solution File: DAT236^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT236^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:49 EDT 2024
% Result : Theorem 112.00s 44.88s
% Output : Refutation 112.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 321
% Syntax : Number of formulae : 587 ( 262 unt; 57 typ; 0 def)
% Number of atoms : 2258 ( 522 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 15190 ( 225 ~; 14 |; 129 &;14240 @)
% ( 0 <=>; 582 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 10 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 665 ( 665 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 59 usr; 20 con; 0-8 aty)
% Number of variables : 3408 ( 40 ^3294 !; 6 ?;3408 :)
% ( 68 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(rBT_Im1923302023_color_type,type,
rBT_Im1923302023_color: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(fun_upd_type,type,
fun_upd:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > TB > TA > TB > TA ) ).
thf(set2_type,type,
set2:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(map_of_type,type,
map_of:
!>[TA: $tType,TB: $tType] : ( ( list @ ( product_prod @ TB @ TA ) ) > TB > ( option @ TA ) ) ).
thf(some_type,type,
some:
!>[TA: $tType] : ( TA > ( option @ TA ) ) ).
thf(strict_mono_type,type,
strict_mono:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA ) > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(rBT_Im1648453169alance_type,type,
rBT_Im1648453169alance:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im1278323832e_left_type,type,
rBT_Im1278323832e_left:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im1053358987_right_type,type,
rBT_Im1053358987_right:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im315265182height_type,type,
rBT_Im315265182height:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > nat ) ).
thf(rBT_Impl_Mirabelle_B_type,type,
rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
thf(rBT_Impl_Mirabelle_R_type,type,
rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
thf(rBT_Im1805589839lor_of_type,type,
rBT_Im1805589839lor_of:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > rBT_Im1923302023_color ) ).
thf(rBT_Im1591839508ombine_type,type,
rBT_Im1591839508ombine:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im954575269ntries_type,type,
rBT_Im954575269ntries:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > ( list @ ( product_prod @ TB @ TA ) ) ) ).
thf(rBT_Im1040612427e_inv1_type,type,
rBT_Im1040612427e_inv1:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1071879905_inv1l_type,type,
rBT_Im1071879905_inv1l:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1040612428e_inv2_type,type,
rBT_Im1040612428e_inv2:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im862805236is_rbt_type,type,
rBT_Im862805236is_rbt:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1714610413bt_del_type,type,
rBT_Im1714610413bt_del:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im1152561598m_left_type,type,
rBT_Im1152561598m_left:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im1808746437_right_type,type,
rBT_Im1808746437_right:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im1259024060reater_type,type,
rBT_Im1259024060reater:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1756508336bt_ins_type,type,
rBT_Im1756508336bt_ins:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA > TA > TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im852463031insert_type,type,
rBT_Im852463031insert:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im241132701t_with_type,type,
rBT_Im241132701t_with:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TA > TA > TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im627674146th_key_type,type,
rBT_Im627674146th_key:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA > TA > TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im2075124343t_less_type,type,
rBT_Im2075124343t_less:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > TB > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im35466040lookup_type,type,
rBT_Im35466040lookup:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > ( option @ TA ) ) ).
thf(rBT_Im759614907sorted_type,type,
rBT_Im759614907sorted:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im945281971_paint_type,type,
rBT_Im945281971_paint:
!>[TA: $tType,TB: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im480247531Branch_type,type,
rBT_Im480247531Branch:
!>[TA: $tType,TB: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ TB @ TA ) > TB > TA > ( rBT_Im246033960le_rbt @ TB @ TA ) > ( rBT_Im246033960le_rbt @ TB @ TA ) ) ).
thf(rBT_Im418718756_Empty_type,type,
rBT_Im418718756_Empty:
!>[TA: $tType,TB: $tType] : ( rBT_Im246033960le_rbt @ TB @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(set_greaterThan_type,type,
set_greaterThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_lessThan_type,type,
set_lessThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(transitive_acyclic_type,type,
transitive_acyclic:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(bb_type,type,
bb: rBT_Im246033960le_rbt @ a @ b ).
thf(c_type,type,
c: rBT_Im1923302023_color ).
thf(k_type,type,
k: a ).
thf(less_type,type,
less: a > a > $o ).
thf(ss_type,type,
ss: b ).
thf(v_type,type,
v: b ).
thf(vaa_type,type,
vaa: rBT_Im246033960le_rbt @ a @ b ).
thf(vbb_type,type,
vbb: a ).
thf(vc_type,type,
vc: rBT_Im246033960le_rbt @ a @ b ).
thf(vdd_type,type,
vdd: b ).
thf(xx_type,type,
xx: a ).
thf(yy_type,type,
yy: a ).
thf(217,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ G @ H )
= ( rBT_Im1278323832e_left @ a @ TA @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) ) @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_local_Orbt__del__from__left_Osimps_I1_J) ).
thf(909,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ G @ H )
= ( rBT_Im1278323832e_left @ a @ TA @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) ) @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB > TB > TB,C: TA,D: TB] :
( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ B @ C @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ C @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_ord_Orbt__ins_Osimps_I1_J) ).
thf(777,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB > TB > TB,C: TA,D: TB] :
( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ B @ C @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ C @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(230,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_local_Oord__eq__less__trans) ).
thf(962,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_220_prod__induct6) ).
thf(468,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)],[81]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(408,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(148,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(683,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1278323832e_left @ TA @ TB @ A @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_balance__left__inv1l) ).
thf(276,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1278323832e_left @ TA @ TB @ A @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: TA,E: TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_balance__right_Osimps_I7_J) ).
thf(994,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: TA,E: TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) )
= ( ( rBT_Im2075124343t_less @ TA @ TB @ A @ D @ C )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ D @ F )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ C )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ord_Orbt__sorted_Osimps_I2_J) ).
thf(741,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) )
= ( ( rBT_Im2075124343t_less @ TA @ TB @ A @ D @ C )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ D @ F )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ C )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(122,axiom,
! [TA: $tType,A: a > TA > TA > TA,B: a,C: TA,D: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im627674146th_key @ a @ TA @ less @ A @ B @ C @ D )
= ( rBT_Im945281971_paint @ a @ TA @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_local_Orbt__insert__with__key__def) ).
thf(597,plain,
! [TA: $tType,A: a > TA > TA > TA,B: a,C: TA,D: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im627674146th_key @ a @ TA @ less @ A @ B @ C @ D )
= ( rBT_Im945281971_paint @ a @ TA @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(259,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1591839508ombine @ a @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_local_Ocombine__rbt__less) ).
thf(1041,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1591839508ombine @ a @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(70,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: TA > TA > TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im241132701t_with @ a @ TA @ less @ B @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_local_Orbt__insertw__rbt__sorted) ).
thf(440,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: TA > TA > TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im241132701t_with @ a @ TA @ less @ B @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: TB,D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TB @ TA,F: TA,G: rBT_Im246033960le_rbt @ TB @ TA] :
( ( ( A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ E @ B ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ G @ B ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( some @ TA @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_ord_Orbt__lookup_Osimps_I2_J) ).
thf(655,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: TB,D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TB @ TA,F: TA,G: rBT_Im246033960le_rbt @ TB @ TA] :
( ( ( A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ E @ B ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ G @ B ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( some @ TA @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( ( rBT_Im1071879905_inv1l @ TA @ TB @ B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1648453169alance @ TA @ TB @ A @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_balance__inv1) ).
thf(269,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( ( rBT_Im1071879905_inv1l @ TA @ TB @ B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1648453169alance @ TA @ TB @ A @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(146,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1648453169alance @ a @ TA @ B @ C @ D @ E ) )
= ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
& ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ E )
& ( less @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_local_Obalance__rbt__less) ).
thf(677,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1648453169alance @ a @ TA @ B @ C @ D @ E ) )
= ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
& ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ E )
& ( less @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o] : ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_ord_Orbt__sorted_Osimps_I1_J) ).
thf(384,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o] : ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(101,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_local_Oins__rbt__sorted) ).
thf(533,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_balance_Osimps_I22_J) ).
thf(500,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_209_prod_Oinject) ).
thf(797,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)],[182]) ).
thf(187,axiom,
! [TA: $tType,A: a,B: a,C: a > TA > TA > TA,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: TA,G: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ F @ G ) )
= ( rBT_Im1648453169alance @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ E ) @ B @ F @ G ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ F @ G ) )
= ( rBT_Im1648453169alance @ a @ TA @ E @ B @ F @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ G ) ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ ( C @ A @ F @ D ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_local_Orbt__ins_Osimps_I2_J) ).
thf(814,plain,
! [TA: $tType,A: a,B: a,C: a > TA > TA > TA,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: TA,G: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ F @ G ) )
= ( rBT_Im1648453169alance @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ E ) @ B @ F @ G ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ F @ G ) )
= ( rBT_Im1648453169alance @ a @ TA @ E @ B @ F @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ G ) ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ B @ ( C @ A @ F @ D ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(154,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) )
= ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ B ) ) )
= ( ( rBT_Im954575269ntries @ a @ TA @ A )
= ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_local_Oset__entries__inject) ).
thf(698,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) )
= ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ B ) ) )
= ( ( rBT_Im954575269ntries @ a @ TA @ A )
= ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(170,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( ~ ( less @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_local_Oantisym__conv3) ).
thf(747,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( ~ ( less @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',fact_221_prod__induct5) ).
thf(930,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)],[224]) ).
thf(58,axiom,
! [TA: $tType] : ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_local_OEmpty__is__rbt) ).
thf(404,plain,
! [TA: $tType] : ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(158,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_local_Oless__not__sym) ).
thf(709,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_combine_Osimps_I1_J) ).
thf(320,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',fact_208_old_Oprod_Oinject) ).
thf(885,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)],[209]) ).
thf(261,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_surj__pair) ).
thf(1046,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)],[261]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im852463031insert @ TA @ TB )
= ( ^ [A: TA > TA > $o] :
( rBT_Im627674146th_key @ TA @ TB @ A
@ ^ [B: TA,C: TB,D: TB] : D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_ord_Orbt__insert__def) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im852463031insert @ TA @ TB )
= ( ^ [A: TA > TA > $o] :
( rBT_Im627674146th_key @ TA @ TB @ A
@ ^ [B: TA,C: TB,D: TB] : D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im945281971_paint @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) )
= ( rBT_Im480247531Branch @ TA @ TB @ A @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_paint_Osimps_I2_J) ).
thf(570,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im945281971_paint @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) )
= ( rBT_Im480247531Branch @ TA @ TB @ A @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(161,axiom,
! [TA: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im945281971_paint @ a @ TA @ A @ B ) )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_local_Opaint__rbt__lookup) ).
thf(719,plain,
! [TA: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im945281971_paint @ a @ TA @ A @ B ) )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ C @ D @ E )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_ord_Orbt__del__from__left_Osimps_I2_J) ).
thf(785,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ C @ D @ E )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(119,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_local_Oless__irrefl) ).
thf(587,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ C )
= D )
=> ( ( ( C
= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( D
!= ( rBT_Im418718756_Empty @ TA @ TB ) ) )
=> ~ ! [E: rBT_Im1923302023_color,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( C
= ( rBT_Im480247531Branch @ TA @ TB @ E @ F @ G @ H @ I ) )
=> ~ ( ( ( A @ B @ G )
=> ( D
= ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ F @ G @ H @ I ) ) )
& ( ~ ( A @ B @ G )
=> ( ( ( A @ G @ B )
=> ( D
= ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ F @ G @ H @ I ) ) )
& ( ~ ( A @ G @ B )
=> ( D
= ( rBT_Im1591839508ombine @ TA @ TB @ F @ I ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_ord_Orbt__del_Oelims) ).
thf(934,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ C )
= D )
=> ( ( ( C
= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( D
!= ( rBT_Im418718756_Empty @ TA @ TB ) ) )
=> ~ ! [E: rBT_Im1923302023_color,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( C
= ( rBT_Im480247531Branch @ TA @ TB @ E @ F @ G @ H @ I ) )
=> ~ ( ( ( A @ B @ G )
=> ( D
= ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ F @ G @ H @ I ) ) )
& ( ~ ( A @ B @ G )
=> ( ( ( A @ G @ B )
=> ( D
= ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ F @ G @ H @ I ) ) )
& ( ~ ( A @ G @ B )
=> ( D
= ( rBT_Im1591839508ombine @ TA @ TB @ F @ I ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(111,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1808746437_right @ a @ TA @ less @ A @ B @ C @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_local_Orbt__del__from__right_Osimps_I3_J) ).
thf(559,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1808746437_right @ a @ TA @ less @ A @ B @ C @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ G @ H @ I )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_ord_Orbt__del__from__left_Osimps_I3_J) ).
thf(416,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ G @ H @ I )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) )] :
( ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) )
=> ( ! [B: TA,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im418718756_Empty @ TA @ TB ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ E ) ) ) ) )
=> ~ ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_ord_Orbt__del__from__left_Ocases) ).
thf(448,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) )] :
( ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) )
=> ( ! [B: TA,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im418718756_Empty @ TA @ TB ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ E ) ) ) ) )
=> ~ ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ G @ H @ I ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_balance__left_Osimps_I10_J) ).
thf(638,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ G @ H @ I ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',fact_207_prod__cases7) ).
thf(853,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)],[196]) ).
thf(90,axiom,
! [TA: $tType,A: product_prod @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) )] :
( ! [B: a,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ G @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ H @ I ) ) ) ) )
=> ( ! [B: a,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ ( rBT_Im418718756_Empty @ a @ TA ) @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ E ) ) ) ) )
=> ~ ! [B: a,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ G @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ H @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_local_Orbt__del__from__left_Ocases) ).
thf(492,plain,
! [TA: $tType,A: product_prod @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) )] :
( ! [B: a,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ G @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ H @ I ) ) ) ) )
=> ( ! [B: a,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ ( rBT_Im418718756_Empty @ a @ TA ) @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ E ) ) ) ) )
=> ~ ! [B: a,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( product_prod @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ a @ TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ G @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ H @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_paint__inv1) ).
thf(353,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_balance__right_Osimps_I8_J) ).
thf(480,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(84,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1808746437_right @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rbt__del__from__right__rbt__less) ).
thf(475,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1808746437_right @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(222,axiom,
! [TA: $tType,A: a,B: a,C: TA,D: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) @ B @ C @ D )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ) @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_local_Orbt__del__from__left_Osimps_I2_J) ).
thf(924,plain,
! [TA: $tType,A: a,B: a,C: TA,D: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) @ B @ C @ D )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(252,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_local_Odual__order_Oasym) ).
thf(1020,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_combine__inv2_I2_J) ).
thf(348,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(263,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_local_Oorder_Oirrefl) ).
thf(1051,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_balance_Osimps_I17_J) ).
thf(821,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(236,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( A != B )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_local_Olinorder__cases) ).
thf(981,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( A != B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ord_Oins__inv1__inv2_I1_J) ).
thf(280,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(206,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( ( rBT_Im35466040lookup @ a @ TA @ less @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B ) )
=> ( ( rBT_Im954575269ntries @ a @ TA @ A )
= ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_local_Oentries__eqI) ).
thf(877,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( ( rBT_Im35466040lookup @ a @ TA @ less @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B ) )
=> ( ( rBT_Im954575269ntries @ a @ TA @ A )
= ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ G @ H @ I )
= ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) ) @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_ord_Orbt__del__from__left_Osimps_I1_J) ).
thf(734,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ G @ H @ I )
= ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) ) @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_color__of_Osimps_I2_J) ).
thf(866,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(61,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1152561598m_left @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_rbt__del__from__left__rbt__less) ).
thf(411,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1152561598m_left @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(67,axiom,
! [TA: $tType,A: a,B: a,C: a > TA > TA > TA,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: TA,G: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ E ) @ B @ F @ G ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ G ) ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ ( C @ A @ F @ D ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_local_Orbt__ins_Osimps_I3_J) ).
thf(428,plain,
! [TA: $tType,A: a,B: a,C: a > TA > TA > TA,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: TA,G: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ E ) @ B @ F @ G ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ G ) ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ C @ A @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ F @ G ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ B @ ( C @ A @ F @ D ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] :
( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_ord_Orbt__del_Osimps_I1_J) ).
thf(293,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] :
( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(228,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_local_OgreaterThan__iff) ).
thf(956,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(99,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1648453169alance @ a @ TA @ B @ C @ D @ E ) )
= ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
& ( rBT_Im1259024060reater @ a @ TA @ less @ A @ E )
& ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_local_Obalance__rbt__greater) ).
thf(527,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1648453169alance @ a @ TA @ B @ C @ D @ E ) )
= ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
& ( rBT_Im1259024060reater @ a @ TA @ less @ A @ E )
& ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im1648453169alance @ TA @ TB @ A @ C @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_balance__inv2) ).
thf(312,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im1648453169alance @ TA @ TB @ A @ C @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_combine__inv1_I2_J) ).
thf(307,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType] : ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_inv2_Osimps_I1_J) ).
thf(380,plain,
! [TA: $tType,TB: $tType] : ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(106,axiom,
! [TA: $tType,A: a] : ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_local_Orbt__greater__simps_I1_J) ).
thf(546,plain,
! [TA: $tType,A: a] : ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im1923302023_color] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_paint__inv1l) ).
thf(366,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im1923302023_color] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(265,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_balance_Osimps_I19_J) ).
thf(1057,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(334,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(212,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( map_of @ a @ TA @ ( rBT_Im954575269ntries @ a @ TA @ A ) )
= ( rBT_Im35466040lookup @ a @ TA @ less @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_local_Omap__of__entries) ).
thf(894,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( map_of @ a @ TA @ ( rBT_Im954575269ntries @ a @ TA @ A ) )
= ( rBT_Im35466040lookup @ a @ TA @ less @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(199,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_local_OlessThan__iff) ).
thf(862,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ A )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ord_Oins__inv1__inv2_I3_J) ).
thf(392,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ A )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',fact_219_prod__induct7) ).
thf(693,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)],[152]) ).
thf(6,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1) ).
thf(275,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_balance_Osimps_I15_J) ).
thf(788,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(80,axiom,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35__C4__2_Oprems_C_I1_J) ).
thf(467,plain,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(194,axiom,
! [TA: $tType] :
( ( rBT_Im852463031insert @ a @ TA @ less )
= ( rBT_Im627674146th_key @ a @ TA @ less
@ ^ [A: a,B: TA,C: TA] : C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_local_Orbt__insert__def) ).
thf(847,plain,
! [TA: $tType] :
( ( rBT_Im852463031insert @ a @ TA @ less )
= ( rBT_Im627674146th_key @ a @ TA @ less
@ ^ [A: a,B: TA,C: TA] : C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ A )
= rBT_Impl_Mirabelle_B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ B )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_combine__inv1_I1_J) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ A )
= rBT_Impl_Mirabelle_B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ B )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fact_215_prod__induct3) ).
thf(435,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)],[68]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im1923302023_color] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_paint__inv2) ).
thf(329,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im1923302023_color] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(78,axiom,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_local_Oless__imp__triv) ).
thf(461,plain,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(255,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: product_prod @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) )] :
( ! [B: TA > TB > TB > TB,C: TA,D: TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ) )
=> ( ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ) )
=> ~ ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_ord__class_Orbt__ins_Ocases) ).
thf(1027,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: product_prod @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) )] :
( ! [B: TA > TB > TB > TB,C: TA,D: TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ) )
=> ( ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ) )
=> ~ ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ B @ C @ D @ E ) )
=> ~ ! [B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_rbt__cases) ).
thf(551,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ B @ C @ D @ E ) )
=> ~ ! [B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] : ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_inv1_Osimps_I1_J) ).
thf(285,plain,
! [TA: $tType,TB: $tType] : ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(205,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_balance_Osimps_I23_J) ).
thf(874,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(128,axiom,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im945281971_paint @ a @ TA @ B @ C ) )
= ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_local_Opaint__rbt__less) ).
thf(615,plain,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im945281971_paint @ a @ TA @ B @ C ) )
= ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',fact_217_prod__induct4) ).
thf(725,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)],[163]) ).
thf(246,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1152561598m_left @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rbt__del__from__left__rbt__greater) ).
thf(1006,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1152561598m_left @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(202,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1053358987_right @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_local_Obalance__right__rbt__greater) ).
thf(869,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1053358987_right @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im1591839508ombine @ TA @ TB @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_combine_Osimps_I6_J) ).
thf(610,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im1591839508ombine @ TA @ TB @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(177,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im627674146th_key @ a @ TA @ less @ B @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_local_Orbt__insertwk__is__rbt) ).
thf(783,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im627674146th_key @ a @ TA @ less @ B @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(239,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( less @ A @ C )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_local_Orbt__less__trans) ).
thf(989,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( less @ A @ C )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(103,axiom,
! [TA: $tType,A: a] : ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_local_Orbt__less__simps_I1_J) ).
thf(537,plain,
! [TA: $tType,A: a] : ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(149,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: TA > TA > TA,C: a,D: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im241132701t_with @ a @ TA @ less @ B @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_local_Orbt__insertw__is__rbt) ).
thf(686,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: TA > TA > TA,C: a,D: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im241132701t_with @ a @ TA @ less @ B @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(89,axiom,
! [A: a,B: a] :
( ( A != B )
= ( ( less @ A @ B )
| ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_local_Oneq__iff) ).
thf(489,plain,
! [A: a,B: a] :
( ( A != B )
= ( ( less @ A @ B )
| ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(232,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_local_Oless__imp__not__less) ).
thf(970,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(109,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1591839508ombine @ a @ TA @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_local_Ocombine__rbt__sorted) ).
thf(554,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1591839508ombine @ a @ TA @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',fact_210_old_Oprod_Oinducts) ).
thf(753,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)],[172]) ).
thf(250,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_balance__right_Osimps_I9_J) ).
thf(1016,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(120,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_local_Oless__imp__neq) ).
thf(590,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(155,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ E ) @ F @ G @ H )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ E ) ) @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_local_Orbt__del__from__left_Osimps_I3_J) ).
thf(701,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ E ) @ F @ G @ H )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ E ) ) @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(76,axiom,
rBT_Im1040612427e_inv1 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32__C4__2_Oprems_C_I5_J) ).
thf(457,plain,
rBT_Im1040612427e_inv1 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(237,axiom,
! [A: a] :
( ( set_greaterThan @ a @ less @ A )
= ( collect @ a @ ( less @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_local_OgreaterThan__def) ).
thf(984,plain,
! [A: a] :
( ( set_greaterThan @ a @ less @ A )
= ( collect @ a @ ( less @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(113,axiom,
rBT_Im1259024060reater @ a @ b @ less @ yy @ bb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31__C4__2_Oprems_C_I4_J) ).
thf(569,plain,
rBT_Im1259024060reater @ a @ b @ less @ yy @ bb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TB > ( option @ TA ),B: TB,C: TA,D: TB > ( option @ TA ),E: TA] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ A @ B @ ( some @ TA @ C ) )
= ( fun_upd @ TB @ ( option @ TA ) @ D @ B @ ( some @ TA @ E ) ) )
=> ( C = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_map__upd__eqD1) ).
thf(371,plain,
! [TA: $tType,TB: $tType,A: TB > ( option @ TA ),B: TB,C: TA,D: TB > ( option @ TA ),E: TA] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ A @ B @ ( some @ TA @ C ) )
= ( fun_upd @ TB @ ( option @ TA ) @ D @ B @ ( some @ TA @ E ) ) )
=> ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(94,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_local_Oorder_Ostrict__trans) ).
thf(503,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_213_prod__cases) ).
thf(647,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)],[138]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ E @ B )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ D )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_ord_Orbt__less__simps_I2_J) ).
thf(997,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ E @ B )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ D )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im241132701t_with @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TB > TB > TB] :
( rBT_Im627674146th_key @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ord_Orbt__insertw__def) ).
thf(343,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im241132701t_with @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TB > TB > TB] :
( rBT_Im627674146th_key @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
( ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im1152561598m_left @ a @ b @ less @ xx @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) @ yy @ ss @ bb ) ) ) )
!= ( ~ ( ( xx != k )
& ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ c @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) @ yy @ ss @ bb ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im1152561598m_left @ a @ b @ less @ xx @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) @ yy @ ss @ bb ) ) ) )
!= ( ~ ( ( xx != k )
& ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ c @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) @ yy @ ss @ bb ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(266,plain,
( ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im1152561598m_left @ a @ b @ less @ xx @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) @ yy @ ss @ bb ) ) ) )
!= ( ~ ( ( xx != k )
& ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ c @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) @ yy @ ss @ bb ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ D )
=> ( ( A @ G )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_rbt_Oinduct) ).
thf(508,plain,
! [TA: $tType,TB: $tType,A: ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ D )
=> ( ( A @ G )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB,L: TA,M: TB,N: rBT_Im246033960le_rbt @ TA @ TB,O: TA,P: TB,Q: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_balance_Osimps_I45_J) ).
thf(921,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB,L: TA,M: TB,N: rBT_Im246033960le_rbt @ TA @ TB,O: TA,P: TB,Q: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(264,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) @ K @ L @ M ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_balance__left_Osimps_I11_J) ).
thf(1054,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) @ K @ L @ M ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_balance__right_Osimps_I6_J) ).
thf(398,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ~ ! [B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_rbt_Oexhaust) ).
thf(674,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ~ ! [B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( rBT_Im480247531Branch @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',fact_206_prod__cases6) ).
thf(530,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)],[100]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_balance__right_Osimps_I11_J) ).
thf(953,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: product_prod @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB )] :
( ! [B: TA] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
=> ~ ! [B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_ord__class_Orbt__del_Ocases) ).
thf(794,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: product_prod @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB )] :
( ! [B: TA] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
=> ~ ! [B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(142,axiom,
( ( rBT_Im315265182height @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
= ( rBT_Im315265182height @ a @ b @ bb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38__C4__2_Oprems_C_I9_J) ).
thf(662,plain,
( ( rBT_Im315265182height @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
= ( rBT_Im315265182height @ a @ b @ bb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(210,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im1808746437_right @ a @ TA @ less @ A @ B @ C @ D @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_local_Orbt__del__from__right_Osimps_I2_J) ).
thf(888,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im1808746437_right @ a @ TA @ less @ A @ B @ C @ D @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ B @ C @ D @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(171,axiom,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_color_Oexhaust) ).
thf(750,plain,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(129,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
| ( A = B )
| ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_local_Oless__linear) ).
thf(618,plain,
! [A: a,B: a] :
( ( less @ A @ B )
| ( A = B )
| ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(66,axiom,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( ( less @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_local_Onot__less__iff__gr__or__eq) ).
thf(425,plain,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( ( less @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(189,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_rbt__del__rbt__less) ).
thf(824,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E ) @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_combine_Osimps_I5_J) ).
thf(856,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E ) @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(115,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( less @ A @ B )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_local_OneqE) ).
thf(573,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( less @ A @ B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color] :
( ( rBT_Im945281971_paint @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_paint_Osimps_I1_J) ).
thf(296,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color] :
( ( rBT_Im945281971_paint @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(117,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1278323832e_left @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_local_Obalance__left__rbt__less) ).
thf(579,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1278323832e_left @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1040612427e_inv1 @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TB @ TA @ B )
& ( rBT_Im1040612427e_inv1 @ TB @ TA @ E )
& ( ( A = rBT_Impl_Mirabelle_B )
| ( ( ( rBT_Im1805589839lor_of @ TB @ TA @ B )
= rBT_Impl_Mirabelle_B )
& ( ( rBT_Im1805589839lor_of @ TB @ TA @ E )
= rBT_Impl_Mirabelle_B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_inv1_Osimps_I2_J) ).
thf(413,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TB @ TA,C: TB,D: TA,E: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1040612427e_inv1 @ TB @ TA @ ( rBT_Im480247531Branch @ TB @ TA @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TB @ TA @ B )
& ( rBT_Im1040612427e_inv1 @ TB @ TA @ E )
& ( ( A = rBT_Impl_Mirabelle_B )
| ( ( ( rBT_Im1805589839lor_of @ TB @ TA @ B )
= rBT_Impl_Mirabelle_B )
& ( ( rBT_Im1805589839lor_of @ TB @ TA @ E )
= rBT_Impl_Mirabelle_B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: TA,D: TA > TB > TB > TB,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( A @ B @ C )
=> ( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ F ) @ C @ G @ H ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ H ) ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ ( D @ B @ G @ E ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ord_Orbt__ins_Osimps_I3_J) ).
thf(562,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: TA,D: TA > TB > TB > TB,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( A @ B @ C )
=> ( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ F ) @ C @ G @ H ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ H ) ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ D @ B @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ C @ ( D @ B @ G @ E ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',fact_205_prod__cases5) ).
thf(904,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)],[215]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) )
= ( rBT_Im1053358987_right @ TA @ TB @ C @ D @ E @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ord_Orbt__del__from__right_Osimps_I1_J) ).
thf(975,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) )
= ( rBT_Im1053358987_right @ TA @ TB @ C @ D @ E @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(190,axiom,
! [TA: $tType,A: ( a > TA > TA > TA ) > a > TA > ( rBT_Im246033960le_rbt @ a @ TA ) > $o,B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ! [F: a > TA > TA > TA,G: a,H: TA] : ( A @ F @ G @ H @ ( rBT_Im418718756_Empty @ a @ TA ) )
=> ( ! [F: a > TA > TA > TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA,J: a,K: TA,L: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( less @ G @ J )
=> ( ( less @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) )
=> ( ! [F: a > TA > TA > TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA,J: a,K: TA,L: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( less @ G @ J )
=> ( ( less @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ I @ J @ K @ L ) ) ) )
=> ( A @ B @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_local_Orbt__ins_Oinduct) ).
thf(826,plain,
! [TA: $tType,A: ( a > TA > TA > TA ) > a > TA > ( rBT_Im246033960le_rbt @ a @ TA ) > $o,B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ! [F: a > TA > TA > TA,G: a,H: TA] : ( A @ F @ G @ H @ ( rBT_Im418718756_Empty @ a @ TA ) )
=> ( ! [F: a > TA > TA > TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA,J: a,K: TA,L: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( less @ G @ J )
=> ( ( less @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) )
=> ( ! [F: a > TA > TA > TA,G: a,H: TA,I: rBT_Im246033960le_rbt @ a @ TA,J: a,K: TA,L: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( less @ G @ J )
=> ( ( less @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ I @ J @ K @ L ) ) ) )
=> ( A @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(159,axiom,
rBT_Im1040612428e_inv2 @ a @ b @ bb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__C4__2_Oprems_C_I8_J) ).
thf(711,plain,
rBT_Im1040612428e_inv2 @ a @ b @ bb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(135,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1053358987_right @ a @ TA @ A @ C @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_local_Obalance__right__rbt__sorted) ).
thf(641,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1053358987_right @ a @ TA @ A @ C @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',fact_216_prod__cases3) ).
thf(445,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)],[72]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType] : ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_inv1l_Osimps_I1_J) ).
thf(382,plain,
! [TA: $tType,TB: $tType] : ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: product_prod @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) )] :
( ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) )
=> ( ! [B: TA,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im418718756_Empty @ TA @ TB ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ E ) ) ) ) )
=> ~ ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_ord__class_Orbt__del__from__left_Ocases) ).
thf(704,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: product_prod @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) )] :
( ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) )
=> ( ! [B: TA,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im418718756_Empty @ TA @ TB ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ E ) ) ) ) )
=> ~ ! [B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( product_prod @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) ) @ B @ ( product_Pair @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ G @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ H @ I ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: TA > ( option @ TB ),B: TA,C: TB] :
( ( ( A @ B )
= ( some @ TB @ C ) )
=> ( ( fun_upd @ TA @ ( option @ TB ) @ A @ B @ ( some @ TB @ C ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_map__upd__triv) ).
thf(377,plain,
! [TA: $tType,TB: $tType,A: TA > ( option @ TB ),B: TA,C: TB] :
( ( ( A @ B )
= ( some @ TB @ C ) )
=> ( ( fun_upd @ TA @ ( option @ TB ) @ A @ B @ ( some @ TB @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_balance_Osimps_I27_J) ).
thf(451,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_ord_Oins__inv1__inv2_I4_J) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(214,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_local_Odual__order_Ostrict__implies__not__eq) ).
thf(900,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(59,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1648453169alance @ a @ TA @ A @ C @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_local_Obalance__rbt__sorted) ).
thf(406,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1648453169alance @ a @ TA @ A @ C @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(248,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ G @ H @ I ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ord_Orbt__del__from__right_Osimps_I3_J) ).
thf(1011,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ G @ H @ I ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ G @ H @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ C @ D ) ) ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_paint__in__tree) ).
thf(419,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ C @ D ) ) ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(166,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_local_Ois__rbt__rbt__sorted) ).
thf(737,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(23,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_6) ).
thf(318,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ B @ E )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ D )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_ord_Orbt__greater__simps_I2_J) ).
thf(880,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) )
= ( ( A @ B @ E )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ D )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(139,axiom,
! [TA: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ B )
& ( rBT_Im1259024060reater @ a @ TA @ less @ C @ E )
& ( rBT_Im759614907sorted @ a @ TA @ less @ B )
& ( rBT_Im759614907sorted @ a @ TA @ less @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_local_Orbt__sorted_Osimps_I2_J) ).
thf(649,plain,
! [TA: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ B )
& ( rBT_Im1259024060reater @ a @ TA @ less @ C @ E )
& ( rBT_Im759614907sorted @ a @ TA @ less @ B )
& ( rBT_Im759614907sorted @ a @ TA @ less @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(260,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im418718756_Empty @ TA @ TB )
!= ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rbt_Odistinct_I1_J) ).
thf(1043,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im418718756_Empty @ TA @ TB )
!= ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ C @ D @ E ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_balance__left_Osimps_I7_J) ).
thf(477,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ C @ D @ E ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_balance_Osimps_I43_J) ).
thf(811,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(132,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_local_Oless__imp__not__eq2) ).
thf(631,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(174,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ B )
= C )
=> ( ( ( B
= ( rBT_Im418718756_Empty @ a @ TA ) )
=> ( C
!= ( rBT_Im418718756_Empty @ a @ TA ) ) )
=> ~ ! [D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( B
= ( rBT_Im480247531Branch @ a @ TA @ D @ E @ F @ G @ H ) )
=> ~ ( ( ( less @ A @ F )
=> ( C
= ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ E @ F @ G @ H ) ) )
& ( ~ ( less @ A @ F )
=> ( ( ( less @ F @ A )
=> ( C
= ( rBT_Im1808746437_right @ a @ TA @ less @ A @ E @ F @ G @ H ) ) )
& ( ~ ( less @ F @ A )
=> ( C
= ( rBT_Im1591839508ombine @ a @ TA @ E @ H ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_local_Orbt__del_Oelims) ).
thf(758,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ B )
= C )
=> ( ( ( B
= ( rBT_Im418718756_Empty @ a @ TA ) )
=> ( C
!= ( rBT_Im418718756_Empty @ a @ TA ) ) )
=> ~ ! [D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( B
= ( rBT_Im480247531Branch @ a @ TA @ D @ E @ F @ G @ H ) )
=> ~ ( ( ( less @ A @ F )
=> ( C
= ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ E @ F @ G @ H ) ) )
& ( ~ ( less @ A @ F )
=> ( ( ( less @ F @ A )
=> ( C
= ( rBT_Im1808746437_right @ a @ TA @ less @ A @ E @ F @ G @ H ) ) )
& ( ~ ( less @ F @ A )
=> ( C
= ( rBT_Im1591839508ombine @ a @ TA @ E @ H ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(102,axiom,
! [TA: $tType] : ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_local_Orbt__sorted_Osimps_I1_J) ).
thf(535,plain,
! [TA: $tType] : ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im315265182height @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) )
= ( rBT_Im315265182height @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_ord_Oins__inv1__inv2_I2_J) ).
thf(323,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im315265182height @ TA @ TB @ ( rBT_Im1756508336bt_ins @ TA @ TB @ B @ C @ D @ E @ A ) )
= ( rBT_Im315265182height @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(121,axiom,
! [TA: $tType,A: a,B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ E ) )
= ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ E )
& ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_local_Oins__rbt__greater) ).
thf(594,plain,
! [TA: $tType,A: a,B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ E ) )
= ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ E )
& ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(130,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_local_Oless__trans) ).
thf(621,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: list @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( set2 @ ( product_prod @ TB @ TA ) @ C ) )
=> ? [D: TA] :
( ( map_of @ TB @ TA @ C @ A )
= ( some @ TA @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_weak__map__of__SomeI) ).
thf(483,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: list @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( set2 @ ( product_prod @ TB @ TA ) @ C ) )
=> ? [D: TA] :
( ( map_of @ TB @ TA @ C @ A )
= ( some @ TA @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(219,axiom,
! [TA: $tType,A: TA > TA > TA] :
( ( rBT_Im241132701t_with @ a @ TA @ less @ A )
= ( rBT_Im627674146th_key @ a @ TA @ less
@ ^ [B: a] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_local_Orbt__insertw__def) ).
thf(915,plain,
! [TA: $tType,A: TA > TA > TA] :
( ( rBT_Im241132701t_with @ a @ TA @ less @ A )
= ( rBT_Im627674146th_key @ a @ TA @ less
@ ^ [B: a] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(253,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( ( rBT_Im315265182height @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) )
= ( rBT_Im315265182height @ a @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_local_Oins__inv1__inv2_I2_J) ).
thf(1022,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( ( rBT_Im315265182height @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) )
= ( rBT_Im315265182height @ a @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(225,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im852463031insert @ a @ TA @ less @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_local_Orbt__insert__rbt__sorted) ).
thf(932,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im852463031insert @ a @ TA @ less @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TA @ TB ),B: TA,C: TB] :
( ( ( map_of @ TA @ TB @ A @ B )
= ( some @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( set2 @ ( product_prod @ TA @ TB ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_map__of__SomeD) ).
thf(959,plain,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TA @ TB ),B: TA,C: TB] :
( ( ( map_of @ TA @ TB @ A @ B )
= ( some @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( set2 @ ( product_prod @ TA @ TB ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_balance_Osimps_I18_J) ).
thf(695,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(8,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_3) ).
thf(278,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(176,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: a,C: a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_local_Ostrict__mono__eq) ).
thf(780,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: a,C: a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(208,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im627674146th_key @ a @ TA @ less @ B @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_local_Orbt__insertwk__rbt__sorted) ).
thf(883,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im627674146th_key @ a @ TA @ less @ B @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
& ( rBT_Im1040612428e_inv2 @ TA @ TB @ E )
& ( ( rBT_Im315265182height @ TA @ TB @ B )
= ( rBT_Im315265182height @ TA @ TB @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_inv2_Osimps_I2_J) ).
thf(1000,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
& ( rBT_Im1040612428e_inv2 @ TA @ TB @ E )
& ( ( rBT_Im315265182height @ TA @ TB @ B )
= ( rBT_Im315265182height @ TA @ TB @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im35466040lookup @ TA @ TB @ A @ ( rBT_Im945281971_paint @ TA @ TB @ B @ C ) )
= ( rBT_Im35466040lookup @ TA @ TB @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_ord_Opaint__rbt__lookup) ).
thf(299,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im35466040lookup @ TA @ TB @ A @ ( rBT_Im945281971_paint @ TA @ TB @ B @ C ) )
= ( rBT_Im35466040lookup @ TA @ TB @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',fact_218_prod__cases4) ).
thf(912,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)],[218]) ).
thf(97,axiom,
! [TA: $tType,A: a > TA > TA > TA,B: a,C: TA] :
( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ A @ B @ C @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ a @ TA ) @ B @ C @ ( rBT_Im418718756_Empty @ a @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_local_Orbt__ins_Osimps_I1_J) ).
thf(521,plain,
! [TA: $tType,A: a > TA > TA > TA,B: a,C: TA] :
( ( rBT_Im1756508336bt_ins @ a @ TA @ less @ A @ B @ C @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ a @ TA ) @ B @ C @ ( rBT_Im418718756_Empty @ a @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(83,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im1923302023_color] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im945281971_paint @ a @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_local_Opaint__rbt__sorted) ).
thf(473,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im1923302023_color] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im945281971_paint @ a @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(162,axiom,
! [TA: $tType,A: a] :
( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_local_Orbt__del_Osimps_I1_J) ).
thf(722,plain,
! [TA: $tType,A: a] :
( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(147,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
= ( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
& ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
& ( ( rBT_Im1805589839lor_of @ a @ TA @ A )
= rBT_Impl_Mirabelle_B )
& ( rBT_Im759614907sorted @ a @ TA @ less @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_local_Ois__rbt__def) ).
thf(680,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
= ( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
& ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
& ( ( rBT_Im1805589839lor_of @ a @ TA @ A )
= rBT_Impl_Mirabelle_B )
& ( rBT_Im759614907sorted @ a @ TA @ less @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) )
= ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ A ) ) )
| ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_combine__in__tree) ).
thf(548,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) ) ) )
= ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ A ) ) )
| ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ B )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1278323832e_left @ TA @ TB @ A @ C @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_balance__left__inv1) ).
thf(355,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ A )
=> ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ B )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1278323832e_left @ TA @ TB @ A @ C @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB] :
( ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ C @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_ord_Orbt__del__from__right_Osimps_I2_J) ).
thf(458,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB] :
( ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ C @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(262,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1053358987_right @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_local_Obalance__right__rbt__less) ).
thf(1049,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
=> ( ( less @ D @ A )
=> ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1053358987_right @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(223,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im1648453169alance @ a @ TA @ A @ C @ D @ B ) @ E )
= ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ A @ C @ D @ B ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_local_Orbt__lookup__balance) ).
thf(927,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im1648453169alance @ a @ TA @ A @ C @ D @ B ) @ E )
= ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ A @ C @ D @ B ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im627674146th_key @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] : ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ B @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_ord_Orbt__insert__with__key__def) ).
thf(374,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im627674146th_key @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] : ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ TA @ TB @ A @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_old_Oprod_Oexhaust) ).
thf(690,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)],[151]) ).
thf(254,axiom,
! [TA: $tType,A: a,B: a,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ B @ C )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_local_Orbt__greater__trans) ).
thf(1025,plain,
! [TA: $tType,A: a,B: a,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ B @ C )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(204,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( rBT_Im1040612428e_inv2 @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_local_Oins__inv1__inv2_I1_J) ).
thf(872,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( rBT_Im1040612428e_inv2 @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im945281971_paint @ TB @ TA @ rBT_Impl_Mirabelle_B @ A ) )
= rBT_Impl_Mirabelle_B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_paint__color__of) ).
thf(282,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im945281971_paint @ TB @ TA @ rBT_Impl_Mirabelle_B @ A ) )
= rBT_Impl_Mirabelle_B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(157,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rbt__del__rbt__sorted) ).
thf(707,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(167,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1591839508ombine @ a @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_local_Ocombine__rbt__greater) ).
thf(739,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1591839508ombine @ a @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(241,axiom,
less @ xx @ yy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28__C4__2_Oprems_C_I10_J) ).
thf(993,plain,
less @ xx @ yy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: TA,D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TA @ TB,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( A @ B @ C )
=> ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ C @ F @ G ) )
= ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ E @ C @ F @ G ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ C @ F @ G ) )
= ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ E @ C @ F @ G ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ C @ F @ G ) )
= ( rBT_Im1591839508ombine @ TA @ TB @ E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ord_Orbt__del_Osimps_I2_J) ).
thf(712,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: TA,D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TA @ TB,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( A @ B @ C )
=> ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ C @ F @ G ) )
= ( rBT_Im1152561598m_left @ TA @ TB @ A @ B @ E @ C @ F @ G ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ C @ F @ G ) )
= ( rBT_Im1808746437_right @ TA @ TB @ A @ B @ E @ C @ F @ G ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im1714610413bt_del @ TA @ TB @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ C @ F @ G ) )
= ( rBT_Im1591839508ombine @ TA @ TB @ E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(245,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( ( ( rBT_Im1805589839lor_of @ a @ TA @ A )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_local_Oins__inv1__inv2_I3_J) ).
thf(1003,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( ( ( rBT_Im1805589839lor_of @ a @ TA @ A )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(180,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1808746437_right @ a @ TA @ less @ A @ B @ C @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) )
= ( rBT_Im1053358987_right @ a @ TA @ B @ C @ D @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_local_Orbt__del__from__right_Osimps_I1_J) ).
thf(791,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1808746437_right @ a @ TA @ less @ A @ B @ C @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) )
= ( rBT_Im1053358987_right @ a @ TA @ B @ C @ D @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im1648453169alance @ TA @ TB @ C @ D @ E @ F ) )
= ( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ C )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ F )
& ( A @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_ord_Obalance__rbt__less) ).
thf(331,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im1648453169alance @ TA @ TB @ C @ D @ E @ F ) )
= ( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ C )
& ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ F )
& ( A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( ( rBT_Im315265182height @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) )
= ( rBT_Im315265182height @ TA @ TB @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_combine__inv2_I1_J) ).
thf(338,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612428e_inv2 @ TA @ TB @ A )
=> ( ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
=> ( ( ( rBT_Im315265182height @ TA @ TB @ A )
= ( rBT_Im315265182height @ TA @ TB @ B ) )
=> ( ( rBT_Im315265182height @ TA @ TB @ ( rBT_Im1591839508ombine @ TA @ TB @ A @ B ) )
= ( rBT_Im315265182height @ TA @ TB @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_balance_Osimps_I28_J) ).
thf(808,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(136,axiom,
rBT_Im1040612427e_inv1 @ a @ b @ bb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__C4__2_Oprems_C_I6_J) ).
thf(643,plain,
rBT_Im1040612427e_inv1 @ a @ b @ bb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(216,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_local_Oless__asym_H) ).
thf(907,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(258,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > a] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( less @ ( B @ D ) @ ( B @ C ) ) )
=> ( transitive_acyclic @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_local_OacyclicI__order) ).
thf(1038,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > a] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( less @ ( B @ D ) @ ( B @ C ) ) )
=> ( transitive_acyclic @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(45,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_2) ).
thf(370,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_balance_Osimps_I16_J) ).
thf(470,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(116,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_local_Odual__order_Ostrict__trans) ).
thf(576,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(169,axiom,
! [A: a] :
( ( set_lessThan @ a @ less @ A )
= ( collect @ a
@ ^ [B: a] : ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_local_OlessThan__def) ).
thf(744,plain,
! [A: a] :
( ( set_lessThan @ a @ less @ A )
= ( collect @ a
@ ^ [B: a] : ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1071879905_inv1l @ TA @ TB @ B )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1053358987_right @ TA @ TB @ A @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_balance__right__inv1l) ).
thf(336,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1071879905_inv1l @ TA @ TB @ B )
=> ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im1053358987_right @ TA @ TB @ A @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(127,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1808746437_right @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_rbt__del__from__right__rbt__greater) ).
thf(613,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: a,F: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1808746437_right @ a @ TA @ less @ E @ B @ D @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(123,axiom,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ B @ C @ D @ E @ F ) )
= ( ( less @ D @ A )
& ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
& ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_local_Orbt__less__simps_I2_J) ).
thf(600,plain,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ B @ C @ D @ E @ F ) )
= ( ( less @ D @ A )
& ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ C )
& ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType,A: ( TA > TB > TB > TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [G: TA > TB > TB > TB,H: TA,I: TB] : ( A @ G @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [G: TA > TB > TB > TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( B @ H @ K )
=> ( A @ G @ H @ I @ J ) )
=> ( ( ~ ( B @ H @ K )
=> ( ( B @ K @ H )
=> ( A @ G @ H @ I @ M ) ) )
=> ( A @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) )
=> ( ! [G: TA > TB > TB > TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( B @ H @ K )
=> ( A @ G @ H @ I @ J ) )
=> ( ( ~ ( B @ H @ K )
=> ( ( B @ K @ H )
=> ( A @ G @ H @ I @ M ) ) )
=> ( A @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ J @ K @ L @ M ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_ord_Orbt__ins_Oinduct) ).
thf(727,plain,
! [TA: $tType,TB: $tType,A: ( TA > TB > TB > TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: TA > TA > $o,C: TA > TB > TB > TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [G: TA > TB > TB > TB,H: TA,I: TB] : ( A @ G @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [G: TA > TB > TB > TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( B @ H @ K )
=> ( A @ G @ H @ I @ J ) )
=> ( ( ~ ( B @ H @ K )
=> ( ( B @ K @ H )
=> ( A @ G @ H @ I @ M ) ) )
=> ( A @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) )
=> ( ! [G: TA > TB > TB > TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( B @ H @ K )
=> ( A @ G @ H @ I @ J ) )
=> ( ( ~ ( B @ H @ K )
=> ( ( B @ K @ H )
=> ( A @ G @ H @ I @ M ) ) )
=> ( A @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ J @ K @ L @ M ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(247,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_balance_Osimps_I39_J) ).
thf(1008,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB,L: TA,M: TB,N: rBT_Im246033960le_rbt @ TA @ TB,O: TA,P: TB,Q: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_balance_Osimps_I29_J) ).
thf(497,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB,L: TA,M: TB,N: rBT_Im246033960le_rbt @ TA @ TB,O: TA,P: TB,Q: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ N @ O @ P @ Q ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(198,axiom,
( ( rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
=> ( ( rBT_Im1040612427e_inv1 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
=> ( ( rBT_Im1040612428e_inv2 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
=> ( ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im1714610413bt_del @ a @ b @ less @ xx @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) ) ) ) )
= ( ( xx != k )
& ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50__C4__2_Ohyps_C) ).
thf(859,plain,
( ( rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
=> ( ( rBT_Im1040612427e_inv1 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
=> ( ( rBT_Im1040612428e_inv2 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) )
=> ( ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im1714610413bt_del @ a @ b @ less @ xx @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) ) ) ) )
= ( ( xx != k )
& ( member @ ( product_prod @ a @ b ) @ ( product_Pair @ a @ b @ k @ v ) @ ( set2 @ ( product_prod @ a @ b ) @ ( rBT_Im954575269ntries @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(240,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_local_Oless__asym) ).
thf(991,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_balance__right_Osimps_I10_J) ).
thf(978,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_balance__left_Osimps_I6_J) ).
thf(386,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: TA,I: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_balance_Osimps_I25_J) ).
thf(556,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: TA,I: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im418718756_Empty @ TA @ TB ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(104,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_local_Oless__imp__not__eq) ).
thf(539,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(150,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1278323832e_left @ a @ TA @ A @ C @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_local_Obalance__left__rbt__sorted) ).
thf(688,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a,D: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( rBT_Im2075124343t_less @ a @ TA @ less @ C @ A )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ C @ B )
=> ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im1278323832e_left @ a @ TA @ A @ C @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(91,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1278323832e_left @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_local_Obalance__left__rbt__greater) ).
thf(495,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
=> ( ( less @ A @ D )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1278323832e_left @ a @ TA @ B @ D @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(211,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB )] :
( ! [B: TA] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
=> ~ ! [B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_ord_Orbt__del_Ocases) ).
thf(891,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB )] :
( ! [B: TA] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
=> ~ ! [B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(98,axiom,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_color_Odistinct_I1_J) ).
thf(524,plain,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(118,axiom,
! [A: rBT_Im1923302023_color > $o,B: rBT_Im1923302023_color] :
( ( A @ rBT_Impl_Mirabelle_R )
=> ( ( A @ rBT_Impl_Mirabelle_B )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_color_Oinduct) ).
thf(581,plain,
! [A: rBT_Im1923302023_color > $o,B: rBT_Im1923302023_color] :
( ( A @ rBT_Impl_Mirabelle_R )
=> ( ( A @ rBT_Impl_Mirabelle_B )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o] : ( rBT_Im862805236is_rbt @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_ord_OEmpty__is__rbt) ).
thf(368,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o] : ( rBT_Im862805236is_rbt @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(193,axiom,
! [TA: $tType,A: product_prod @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) )] :
( ! [B: a > TA > TA > TA,C: a,D: TA] :
( A
!= ( product_Pair @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ B @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ ( rBT_Im418718756_Empty @ a @ TA ) ) ) ) )
=> ( ! [B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ B @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ) )
=> ~ ! [B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ B @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_local_Orbt__ins_Ocases) ).
thf(844,plain,
! [TA: $tType,A: product_prod @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) )] :
( ! [B: a > TA > TA > TA,C: a,D: TA] :
( A
!= ( product_Pair @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ B @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ ( rBT_Im418718756_Empty @ a @ TA ) ) ) ) )
=> ( ! [B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ B @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ) )
=> ~ ! [B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA,F: a,G: TA,H: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ ( a > TA > TA > TA ) @ ( product_prod @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) ) @ B @ ( product_Pair @ a @ ( product_prod @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) ) @ C @ ( product_Pair @ TA @ ( rBT_Im246033960le_rbt @ a @ TA ) @ D @ ( rBT_Im480247531Branch @ a @ TA @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(24,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_5) ).
thf(319,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im945281971_paint @ TA @ TB @ C @ D ) )
= ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_ord_Opaint__rbt__less) ).
thf(304,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im945281971_paint @ TA @ TB @ C @ D ) )
= ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_balance_Osimps_I24_J) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ G @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: rBT_Im1923302023_color,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E )
= ( rBT_Im480247531Branch @ TA @ TB @ F @ G @ H @ I @ J ) )
= ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rbt_Oinject) ).
thf(652,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: rBT_Im1923302023_color,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E )
= ( rBT_Im480247531Branch @ TA @ TB @ F @ G @ H @ I @ J ) )
= ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im862805236is_rbt @ TA @ TB @ A @ B )
=> ( rBT_Im759614907sorted @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ord_Ois__rbt__rbt__sorted) ).
thf(351,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im862805236is_rbt @ TA @ TB @ A @ B )
=> ( rBT_Im759614907sorted @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(256,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_balance__left_Osimps_I9_J) ).
thf(1030,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1071879905_inv1l @ TA @ TB @ B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ A )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1053358987_right @ TA @ TB @ A @ C @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_balance__right__inv1) ).
thf(290,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ A )
=> ( ( rBT_Im1071879905_inv1l @ TA @ TB @ B )
=> ( ( ( rBT_Im1805589839lor_of @ TA @ TB @ A )
= rBT_Impl_Mirabelle_B )
=> ( rBT_Im1040612427e_inv1 @ TA @ TB @ ( rBT_Im1053358987_right @ TA @ TB @ A @ C @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(144,axiom,
! [TA: $tType,A: a,B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ D @ A ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ F @ A ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( some @ TA @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_local_Orbt__lookup_Osimps_I2_J) ).
thf(667,plain,
! [TA: $tType,A: a,B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ D @ A ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ F @ A ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( some @ TA @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_ord_Orbt__less__simps_I1_J) ).
thf(346,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im2075124343t_less @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) )] :
( ! [B: TA > TB > TB > TB,C: TA,D: TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ) )
=> ( ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ) )
=> ~ ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_ord_Orbt__ins_Ocases) ).
thf(800,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) )] :
( ! [B: TA > TB > TB > TB,C: TA,D: TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ) )
=> ( ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ E @ F @ G @ H ) ) ) ) )
=> ~ ! [B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] :
( A
!= ( product_Pair @ ( TA > TB > TB > TB ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) ) @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) ) @ C @ ( product_Pair @ TB @ ( rBT_Im246033960le_rbt @ TA @ TB ) @ D @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ E @ F @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im945281971_paint @ TA @ TB @ C @ D ) )
= ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_ord_Opaint__rbt__greater) ).
thf(287,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im945281971_paint @ TA @ TB @ C @ D ) )
= ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im418718756_Empty @ TB @ TA ) )
= rBT_Impl_Mirabelle_B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_color__of_Osimps_I1_J) ).
thf(315,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1805589839lor_of @ TB @ TA @ ( rBT_Im418718756_Empty @ TB @ TA ) )
= rBT_Impl_Mirabelle_B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,A: ( rBT_Im246033960le_rbt @ TA @ TB ) > ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: rBT_Im246033960le_rbt @ TA @ TB,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [D: rBT_Im246033960le_rbt @ TA @ TB] : ( A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D )
=> ( ! [D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] : ( A @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ F @ G @ H ) @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ G @ H )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ H @ I @ J @ K ) ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ G @ H )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ H @ I @ J @ K ) ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_combine_Oinduct) ).
thf(835,plain,
! [TA: $tType,TB: $tType,A: ( rBT_Im246033960le_rbt @ TA @ TB ) > ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: rBT_Im246033960le_rbt @ TA @ TB,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [D: rBT_Im246033960le_rbt @ TA @ TB] : ( A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D )
=> ( ! [D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TA @ TB,F: TA,G: TB,H: rBT_Im246033960le_rbt @ TA @ TB] : ( A @ ( rBT_Im480247531Branch @ TA @ TB @ D @ E @ F @ G @ H ) @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ G @ H )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ H @ I @ J @ K ) ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ G @ H )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ H @ I @ J @ K ) ) )
=> ( ! [D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) )
=> ( A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_balance__right_Osimps_I1_J) ).
thf(422,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1053358987_right @ TA @ TB @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ D @ E @ F @ G ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(5,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_4) ).
thf(273,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(200,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ yy @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39__C4__2_Oprems_C_I3_J) ).
thf(865,plain,
rBT_Im2075124343t_less @ a @ b @ less @ yy @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(124,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_local_Oorder_Ostrict__implies__not__eq) ).
thf(603,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(191,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im852463031insert @ a @ TA @ less @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_local_Orbt__insert__is__rbt) ).
thf(833,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im852463031insert @ a @ TA @ less @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(231,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_combine_Osimps_I2_J) ).
thf(967,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1591839508ombine @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im862805236is_rbt @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
& ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
& ( ( rBT_Im1805589839lor_of @ TA @ TB @ B )
= rBT_Impl_Mirabelle_B )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_ord_Ois__rbt__def) ).
thf(326,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im862805236is_rbt @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
& ( rBT_Im1040612428e_inv2 @ TA @ TB @ B )
& ( ( rBT_Im1805589839lor_of @ TA @ TB @ B )
= rBT_Impl_Mirabelle_B )
& ( rBT_Im759614907sorted @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ E @ F @ G )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_balance__left_Osimps_I1_J) ).
thf(918,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ E @ F @ G )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_ord_Orbt__greater__simps_I1_J) ).
thf(341,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA] : ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(95,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( rBT_Im1071879905_inv1l @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_local_Oins__inv1__inv2_I4_J) ).
thf(506,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a > TA > TA > TA,C: a,D: TA] :
( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
=> ( ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
=> ( rBT_Im1071879905_inv1l @ a @ TA @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im1648453169alance @ TA @ TB @ C @ D @ E @ F ) )
= ( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ C )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ F )
& ( A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_ord_Obalance__rbt__greater) ).
thf(358,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ ( rBT_Im1648453169alance @ TA @ TB @ C @ D @ E @ F ) )
= ( ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ C )
& ( rBT_Im1259024060reater @ TA @ TB @ A @ B @ F )
& ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_balance_Osimps_I21_J) ).
thf(437,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im246033960le_rbt @ TA @ TB,H: TA,I: TB,J: rBT_Im246033960le_rbt @ TA @ TB,K: TA,L: TB,M: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ D @ E @ F @ G ) @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ J @ K @ L @ M ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(213,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im852463031insert @ a @ TA @ less @ B @ C @ A ) )
= ( fun_upd @ a @ ( option @ TA ) @ ( rBT_Im35466040lookup @ a @ TA @ less @ A ) @ B @ ( some @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_local_Orbt__lookup__rbt__insert) ).
thf(897,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im852463031insert @ a @ TA @ less @ B @ C @ A ) )
= ( fun_upd @ a @ ( option @ TA ) @ ( rBT_Im35466040lookup @ a @ TA @ less @ A ) @ B @ ( some @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_balance_Osimps_I20_J) ).
thf(664,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im1923302023_color,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',fact_212_Pair__inject) ).
thf(1033,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)],[257]) ).
thf(133,axiom,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im945281971_paint @ a @ TA @ B @ C ) )
= ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_local_Opaint__rbt__greater) ).
thf(635,plain,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im945281971_paint @ a @ TA @ B @ C ) )
= ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(238,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_rbt__del__rbt__greater) ).
thf(987,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im1714610413bt_del @ a @ TA @ less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(79,axiom,
! [TA: $tType,A: product_prod @ a @ ( rBT_Im246033960le_rbt @ a @ TA )] :
( ! [B: a] :
( A
!= ( product_Pair @ a @ ( rBT_Im246033960le_rbt @ a @ TA ) @ B @ ( rBT_Im418718756_Empty @ a @ TA ) ) )
=> ~ ! [B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: a,F: TA,G: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( rBT_Im246033960le_rbt @ a @ TA ) @ B @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_local_Orbt__del_Ocases) ).
thf(464,plain,
! [TA: $tType,A: product_prod @ a @ ( rBT_Im246033960le_rbt @ a @ TA )] :
( ! [B: a] :
( A
!= ( product_Pair @ a @ ( rBT_Im246033960le_rbt @ a @ TA ) @ B @ ( rBT_Im418718756_Empty @ a @ TA ) ) )
=> ~ ! [B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: a,F: TA,G: rBT_Im246033960le_rbt @ a @ TA] :
( A
!= ( product_Pair @ a @ ( rBT_Im246033960le_rbt @ a @ TA ) @ B @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(251,axiom,
rBT_Im759614907sorted @ a @ b @ less @ bb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27__C4__2_Oprems_C_I2_J) ).
thf(1019,plain,
rBT_Im759614907sorted @ a @ b @ less @ bb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
& ( rBT_Im1040612427e_inv1 @ TA @ TB @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_inv1l_Osimps_I2_J) ).
thf(644,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: rBT_Im246033960le_rbt @ TA @ TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1071879905_inv1l @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( ( rBT_Im1040612427e_inv1 @ TA @ TB @ B )
& ( rBT_Im1040612427e_inv1 @ TA @ TB @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(195,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( ( rBT_Im954575269ntries @ a @ TA @ A )
= ( rBT_Im954575269ntries @ a @ TA @ B ) )
= ( ( rBT_Im35466040lookup @ a @ TA @ less @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_local_Oentries__rbt__lookup) ).
thf(850,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ( ( rBT_Im954575269ntries @ a @ TA @ A )
= ( rBT_Im954575269ntries @ a @ TA @ B ) )
= ( ( rBT_Im35466040lookup @ a @ TA @ less @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_balance_Osimps_I14_J) ).
thf(442,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(203,axiom,
rBT_Im1040612428e_inv2 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33__C4__2_Oprems_C_I7_J) ).
thf(871,plain,
rBT_Im1040612428e_inv2 @ a @ b @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ vaa @ vbb @ vdd @ vc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(125,axiom,
! [TA: $tType,A: a,B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ E ) )
= ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ E )
& ( less @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_local_Oins__rbt__less) ).
thf(607,plain,
! [TA: $tType,A: a,B: a > TA > TA > TA,C: a,D: TA,E: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ ( rBT_Im1756508336bt_ins @ a @ TA @ less @ B @ C @ D @ E ) )
= ( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ E )
& ( less @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(55,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(395,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)],[55]) ).
thf(131,axiom,
! [TA: $tType,A: a,B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) )
= ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ D @ B @ E @ F ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) )
= ( rBT_Im1808746437_right @ a @ TA @ less @ A @ D @ B @ E @ F ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) )
= ( rBT_Im1591839508ombine @ a @ TA @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_local_Orbt__del_Osimps_I2_J) ).
thf(624,plain,
! [TA: $tType,A: a,B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) )
= ( rBT_Im1152561598m_left @ a @ TA @ less @ A @ D @ B @ E @ F ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) )
= ( rBT_Im1808746437_right @ a @ TA @ less @ A @ D @ B @ E @ F ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im1714610413bt_del @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) )
= ( rBT_Im1591839508ombine @ a @ TA @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(88,axiom,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ B @ C @ D @ E @ F ) )
= ( ( less @ A @ D )
& ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
& ( rBT_Im1259024060reater @ a @ TA @ less @ A @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_local_Orbt__greater__simps_I2_J) ).
thf(486,plain,
! [TA: $tType,A: a,B: rBT_Im1923302023_color,C: rBT_Im246033960le_rbt @ a @ TA,D: a,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im480247531Branch @ a @ TA @ B @ C @ D @ E @ F ) )
= ( ( less @ A @ D )
& ( rBT_Im1259024060reater @ a @ TA @ less @ A @ C )
& ( rBT_Im1259024060reater @ a @ TA @ less @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(184,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Oord__less__eq__trans) ).
thf(803,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TB > ( option @ TA ),B: TB,C: TA,D: TB,E: TA] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ A @ B @ ( some @ TA @ C ) @ D )
= ( some @ TA @ E ) )
= ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( A @ D )
= ( some @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_map__upd__Some__unfold) ).
thf(309,plain,
! [TA: $tType,TB: $tType,A: TB > ( option @ TA ),B: TB,C: TA,D: TB,E: TA] :
( ( ( fun_upd @ TB @ ( option @ TA ) @ A @ B @ ( some @ TA @ C ) @ D )
= ( some @ TA @ E ) )
= ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( A @ D )
= ( some @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(105,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ! [D: TA] :
( ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ C )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_local_Orbt__lookup__from__in__tree) ).
thf(543,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ! [D: TA] :
( ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ C )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(173,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ G @ H @ I ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_balance__left_Osimps_I8_J) ).
thf(755,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB,F: rBT_Im246033960le_rbt @ TA @ TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) @ G @ H @ I ) )
= ( rBT_Im418718756_Empty @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB,L: TA,M: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_balance_Osimps_I26_J) ).
thf(454,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB,B: TA,C: TB,D: rBT_Im246033960le_rbt @ TA @ TB,E: TA,F: TB,G: rBT_Im1923302023_color,H: rBT_Im246033960le_rbt @ TA @ TB,I: TA,J: TB,K: rBT_Im246033960le_rbt @ TA @ TB,L: TA,M: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ G @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ H @ I @ J @ K ) @ L @ M @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im246033960le_rbt @ TA @ TB,C: rBT_Im1923302023_color] :
( ( rBT_Im759614907sorted @ TA @ TB @ A @ B )
=> ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im945281971_paint @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_ord_Opaint__rbt__sorted) ).
thf(364,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: rBT_Im246033960le_rbt @ TA @ TB,C: rBT_Im1923302023_color] :
( ( rBT_Im759614907sorted @ TA @ TB @ A @ B )
=> ( rBT_Im759614907sorted @ TA @ TB @ A @ ( rBT_Im945281971_paint @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(249,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_local_Oorder_Oasym) ).
thf(1014,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(233,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ B )
= ( some @ TA @ C ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ B @ C ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_local_Orbt__lookup__in__tree) ).
thf(972,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ B )
= ( some @ TA @ C ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ B @ C ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1060,plain,
$false,
inference(cvc4,[status(thm)],[909,777,962,468,408,683,276,994,741,597,1041,440,655,269,677,384,533,500,797,814,698,747,930,404,709,320,885,1046,389,570,719,785,587,934,559,416,448,638,853,492,353,480,475,924,1020,348,1051,821,981,280,877,734,866,411,428,293,956,527,312,307,380,546,366,1057,334,894,302,862,392,693,275,788,467,847,361,435,329,461,1027,551,285,874,615,725,1006,869,610,783,989,537,686,489,970,554,753,1016,590,701,457,984,569,371,503,647,997,343,266,508,921,1054,398,674,530,953,794,662,888,750,618,425,824,856,573,296,579,413,562,904,975,826,711,641,445,382,704,377,451,271,900,406,1011,419,737,318,880,649,1043,477,811,631,758,535,323,594,621,483,915,1022,932,959,695,278,780,883,1000,299,912,521,473,722,680,548,355,458,1049,927,374,690,1025,872,282,707,739,993,712,1003,791,331,338,808,643,907,1038,370,470,576,744,336,613,600,727,1008,497,859,991,978,386,556,539,688,495,891,524,581,368,844,319,304,401,652,351,1030,290,667,346,800,287,315,835,422,273,865,603,833,967,326,918,341,506,358,437,897,664,1033,635,987,464,1019,644,850,442,871,607,395,624,486,803,309,543,755,454,364,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT236^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n025.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 12:44:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.11 % [INFO] Parsing done (272ms).
% 1.85/1.12 % [INFO] Running in sequential loop mode.
% 2.66/1.33 % [INFO] eprover registered as external prover.
% 2.66/1.33 % [INFO] cvc4 registered as external prover.
% 2.66/1.34 % [INFO] Scanning for conjecture ...
% 2.82/1.45 % [INFO] Found a conjecture and 264 axioms. Running axiom selection ...
% 3.37/1.55 % [INFO] Axiom selection finished. Selected 263 axioms (removed 1 axioms).
% 4.53/1.86 % [INFO] Problem is higher-order (TPTP THF).
% 4.53/1.88 % [INFO] Type checking passed.
% 4.53/1.89 % [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 ...
% 10.78/3.56 % [INFO] [Domain constraints] Detected constraint on rBT_Im1923302023_color
% 10.78/3.56 % [INFO] [Domain constraints] dom(rBT_Im1923302023_color) ⊆ {rBT_Impl_Mirabelle_R,rBT_Impl_Mirabelle_B}
% 112.00/44.88 % External prover 'cvc4' found a proof!
% 112.00/44.88 % [INFO] Killing All external provers ...
% 112.00/44.88 % Time passed: 44360ms (effective reasoning time: 43752ms)
% 112.00/44.88 % 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)>
% 112.00/44.88 % Axioms used in derivation (263): fact_65_rbt__del__from__right__rbt__greater, fact_249_balance_Osimps_I20_J, fact_140_balance__left_Osimps_I7_J, fact_18_local_OneqE, fact_190_ord_Opaint__rbt__sorted, fact_216_prod__cases3, fact_115_local_Orbt__del_Osimps_I1_J, fact_201_ord_Oins__inv1__inv2_I3_J, fact_74_local_Orbt__insertwk__rbt__sorted, fact_59_local_OlessThan__def, fact_109_local_Orbt__del_Oelims, fact_220_prod__induct6, fact_50__C4__2_Ohyps_C, fact_247_balance_Osimps_I18_J, fact_141_balance__left_Osimps_I8_J, fact_156_ord_Orbt__del_Osimps_I1_J, fact_189_color__of_Osimps_I2_J, fact_159_inv1l_Osimps_I1_J, fact_171_combine_Osimps_I6_J, fact_128_rbt__cases, fact_198_paint__inv1, fact_30_local_Orbt__less__trans, fact_107_combine__in__tree, fact_121_local_Orbt__lookup_Osimps_I2_J, fact_222_map__of__SomeD, fact_21_local_Oord__eq__less__trans, fact_38__C4__2_Oprems_C_I9_J, fact_124_local_Orbt__del__from__right_Osimps_I2_J, fact_254_balance_Osimps_I26_J, fact_146_rbt_Odistinct_I1_J, fact_56_local_Orbt__sorted_Osimps_I2_J, fact_116_local_OEmpty__is__rbt, fact_197_inv1_Osimps_I2_J, fact_187_paint_Osimps_I2_J, fact_142_ord__class_Orbt__del_Ocases, fact_169_balance__right_Osimps_I8_J, fact_223_weak__map__of__SomeI, fact_203_balance__right__inv1, fact_73_local_Oins__rbt__greater, fact_131_ord__class_Orbt__del__from__left_Ocases, fact_72_local_Oins__rbt__less, tcon_fun___Orderings_Oord, fact_255_balance_Osimps_I28_J, fact_136_balance__left_Osimps_I11_J, tcon_HOL_Obool___Orderings_Oorder_5, fact_77_ord_Oins__inv1__inv2_I2_J, fact_51_local_Orbt__greater__simps_I2_J, tcon_Set_Oset___Orderings_Oorder_3, fact_132_ord_Orbt__del__from__left_Ocases, fact_4_local_Odual__order_Ostrict__implies__not__eq, fact_207_prod__cases7, fact_96_local_Orbt__insertwk__is__rbt, fact_168_balance__right_Osimps_I7_J, fact_147_balance__left_Osimps_I1_J, fact_185_local_Opaint__rbt__lookup, fact_130_ord_Orbt__ins_Oinduct, fact_154_ord_Orbt__greater__simps_I1_J, fact_152_inv2_Osimps_I1_J, fact_86_local_Orbt__insert__is__rbt, fact_153_ord_Orbt__less__simps_I1_J, fact_16_local_Oless__trans, fact_215_prod__induct3, fact_97_combine__inv1_I2_J, fact_246_balance_Osimps_I17_J, fact_167_ord_Orbt__ins_Osimps_I1_J, fact_98_balance__right__inv1l, fact_83_ord_Orbt__greater__simps_I2_J, fact_93_local_Ocombine__rbt__less, fact_80_ord_Orbt__sorted_Osimps_I2_J, fact_102_ord_Ois__rbt__rbt__sorted, fact_135_balance__left_Osimps_I6_J, fact_12_local_Oless__imp__triv, fact_35__C4__2_Oprems_C_I1_J, fact_118_local_Obalance__left__rbt__greater, fact_240_balance_Osimps_I39_J, fact_24_local_Oorder_Oirrefl, fact_119_local_Orbt__del__from__left_Ocases, fact_76_local_Orbt__insert__def, fact_31__C4__2_Oprems_C_I4_J, fact_78_ord_Oins__inv1__inv2_I1_J, fact_200_ord_Orbt__insert__with__key__def, fact_53_ord_Orbt__del__from__left_Osimps_I3_J, fact_165_combine_Osimps_I2_J, fact_46_Collect__mem__eq, fact_250_balance_Osimps_I21_J, fact_228_local_Obalance__rbt__greater, fact_55_local_OgreaterThan__def, fact_108_local_Obalance__left__rbt__sorted, fact_214_surj__pair, fact_113_local_Orbt__del_Ocases, fact_8_local_Oless__imp__neq, fact_242_balance_Osimps_I45_J, tcon_Nat_Onat___Orderings_Oord_2, fact_120_local_Orbt__ins_Ocases, fact_110_local_Orbt__del__from__right_Osimps_I1_J, fact_25_local_Oorder_Ostrict__implies__not__eq, fact_231_map__upd__triv, fact_7_local_Oless__asym_H, fact_64_rbt__del__from__right__rbt__less, fact_211_old_Oprod_Oexhaust, fact_210_old_Oprod_Oinducts, fact_158_balance__right_Osimps_I6_J, fact_174_ord_Orbt__del__from__left_Osimps_I2_J, fact_40_rbt__del__rbt__greater, fact_123_local_Orbt__ins_Osimps_I1_J, fact_37_rbt__del__from__left__rbt__less, fact_177_local_Ois__rbt__def, fact_9_local_Oless__imp__not__eq, fact_253_balance_Osimps_I25_J, fact_87_local_Oins__inv1__inv2_I4_J, fact_229_local_Orbt__lookup__balance, fact_75_local_Orbt__insertw__def, fact_91_local_Ocombine__rbt__sorted, fact_17_local_Olinorder__cases, fact_100_combine__inv2_I1_J, fact_62_local_Orbt__lookup__from__in__tree, fact_217_prod__induct4, fact_32__C4__2_Oprems_C_I5_J, fact_81_ord_Orbt__ins_Osimps_I3_J, fact_237_balance_Osimps_I23_J, fact_191_paint__inv2, fact_5_local_Odual__order_Ostrict__trans, fact_133_ord__class_Orbt__ins_Ocases, fact_213_prod__cases, fact_89_local_Orbt__del_Osimps_I2_J, fact_244_balance_Osimps_I15_J, fact_179_local_Orbt__insert__with__key__def, fact_11_local_Oless__imp__not__less, fact_112_local_Orbt__del__from__left_Osimps_I2_J, fact_6_local_Oless__asym, fact_58_local_Orbt__insertw__rbt__sorted, fact_164_ord_Orbt__lookup_Osimps_I2_J, fact_15_local_Oless__not__sym, fact_160_ord_OEmpty__is__rbt, fact_230_map__upd__eqD1, fact_23_local_Oorder_Oasym, fact_95_local_Obalance__right__rbt__less, fact_166_balance__left__inv1l, fact_199_combine__inv1_I1_J, fact_54_local_OacyclicI__order, fact_45_mem__Collect__eq, fact_61_local_Orbt__ins_Osimps_I3_J, fact_202_balance__left__inv1, fact_94_local_Obalance__right__rbt__greater, fact_227_local_Obalance__rbt__less, fact_63_local_Oins__rbt__sorted, fact_69_local_Oins__inv1__inv2_I2_J, fact_114_local_Orbt__sorted_Osimps_I1_J, fact_10_local_Oless__imp__not__eq2, fact_173_ord_Orbt__del__from__right_Osimps_I2_J, fact_34_rbt_Oinject, fact_196_color__of_Osimps_I1_J, fact_28__C4__2_Oprems_C_I10_J, fact_137_balance__left_Osimps_I10_J, fact_138_balance__left_Osimps_I9_J, fact_151_ord_Orbt__sorted_Osimps_I1_J, fact_172_balance__right_Osimps_I1_J, fact_85_local_Orbt__insertw__is__rbt, fact_105_ord_Orbt__insertw__def, fact_157_combine_Osimps_I1_J, fact_161_balance__right_Osimps_I11_J, fact_47_Collect__cong, fact_44_local_Orbt__del__from__left_Osimps_I3_J, fact_57_local_Orbt__insert__rbt__sorted, fact_66_local_Oentries__rbt__lookup, fact_43_local_Oset__entries__inject, fact_134_ord_Orbt__ins_Ocases, fact_163_ord_Orbt__del__from__left_Osimps_I1_J, fact_26_local_Oorder_Ostrict__trans, fact_103_ord_Oins__inv1__inv2_I4_J, fact_117_local_Obalance__left__rbt__less, fact_155_inv1_Osimps_I1_J, fact_88_local_Ois__rbt__rbt__sorted, fact_245_balance_Osimps_I16_J, fact_236_balance__inv2, fact_181_local_Opaint__rbt__sorted, fact_239_balance_Osimps_I29_J, fact_219_prod__induct7, fact_60_local_Orbt__del__from__right_Osimps_I3_J, fact_111_local_Orbt__lookup__in__tree, fact_188_paint_Osimps_I1_J, fact_92_local_Ocombine__rbt__greater, fact_129_combine_Oinduct, fact_127_local_Orbt__greater__simps_I1_J, fact_0__C4__2_Oprems_C_I6_J, fact_248_balance_Osimps_I19_J, fact_209_prod_Oinject, fact_251_balance_Osimps_I22_J, fact_224_local_Orbt__lookup__rbt__insert, fact_180_local_Omap__of__entries, fact_90_local_Obalance__right__rbt__sorted, fact_162_balance__right_Osimps_I10_J, fact_22_local_Oord__less__eq__trans, fact_205_prod__cases5, fact_208_old_Oprod_Oinject, fact_204_ord_Ois__rbt__def, fact_39__C4__2_Oprems_C_I3_J, fact_225_local_Obalance__rbt__sorted, fact_101_combine__inv2_I2_J, fact_104_ord_Orbt__insert__def, fact_186_paint__in__tree, fact_106_ord_Orbt__del_Osimps_I2_J, fact_232_map__upd__Some__unfold, fact_3_local_Odual__order_Oasym, fact_243_balance_Osimps_I14_J, fact_252_balance_Osimps_I24_J, fact_70_local_OlessThan__iff, fact_184_local_Opaint__rbt__less, fact_49_local_Ostrict__mono__eq, fact_19_local_Oneq__iff, fact_221_prod__induct5, fact_235_balance__inv1, fact_194_ord_Opaint__rbt__lookup, fact_2_local_Oantisym__conv3, fact_99_inv1l_Osimps_I2_J, fact_14_local_Oless__linear, fact_175_ord_Orbt__del__from__right_Osimps_I1_J, fact_206_prod__cases6, fact_67_local_Oentries__eqI, fact_125_local_Orbt__del__from__left_Osimps_I1_J, fact_218_prod__cases4, fact_143_ord_Orbt__del_Ocases, tcon_fun___Orderings_Oorder, fact_84_ord_Orbt__less__simps_I2_J, fact_52_local_Orbt__less__simps_I2_J, fact_238_balance_Osimps_I27_J, fact_36_rbt__del__from__left__rbt__greater, fact_234_ord_Obalance__rbt__less, fact_150_color_Odistinct_I1_J, fact_126_local_Orbt__less__simps_I1_J, fact_122_local_Orbt__ins_Oinduct, fact_170_combine_Osimps_I5_J, tcon_Nat_Onat___Orderings_Oorder_1, fact_82_ord_Orbt__del__from__right_Osimps_I3_J, fact_195_paint__inv1l, fact_233_ord_Obalance__rbt__greater, fact_33__C4__2_Oprems_C_I7_J, fact_79_inv2_Osimps_I2_J, fact_20_local_Onot__less__iff__gr__or__eq, fact_192_ord_Opaint__rbt__greater, fact_41_rbt__del__rbt__less, fact_193_ord_Opaint__rbt__less, fact_42_rbt__del__rbt__sorted, fact_241_balance_Osimps_I43_J, tcon_HOL_Obool___Orderings_Oord_6, fact_149_color_Oinduct, fact_71_local_OgreaterThan__iff, fact_176_ord_Orbt__del_Oelims, fact_144_rbt_Oexhaust, fact_27__C4__2_Oprems_C_I2_J, fact_182_paint__color__of, fact_145_rbt_Oinduct, fact_1__C4__2_Oprems_C_I8_J, fact_68_local_Oins__inv1__inv2_I1_J, fact_178_local_Oins__inv1__inv2_I3_J, fact_212_Pair__inject, fact_226_local_Orbt__ins_Osimps_I2_J, tcon_Set_Oset___Orderings_Oord_4, fact_148_color_Oexhaust, fact_29_local_Orbt__greater__trans, fact_139_balance__right_Osimps_I9_J, fact_13_local_Oless__irrefl, fact_183_local_Opaint__rbt__greater
% 112.00/44.88 % No. of inferences in proof: 530
% 112.00/44.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 44360 ms resp. 43752 ms w/o parsing
% 112.54/45.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 112.54/45.08 % [INFO] Killing All external provers ...
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