TSTP Solution File: DAT234^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT234^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 31.19s 10.44s
% Output : Refutation 32.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 311
% Syntax : Number of formulae : 574 ( 273 unt; 50 typ; 0 def)
% Number of atoms : 1533 ( 460 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 13988 ( 192 ~; 26 |; 112 &;13110 @)
% ( 0 <=>; 548 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 10 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 542 ( 542 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 20 con; 0-7 aty)
% Number of variables : 3334 ( 46 ^3188 !; 48 ?;3334 :)
% ( 52 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(rBT_Im1923302023_color_type,type,
rBT_Im1923302023_color: $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(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(set2_type,type,
set2:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(lexordp_type,type,
lexordp:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(lexordp_eq_type,type,
lexordp_eq:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(map_of_type,type,
map_of:
!>[TA: $tType,TB: $tType] : ( ( list @ ( product_prod @ TB @ TA ) ) > TB > ( option @ TA ) ) ).
thf(none_type,type,
none:
!>[TA: $tType] : ( option @ TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(strict_mono_type,type,
strict_mono:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA ) > $o ) ).
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_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_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_Im862805236is_rbt_type,type,
rBT_Im862805236is_rbt:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
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(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_type,type,
a2: rBT_Im246033960le_rbt @ a @ b ).
thf(b2_type,type,
b2: rBT_Im246033960le_rbt @ a @ b ).
thf(c_type,type,
c: rBT_Im246033960le_rbt @ a @ b ).
thf(d_type,type,
d: rBT_Im246033960le_rbt @ a @ b ).
thf(k_type,type,
k: a ).
thf(l_type,type,
l: rBT_Im246033960le_rbt @ a @ b ).
thf(less_type,type,
less: a > a > $o ).
thf(r_type,type,
r: rBT_Im246033960le_rbt @ a @ b ).
thf(v_type,type,
v: b ).
thf(w_type,type,
w: b ).
thf(x_type,type,
x: a ).
thf(y_type,type,
y: a ).
thf(181,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_97_local_Oins__rbt__less) ).
thf(892,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)],[181]) ).
thf(237,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_local_Oorder_Ostrict__implies__not__eq) ).
thf(1036,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(153,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_61_local_Obalance__rbt__sorted) ).
thf(809,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)],[153]) ).
thf(104,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_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_R @ ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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_206_balance__right_Osimps_I5_J) ).
thf(629,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_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_R @ ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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)],[104]) ).
thf(37,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,N: TA,O: TB,P: 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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) @ K @ L @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_balance_Osimps_I13_J) ).
thf(365,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,N: TA,O: TB,P: 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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) @ K @ L @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,axiom,
! [TA: $tType] :
( ( lexordp_eq @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C = D ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_ord_Olexordp__eq_Osimps) ).
thf(347,plain,
! [TA: $tType] :
( ( lexordp_eq @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C = D ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(251,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_60_local_Orbt__sorted_Osimps_I2_J) ).
thf(1083,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)],[251]) ).
thf(198,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_local_Oless__irrefl) ).
thf(941,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(225,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
| ( A = B )
| ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_local_Oless__linear) ).
thf(1005,plain,
! [A: a,B: a] :
( ( less @ A @ B )
| ( A = B )
| ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(133,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] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_balance_Osimps_I4_J) ).
thf(730,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] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(249,axiom,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( ( less @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_local_Onot__less__iff__gr__or__eq) ).
thf(1068,plain,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( ( less @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(220,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_29_combine__rbt__greater) ).
thf(994,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)],[220]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im954575269ntries @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( nil @ ( product_prod @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_entries_Osimps_I1_J) ).
thf(597,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im954575269ntries @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( nil @ ( product_prod @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(76,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_B @ F @ C @ G @ H ) )
= ( rBT_Im1648453169alance @ TA @ TB @ ( 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_B @ F @ C @ G @ H ) )
= ( rBT_Im1648453169alance @ TA @ TB @ 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_B @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ C @ ( D @ B @ G @ E ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_ord_Orbt__ins_Osimps_I2_J) ).
thf(500,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_B @ F @ C @ G @ H ) )
= ( rBT_Im1648453169alance @ TA @ TB @ ( 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_B @ F @ C @ G @ H ) )
= ( rBT_Im1648453169alance @ TA @ TB @ 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_B @ F @ C @ G @ H ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ C @ ( D @ B @ G @ E ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(148,axiom,
! [TA: $tType] : ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_local_Orbt__sorted_Osimps_I1_J) ).
thf(797,plain,
! [TA: $tType] : ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(66,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
~ ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_ord_Olexordp__eq__simps_I3_J) ).
thf(472,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
~ ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(125,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_200_balance__right_Osimps_I10_J) ).
thf(698,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)],[125]) ).
thf(189,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_local_OlessThan__iff) ).
thf(913,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(247,axiom,
! [A: list @ a] :
( ! [B: a] :
~ ( less @ B @ B )
=> ~ ( lexordp @ a @ less @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_local_Olexordp__irreflexive) ).
thf(1063,plain,
! [A: list @ a] :
( ! [B: a] :
~ ( less @ B @ B )
=> ~ ( lexordp @ a @ less @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(30,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_169_ord_Orbt__ins_Osimps_I3_J) ).
thf(340,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)],[30]) ).
thf(50,axiom,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_color_Odistinct_I1_J) ).
thf(404,plain,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(184,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ~ ( lexordp @ a @ less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_local_Olexordp__antisym) ).
thf(898,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ~ ( lexordp @ a @ less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(223,axiom,
rBT_Im1259024060reater @ a @ b @ less @ k @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_assms_I4_J) ).
thf(1001,plain,
rBT_Im1259024060reater @ a @ b @ less @ k @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(18,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_126_balance_Osimps_I29_J) ).
thf(301,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)],[18]) ).
thf(23,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_82_ord_Ois__rbt__rbt__sorted) ).
thf(320,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)],[23]) ).
thf(57,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_136_balance_Osimps_I20_J) ).
thf(436,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)],[57]) ).
thf(212,axiom,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp_eq @ a @ less @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_local_Olexordp__eq__simps_I4_J) ).
thf(973,plain,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp_eq @ a @ less @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(178,axiom,
( ( rBT_Im1591839508ombine @ a @ b @ b2 @ c )
= ( rBT_Im418718756_Empty @ a @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Empty) ).
thf(885,plain,
( ( rBT_Im1591839508ombine @ a @ b @ b2 @ c )
= ( rBT_Im418718756_Empty @ a @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(45,axiom,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_color_Oexhaust) ).
thf(389,plain,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(244,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_25_local_Orbt__greater__trans) ).
thf(1055,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)],[244]) ).
thf(132,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ! [E: list @ TA] : ( D @ ( nil @ TA ) @ E )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_ord_Olexordp__eq_Oinducts) ).
thf(719,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ! [E: list @ TA] : ( D @ ( nil @ TA ) @ E )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(141,axiom,
! [TA: $tType,A: a] : ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_local_Orbt__greater__simps_I1_J) ).
thf(751,plain,
! [TA: $tType,A: a] : ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(202,axiom,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_local_Oless__imp__triv) ).
thf(949,plain,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(62,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_124_balance_Osimps_I23_J) ).
thf(460,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)],[62]) ).
thf(56,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_remdups__adj_Oinduct) ).
thf(421,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(176,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: a,C: a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( ( less @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_local_Ostrict__monoD) ).
thf(881,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: a,C: a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( ( less @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_not__Cons__self2) ).
thf(325,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_splice_Oinduct) ).
thf(289,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(256,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_71_local_Opaint__rbt__less) ).
thf(1100,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)],[256]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,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 @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_151_balance_Osimps_I42_J) ).
thf(638,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,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 @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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)],[107]) ).
thf(167,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_210_local_Oentries__eqI) ).
thf(853,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)],[167]) ).
thf(228,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( ~ ( less @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_local_Oantisym__conv3) ).
thf(1013,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( ~ ( less @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(12,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_197_balance__left_Osimps_I11_J) ).
thf(284,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)],[12]) ).
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,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_R @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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_177_balance_Osimps_I9_J) ).
thf(591,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_R @ G @ H @ I @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ J @ K @ L @ M ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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)],[93]) ).
thf(238,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_64_local_Orbt__insertw__is__rbt) ).
thf(1040,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)],[238]) ).
thf(102,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_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ 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_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_balance_Osimps_I40_J) ).
thf(623,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_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ 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_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(161,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_local_Oorder_Ostrict__trans) ).
thf(834,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(80,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_remdups__adj_Ocases) ).
thf(514,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(152,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA] :
( ( strict_mono @ a @ TA @ less @ A )
= ( ! [B: a,C: a] :
( ( less @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_local_Ostrict__mono__def) ).
thf(806,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA] :
( ( strict_mono @ a @ TA @ less @ A )
= ( ! [B: a,C: a] :
( ( less @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(33,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_77_ord_Obalance__rbt__less) ).
thf(353,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)],[33]) ).
thf(242,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_43_local_Obalance__left__rbt__less) ).
thf(1051,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)],[242]) ).
thf(69,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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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_R @ ( 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_175_balance_Osimps_I3_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,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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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_R @ ( 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)],[69]) ).
thf(121,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(687,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)],[121]) ).
thf(113,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_ord_Olexordp__eq__refl) ).
thf(660,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(77,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_138_balance_Osimps_I22_J) ).
thf(507,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)],[77]) ).
thf(15,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_B @ G @ H @ I @ J ) @ K @ L @ M ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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_Im1648453169alance @ TA @ TB @ J @ K @ L @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_balance__left_Osimps_I5_J) ).
thf(292,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_B @ G @ H @ I @ J ) @ K @ L @ M ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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_Im1648453169alance @ TA @ TB @ J @ K @ L @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ M ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(42,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_132_balance_Osimps_I16_J) ).
thf(380,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)],[42]) ).
thf(118,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: TA,I: 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_Im418718756_Empty @ TA @ TB ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( 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_Im418718756_Empty @ TA @ TB ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_balance_Osimps_I36_J) ).
thf(678,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: TA,I: 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_Im418718756_Empty @ TA @ TB ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( 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_Im418718756_Empty @ TA @ TB ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(6,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_ord_Olexordp__eq_OCons) ).
thf(270,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(146,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_local_Oless__asym) ).
thf(793,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(193,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_44_local_Obalance__right__rbt__less) ).
thf(925,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)],[193]) ).
thf(245,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_79_ord_Opaint__rbt__greater) ).
thf(1057,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)],[245]) ).
thf(79,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_112_ord_OEmpty__is__rbt) ).
thf(512,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)],[79]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o] :
( ( rBT_Im35466040lookup @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( ^ [B: TA] : ( none @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_ord_Orbt__lookup__Empty) ).
thf(439,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o] :
( ( rBT_Im35466040lookup @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( ^ [B: TA] : ( none @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(28,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_Im1053358987_right @ 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_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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_202_balance__right_Osimps_I3_J) ).
thf(334,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_Im1053358987_right @ 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_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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)],[28]) ).
thf(188,axiom,
( ( less @ x @ y )
& ( rBT_Im1259024060reater @ a @ b @ less @ y @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__092_060open_062x_A_060_Ay_A_092_060and_062_Ay_A_092_060guillemotleft_062_124_Ad_092_060close_062) ).
thf(910,plain,
( ( less @ x @ y )
& ( rBT_Im1259024060reater @ a @ b @ less @ y @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(158,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_local_Olexordp__eq_OCons) ).
thf(825,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(170,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_120_local_Orbt__ins_Osimps_I2_J) ).
thf(862,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)],[170]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_map__tailrec__rev_Oinduct) ).
thf(561,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(46,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_180_ord_Orbt__ins_Osimps_I1_J) ).
thf(392,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)],[46]) ).
thf(139,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ B @ A )
= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_local_Orbt__lookup__rbt__less) ).
thf(746,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ B @ A )
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(254,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_local_Olexordp__eq__simps_I1_J) ).
thf(1091,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(239,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
| ( A = B )
| ( lexordp @ a @ less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_local_Olexordp__linear) ).
thf(1042,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
| ( A = B )
| ( lexordp @ a @ less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(203,axiom,
( ( rBT_Im759614907sorted @ a @ b @ less @ b2 )
=> ( ( rBT_Im759614907sorted @ a @ b @ less @ c )
=> ( ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 )
=> ( ( rBT_Im1259024060reater @ a @ b @ less @ k @ c )
=> ( rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83__C4_Ohyps_C) ).
thf(952,plain,
( ( rBT_Im759614907sorted @ a @ b @ less @ b2 )
=> ( ( rBT_Im759614907sorted @ a @ b @ less @ c )
=> ( ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 )
=> ( ( rBT_Im1259024060reater @ a @ b @ less @ k @ c )
=> ( rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_balance_Osimps_I32_J) ).
thf(407,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(123,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_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) )
= ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_balance__left_Osimps_I2_J) ).
thf(693,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_Im1278323832e_left @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ C @ D @ E @ F ) )
= ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(8,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(275,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(144,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_53_local_Orbt__insertwk__rbt__sorted) ).
thf(788,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)],[144]) ).
thf(190,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_54_local_Ois__rbt__rbt__sorted) ).
thf(916,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)],[190]) ).
thf(165,axiom,
! [A: a] :
( ( set_lessThan @ a @ less @ A )
= ( collect @ a
@ ^ [B: a] : ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_local_OlessThan__def) ).
thf(847,plain,
! [A: a] :
( ( set_lessThan @ a @ less @ A )
= ( collect @ a
@ ^ [B: a] : ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(175,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_59_local_Opaint__rbt__sorted) ).
thf(879,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)],[175]) ).
thf(129,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_106_ord_Orbt__insert__def) ).
thf(710,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)],[129]) ).
thf(137,axiom,
rBT_Im1259024060reater @ a @ b @ less @ x @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30__092_060open_062x_A_092_060guillemotleft_062_124_Ac_092_060close_062) ).
thf(742,plain,
rBT_Im1259024060reater @ a @ b @ less @ x @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(173,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
| ( lexordp_eq @ a @ less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_local_Olexordp__eq__linear) ).
thf(874,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
| ( lexordp_eq @ a @ less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(22,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_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_B @ G @ H @ I @ J ) )
= ( 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_R @ G @ H @ I @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_balance__left_Osimps_I3_J) ).
thf(317,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_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_B @ G @ H @ I @ J ) )
= ( 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_R @ G @ H @ I @ J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,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_75_ord_Orbt__less__simps_I2_J) ).
thf(615,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)],[99]) ).
thf(262,axiom,
rBT_Im1259024060reater @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114__C4_Oprems_C_I4_J) ).
thf(1121,plain,
rBT_Im1259024060reater @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(258,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119__C4_Oprems_C_I3_J) ).
thf(1111,plain,
rBT_Im2075124343t_less @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(34,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_ord_Olexordp__eq__simps_I2_J) ).
thf(356,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(171,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_165_local_Opaint__rbt__lookup) ).
thf(869,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)],[171]) ).
thf(261,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp_eq @ a @ less @ C @ D )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_local_Olexordp__eq_OCons__eq) ).
thf(1118,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp_eq @ a @ less @ C @ D )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(218,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_31_local_Obalance__right__rbt__greater) ).
thf(989,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)],[218]) ).
thf(111,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_list__nonempty__induct) ).
thf(650,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(201,axiom,
rBT_Im759614907sorted @ a @ b @ less @ l,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_assms_I1_J) ).
thf(948,plain,
rBT_Im759614907sorted @ a @ b @ less @ l,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_list_Odistinct_I1_J) ).
thf(328,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(233,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_local_Oless__asym_H) ).
thf(1028,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(72,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,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ 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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_balance_Osimps_I11_J) ).
thf(488,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,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ 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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(142,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_32_local_Obalance__left__rbt__greater) ).
thf(753,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)],[142]) ).
thf(115,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_111_balance__right_Osimps_I6_J) ).
thf(669,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)],[115]) ).
thf(229,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_52_local_Orbt__insert__rbt__sorted) ).
thf(1016,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)],[229]) ).
thf(211,axiom,
! [TA: $tType,A: a] :
( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) @ A )
= ( none @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_local_Orbt__lookup_Osimps_I1_J) ).
thf(970,plain,
! [TA: $tType,A: a] :
( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) @ A )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(162,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_local_Oless__trans) ).
thf(837,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(260,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_local_Odual__order_Ostrict__implies__not__eq) ).
thf(1114,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(110,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_134_balance_Osimps_I18_J) ).
thf(647,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)],[110]) ).
thf(126,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_133_balance_Osimps_I17_J) ).
thf(701,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)],[126]) ).
thf(246,axiom,
! [A: a,B: list @ a] :
~ ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( nil @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_local_Olexordp__eq__simps_I3_J) ).
thf(1060,plain,
! [A: a,B: list @ a] :
~ ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(224,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_local_OgreaterThan__iff) ).
thf(1002,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(89,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] :
( ( 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_Im418718756_Empty @ TA @ TB ) )
= ( 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_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_balance_Osimps_I37_J) ).
thf(569,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] :
( ( 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_Im418718756_Empty @ TA @ TB ) )
= ( 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_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(39,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_141_balance_Osimps_I26_J) ).
thf(371,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)],[39]) ).
thf(4,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_4) ).
thf(266,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,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_109_balance__left_Osimps_I6_J) ).
thf(311,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)],[20]) ).
thf(112,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_transpose_Ocases) ).
thf(657,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(48,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_100_rbt_Odistinct_I1_J) ).
thf(398,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)],[48]) ).
thf(232,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_local_Olexordp__eq_ONil) ).
thf(1026,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: ( TA > TB > TB > TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [F: TA > TB > TB > TB,G: TA,H: TB] : ( A @ F @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [F: TA > TB > TB > TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( ord_less @ TA @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( ord_less @ TA @ G @ J )
=> ( ( ord_less @ TA @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) )
=> ( ! [F: TA > TB > TB > TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( ord_less @ TA @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( ord_less @ TA @ G @ J )
=> ( ( ord_less @ TA @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ I @ J @ K @ L ) ) ) )
=> ( A @ B @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_ord__class_Orbt__ins_Oinduct) ).
thf(662,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: ( TA > TB > TB > TB ) > TA > TB > ( rBT_Im246033960le_rbt @ TA @ TB ) > $o,B: TA > TB > TB > TB,C: TA,D: TB,E: rBT_Im246033960le_rbt @ TA @ TB] :
( ! [F: TA > TB > TB > TB,G: TA,H: TB] : ( A @ F @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ! [F: TA > TB > TB > TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( ord_less @ TA @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( ord_less @ TA @ G @ J )
=> ( ( ord_less @ TA @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) )
=> ( ! [F: TA > TB > TB > TB,G: TA,H: TB,I: rBT_Im246033960le_rbt @ TA @ TB,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( ( ord_less @ TA @ G @ J )
=> ( A @ F @ G @ H @ I ) )
=> ( ( ~ ( ord_less @ TA @ G @ J )
=> ( ( ord_less @ TA @ J @ G )
=> ( A @ F @ G @ H @ L ) ) )
=> ( A @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ I @ J @ K @ L ) ) ) )
=> ( A @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(252,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_63_local_Orbt__insert__is__rbt) ).
thf(1086,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)],[252]) ).
thf(197,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_68_local_Obalance__rbt__greater) ).
thf(938,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)],[197]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: TA,C: TB,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_balance_Osimps_I33_J) ).
thf(558,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,B: TA,C: TB,D: TA,E: TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ C @ ( rBT_Im418718756_Empty @ TA @ TB ) ) @ D @ E @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(250,axiom,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ! [D: list @ a] : ( C @ ( nil @ a ) @ D )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ~ ( less @ D @ E )
=> ( ~ ( less @ E @ D )
=> ( ( lexordp_eq @ a @ less @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_local_Olexordp__eq_Oinducts) ).
thf(1071,plain,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ! [D: list @ a] : ( C @ ( nil @ a ) @ D )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ~ ( less @ D @ E )
=> ( ~ ( less @ E @ D )
=> ( ( lexordp_eq @ a @ less @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(17,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_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_balance__right_Osimps_I2_J) ).
thf(298,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_Im1053358987_right @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(100,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_110_combine_Osimps_I1_J) ).
thf(618,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)],[100]) ).
thf(257,axiom,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp @ a @ less @ A @ B )
=> ( ! [D: a,E: list @ a] : ( C @ ( nil @ a ) @ ( cons @ a @ D @ E ) )
=> ( ! [D: a,E: list @ a,F: a,G: list @ a] :
( ( less @ D @ F )
=> ( C @ ( cons @ a @ D @ E ) @ ( cons @ a @ F @ G ) ) )
=> ( ! [D: a,E: list @ a,F: list @ a] :
( ( lexordp @ a @ less @ E @ F )
=> ( ( C @ E @ F )
=> ( C @ ( cons @ a @ D @ E ) @ ( cons @ a @ D @ F ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_local_Olexordp__induct) ).
thf(1103,plain,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp @ a @ less @ A @ B )
=> ( ! [D: a,E: list @ a] : ( C @ ( nil @ a ) @ ( cons @ a @ D @ E ) )
=> ( ! [D: a,E: list @ a,F: a,G: list @ a] :
( ( less @ D @ F )
=> ( C @ ( cons @ a @ D @ E ) @ ( cons @ a @ F @ G ) ) )
=> ( ! [D: a,E: list @ a,F: list @ a] :
( ( lexordp @ a @ less @ E @ F )
=> ( ( C @ E @ F )
=> ( C @ ( cons @ a @ D @ E ) @ ( cons @ a @ D @ F ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(3,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_2) ).
thf(264,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(168,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( less @ A @ B )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_local_OneqE) ).
thf(856,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( less @ A @ B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
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: 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_128_balance_Osimps_I43_J) ).
thf(733,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)],[134]) ).
thf(156,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_220_local_Omap__of__entries) ).
thf(819,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)],[156]) ).
thf(138,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_local_Odual__order_Ostrict__trans) ).
thf(743,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(206,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_42_combine__rbt__less) ).
thf(958,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)],[206]) ).
thf(10,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(281,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(53,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ord_Olexordp__eq__simps_I1_J) ).
thf(413,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(108,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_135_balance_Osimps_I19_J) ).
thf(641,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)],[108]) ).
thf(90,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: 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 @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ 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 @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ 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_152_balance_Osimps_I44_J) ).
thf(572,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: 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 @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ 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 @ A @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ B @ C @ D @ E ) @ F @ 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)],[90]) ).
thf(130,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_125_balance_Osimps_I27_J) ).
thf(713,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)],[130]) ).
thf(64,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_neq__Nil__conv) ).
thf(466,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(151,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_local_Oless__imp__not__less) ).
thf(804,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(127,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] :
( ( rBT_Im1648453169alance @ 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 @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_balance_Osimps_I10_J) ).
thf(704,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] :
( ( rBT_Im1648453169alance @ 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 @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(200,axiom,
rBT_Im759614907sorted @ a @ b @ less @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_assms_I2_J) ).
thf(947,plain,
rBT_Im759614907sorted @ a @ b @ less @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(32,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_129_balance_Osimps_I45_J) ).
thf(350,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)],[32]) ).
thf(116,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_139_balance_Osimps_I24_J) ).
thf(672,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)],[116]) ).
thf(214,axiom,
! [A: a,B: a] :
( ( A != B )
= ( ( less @ A @ B )
| ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_local_Oneq__iff) ).
thf(979,plain,
! [A: a,B: a] :
( ( A != B )
= ( ( less @ A @ B )
| ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(185,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_93_local_Orbt__insertw__def) ).
thf(900,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)],[185]) ).
thf(160,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_66_local_Orbt__greater__simps_I2_J) ).
thf(831,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)],[160]) ).
thf(119,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_B @ C @ D @ E @ F ) @ G @ H @ I ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im1648453169alance @ TA @ TB @ F @ G @ H @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_balance__left_Osimps_I4_J) ).
thf(681,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_B @ C @ D @ E @ F ) @ G @ H @ I ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im1648453169alance @ TA @ TB @ F @ G @ H @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(241,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_81_ord_Orbt__sorted_Osimps_I2_J) ).
thf(1048,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)],[241]) ).
thf(135,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_185_combine_Osimps_I6_J) ).
thf(736,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)],[135]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_list_Oinject) ).
thf(377,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(221,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_69_local_Obalance__rbt__less) ).
thf(996,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)],[221]) ).
thf(36,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_142_balance_Osimps_I28_J) ).
thf(362,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)],[36]) ).
thf(60,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,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_balance_Osimps_I6_J) ).
thf(451,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,J: TA,K: TB,L: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ C @ D @ E @ F ) ) @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ I @ J @ K @ L ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(88,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_78_ord_Opaint__rbt__sorted) ).
thf(567,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)],[88]) ).
thf(180,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_49_local_Obalance__left__rbt__sorted) ).
thf(890,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)],[180]) ).
thf(68,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_187_balance__right_Osimps_I8_J) ).
thf(477,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)],[68]) ).
thf(154,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_local_Oord__eq__less__trans) ).
thf(811,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(74,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_181_balance__left_Osimps_I7_J) ).
thf(494,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)],[74]) ).
thf(155,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_70_local_Opaint__rbt__greater) ).
thf(816,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)],[155]) ).
thf(97,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_154_balance__right_Osimps_I9_J) ).
thf(609,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)],[97]) ).
thf(94,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_131_balance_Osimps_I15_J) ).
thf(594,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)],[94]) ).
thf(149,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_local_Olexordp__eq__refl) ).
thf(799,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(101,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_105_ord_Orbt__less__simps_I1_J) ).
thf(621,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)],[101]) ).
thf(70,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(483,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(182,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_62_local_Orbt__insertwk__is__rbt) ).
thf(895,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)],[182]) ).
thf(209,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_92_local_Orbt__insert__def) ).
thf(964,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)],[209]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,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_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_150_balance_Osimps_I41_J) ).
thf(626,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,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_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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)],[103]) ).
thf(259,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_84_local_Oins__rbt__sorted) ).
thf(1112,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)],[259]) ).
thf(82,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: list @ TA] : ( C != D ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_ord_Olexordp__eq_Ocases) ).
thf(521,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: list @ TA] : ( C != D ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(216,axiom,
! [TA: $tType] :
( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( ^ [A: a] : ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_local_Orbt__lookup__Empty) ).
thf(983,plain,
! [TA: $tType] :
( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) )
= ( ^ [A: a] : ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(177,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_36_local_Orbt__less__trans) ).
thf(883,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)],[177]) ).
thf(217,axiom,
( ( less @ k @ y )
& ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57__092_060open_062k_A_060_Ay_A_092_060and_062_Ab_A_124_092_060guillemotleft_062_Ak_092_060close_062) ).
thf(986,plain,
( ( less @ k @ y )
& ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(5,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] :
( ( 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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) @ K @ L @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_balance_Osimps_I12_J) ).
thf(267,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] :
( ( 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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) @ K @ L @ ( rBT_Im418718756_Empty @ TA @ TB ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(192,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( lexordp_eq @ a @ less @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_local_Olexordp__eq__antisym) ).
thf(922,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( lexordp_eq @ a @ less @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(248,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_99_local_Orbt__less__simps_I1_J) ).
thf(1066,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)],[248]) ).
thf(9,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_140_balance_Osimps_I25_J) ).
thf(278,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)],[9]) ).
thf(236,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_50_local_Obalance__right__rbt__sorted) ).
thf(1034,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)],[236]) ).
thf(117,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_137_balance_Osimps_I21_J) ).
thf(675,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)],[117]) ).
thf(199,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_27_local_Ostrict__mono__eq) ).
thf(944,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)],[199]) ).
thf(147,axiom,
! [TA: $tType] : ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_local_OEmpty__is__rbt) ).
thf(795,plain,
! [TA: $tType] : ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(140,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_local_Odual__order_Oasym) ).
thf(749,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(230,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_local_Oord__less__eq__trans) ).
thf(1018,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(83,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_182_balance__left_Osimps_I8_J) ).
thf(553,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)],[83]) ).
thf(194,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56__C3_C) ).
thf(927,plain,
rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(40,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_171_rbt__cases) ).
thf(374,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)],[40]) ).
thf(122,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_199_balance__right_Osimps_I11_J) ).
thf(690,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)],[122]) ).
thf(16,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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( 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_Im418718756_Empty @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_balance_Osimps_I35_J) ).
thf(295,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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( 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_Im418718756_Empty @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(172,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_104_ord_Orbt__greater__simps_I1_J) ).
thf(872,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)],[172]) ).
thf(128,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,N: TA,O: TB,P: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) ) @ K @ L @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_balance_Osimps_I7_J) ).
thf(707,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,N: TA,O: TB,P: rBT_Im246033960le_rbt @ TA @ TB] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) ) @ K @ L @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ M @ N @ O @ P ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(179,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: a,C: a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( less @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_local_Ostrict__mono__less) ).
thf(887,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: a,C: a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( less @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(204,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ y @ b2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58__092_060open_062b_A_124_092_060guillemotleft_062_Ay_092_060close_062) ).
thf(954,plain,
rBT_Im2075124343t_less @ a @ b @ less @ y @ b2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(136,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_183_balance__right_Osimps_I1_J) ).
thf(739,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)],[136]) ).
thf(1,conjecture,
rBT_Im1259024060reater @ a @ b @ less @ x @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( rBT_Im1259024060reater @ a @ b @ less @ x @ d ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(263,plain,
~ ( rBT_Im1259024060reater @ a @ b @ less @ x @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(243,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_local_Oless__not__sym) ).
thf(1053,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(27,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_80_ord_Opaint__rbt__less) ).
thf(331,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)],[27]) ).
thf(163,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_local_Oless__imp__neq) ).
thf(840,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(63,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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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_189_balance_Osimps_I2_J) ).
thf(463,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_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ A @ B @ C @ D ) @ E @ F @ G ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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)],[63]) ).
thf(35,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_113_combine_Osimps_I2_J) ).
thf(359,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)],[35]) ).
thf(187,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ B @ A )
= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_local_Orbt__lookup__rbt__greater) ).
thf(907,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ B @ A )
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(231,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Oorder_Oirrefl) ).
thf(1023,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(96,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_172_combine_Oinduct) ).
thf(600,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)],[96]) ).
thf(44,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_179_balance__left_Osimps_I1_J) ).
thf(386,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)],[44]) ).
thf(226,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_local_Oorder_Oasym) ).
thf(1008,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(21,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_198_balance__left_Osimps_I10_J) ).
thf(314,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)],[21]) ).
thf(98,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] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) ) @ K @ L @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_balance_Osimps_I5_J) ).
thf(612,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] :
( ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) ) @ K @ L @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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 @ ( rBT_Im418718756_Empty @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(169,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_209_local_Oentries__rbt__lookup) ).
thf(859,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)],[169]) ).
thf(219,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA] :
( ! [B: a,C: a] :
( ( less @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) )
=> ( strict_mono @ a @ TA @ less @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_local_Ostrict__monoI) ).
thf(991,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA] :
( ! [B: a,C: a] :
( ( less @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) )
=> ( strict_mono @ a @ TA @ less @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
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] :
( ( 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_153_balance__left_Osimps_I9_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] :
( ( 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)],[75]) ).
thf(174,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_67_local_Orbt__less__simps_I2_J) ).
thf(876,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)],[174]) ).
thf(84,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq @ TA @ A @ D @ E )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ord_Olexordp__eq_OCons__eq) ).
thf(556,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq @ TA @ A @ D @ E )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1259024060reater @ TB @ TA @ A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ C @ B )
= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_ord_Orbt__lookup__rbt__greater) ).
thf(1010,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im1259024060reater @ TB @ TA @ A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ C @ B )
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(213,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_76_ord_Obalance__rbt__greater) ).
thf(976,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)],[213]) ).
thf(186,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_local_Oless__imp__not__eq) ).
thf(903,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(38,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_R @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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_174_balance_Osimps_I1_J) ).
thf(368,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_R @ A @ B @ C @ D ) @ E @ F @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ G @ H @ I @ J ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( 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)],[38]) ).
thf(164,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_249_local_Oset__entries__inject) ).
thf(844,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)],[164]) ).
thf(92,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_65_rbt_Oinject) ).
thf(588,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)],[92]) ).
thf(19,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_173_ord_Orbt__ins_Oinduct) ).
thf(304,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)],[19]) ).
thf(105,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_R @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ G @ H @ I ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_balance_Osimps_I8_J) ).
thf(632,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_R @ C @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ F @ G @ H @ I ) ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ TA @ TB ) @ A @ B @ C ) @ D @ E @ ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_B @ F @ G @ H @ I ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(49,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_list_Oexhaust) ).
thf(401,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_list__induct2_H) ).
thf(418,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(208,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ k @ l,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_assms_I3_J) ).
thf(963,plain,
rBT_Im2075124343t_less @ a @ b @ less @ k @ l,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_list_OdiscI) ).
thf(517,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(234,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
= ( ? [C: list @ a] :
( ( A
= ( nil @ a ) )
& ( B = C ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ( less @ C @ D ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ~ ( less @ C @ D )
& ~ ( less @ D @ C )
& ( lexordp_eq @ a @ less @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_local_Olexordp__eq_Osimps) ).
thf(1030,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
= ( ? [C: list @ a] :
( ( A
= ( nil @ a ) )
& ( B = C ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ( less @ C @ D ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ~ ( less @ C @ D )
& ~ ( less @ D @ C )
& ( lexordp_eq @ a @ less @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(78,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_ord_Olexordp__eq_ONil) ).
thf(510,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(7,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_B @ D @ E @ F @ G ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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_208_balance__right_Osimps_I4_J) ).
thf(272,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_B @ D @ E @ F @ G ) ) @ H @ I @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( rBT_Im480247531Branch @ TA @ TB @ rBT_Impl_Mirabelle_R @ ( rBT_Im1648453169alance @ TA @ TB @ ( rBT_Im945281971_paint @ TA @ TB @ rBT_Impl_Mirabelle_R @ 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)],[7]) ).
thf(43,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_157_ord_Orbt__insert__with__key__def) ).
thf(383,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)],[43]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im2075124343t_less @ TB @ TA @ A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ C @ B )
= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_ord_Orbt__lookup__rbt__less) ).
thf(684,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: rBT_Im246033960le_rbt @ TB @ TA] :
( ( rBT_Im2075124343t_less @ TB @ TA @ A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ C @ B )
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(240,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_121_local_Orbt__insert__with__key__def) ).
thf(1045,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)],[240]) ).
thf(131,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_130_balance_Osimps_I14_J) ).
thf(716,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)],[131]) ).
thf(13,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(287,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(222,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_51_local_Orbt__insertw__rbt__sorted) ).
thf(999,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)],[222]) ).
thf(145,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_160_local_Orbt__ins_Osimps_I1_J) ).
thf(790,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)],[145]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB] :
( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im418718756_Empty @ TB @ TA ) @ B )
= ( none @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_ord_Orbt__lookup_Osimps_I1_J) ).
thf(410,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB] :
( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im418718756_Empty @ TB @ TA ) @ B )
= ( none @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(210,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_96_local_Oins__rbt__greater) ).
thf(967,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)],[210]) ).
thf(87,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_108_paint_Osimps_I1_J) ).
thf(564,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)],[87]) ).
thf(235,axiom,
rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55__C2_C) ).
thf(1033,plain,
rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(159,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_74_ord_Orbt__greater__simps_I2_J) ).
thf(828,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)],[159]) ).
thf(124,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_103_ord_Orbt__sorted_Osimps_I1_J) ).
thf(696,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)],[124]) ).
thf(205,axiom,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( lexordp_eq @ a @ less @ B @ C )
=> ( lexordp_eq @ a @ less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_local_Olexordp__eq__trans) ).
thf(955,plain,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( lexordp_eq @ a @ less @ B @ C )
=> ( lexordp_eq @ a @ less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(11,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_3) ).
thf(283,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(191,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_local_Oless__imp__not__eq2) ).
thf(918,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(150,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_162_local_Orbt__lookup__balance) ).
thf(801,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)],[150]) ).
thf(183,axiom,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115__C4_Oprems_C_I2_J) ).
thf(897,plain,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(67,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_73_paint_Osimps_I2_J) ).
thf(474,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)],[67]) ).
thf(207,axiom,
! [A: list @ a] :
( ( lexordp_eq @ a @ less @ A @ ( nil @ a ) )
= ( A
= ( nil @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_local_Olexordp__eq__simps_I2_J) ).
thf(960,plain,
! [A: list @ a] :
( ( lexordp_eq @ a @ less @ A @ ( nil @ a ) )
= ( A
= ( nil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,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 @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_145_balance_Osimps_I34_J) ).
thf(635,plain,
! [TA: $tType,TB: $tType,A: rBT_Im1923302023_color,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 @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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_Im480247531Branch @ TA @ TB @ A @ ( rBT_Im418718756_Empty @ TA @ TB ) @ B @ 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)],[106]) ).
thf(195,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_161_local_Orbt__ins_Oinduct) ).
thf(928,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)],[195]) ).
thf(54,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq @ TA @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_ord_Olexordp__eq__simps_I4_J) ).
thf(415,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq @ TA @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(91,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_101_rbt_Oinduct) ).
thf(575,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)],[91]) ).
thf(109,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_186_balance__right_Osimps_I7_J) ).
thf(644,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)],[109]) ).
thf(157,axiom,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_local_Olexordp__irreflexive_H) ).
thf(822,plain,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(166,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( A != B )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_local_Olinorder__cases) ).
thf(850,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( A != B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(215,axiom,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122__C4_Oprems_C_I1_J) ).
thf(982,plain,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(59,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_list_Oinducts) ).
thf(442,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(255,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_163_local_Orbt__ins_Osimps_I3_J) ).
thf(1093,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)],[255]) ).
thf(47,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_170_ord_Opaint__rbt__lookup) ).
thf(395,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)],[47]) ).
thf(24,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_127_balance_Osimps_I39_J) ).
thf(322,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)],[24]) ).
thf(71,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_1) ).
thf(486,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(29,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_102_rbt_Oexhaust) ).
thf(337,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)],[29]) ).
thf(65,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_184_combine_Osimps_I5_J) ).
thf(469,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)],[65]) ).
thf(196,axiom,
! [A: a] :
( ( set_greaterThan @ a @ less @ A )
= ( collect @ a @ ( less @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_local_OgreaterThan__def) ).
thf(935,plain,
! [A: a] :
( ( set_greaterThan @ a @ less @ A )
= ( collect @ a @ ( less @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(143,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: list @ a] : ( B != C ) )
=> ( ! [C: a] :
( ? [D: list @ a] :
( A
= ( cons @ a @ C @ D ) )
=> ! [D: a] :
( ? [E: list @ a] :
( B
= ( cons @ a @ D @ E ) )
=> ~ ( less @ C @ D ) ) )
=> ~ ! [C: a,D: a,E: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
=> ! [F: list @ a] :
( ( B
= ( cons @ a @ D @ F ) )
=> ( ~ ( less @ C @ D )
=> ( ~ ( less @ D @ C )
=> ~ ( lexordp_eq @ a @ less @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_local_Olexordp__eq_Ocases) ).
thf(755,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: list @ a] : ( B != C ) )
=> ( ! [C: a] :
( ? [D: list @ a] :
( A
= ( cons @ a @ C @ D ) )
=> ! [D: a] :
( ? [E: list @ a] :
( B
= ( cons @ a @ D @ E ) )
=> ~ ( less @ C @ D ) ) )
=> ~ ! [C: a,D: a,E: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
=> ! [F: list @ a] :
( ( B
= ( cons @ a @ D @ F ) )
=> ( ~ ( less @ C @ D )
=> ( ~ ( less @ D @ C )
=> ~ ( lexordp_eq @ a @ less @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(61,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_167_color_Oinduct) ).
thf(454,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)],[61]) ).
thf(73,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_107_ord_Orbt__insertw__def) ).
thf(491,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)],[73]) ).
thf(253,axiom,
( ( less @ x @ k )
& ( rBT_Im1259024060reater @ a @ b @ less @ k @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35__092_060open_062x_A_060_Ak_A_092_060and_062_Ak_A_092_060guillemotleft_062_124_Ac_092_060close_062) ).
thf(1088,plain,
( ( less @ x @ k )
& ( rBT_Im1259024060reater @ a @ b @ less @ k @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1122,plain,
$false,
inference(e,[status(thm)],[892,1036,809,629,365,347,1083,941,1005,730,1068,994,597,500,797,472,698,913,1063,340,404,898,1001,301,320,436,973,885,389,1055,719,751,949,460,421,881,325,289,1100,638,853,1013,284,591,1040,623,834,514,806,353,1051,480,687,660,507,292,380,678,270,793,925,1057,512,439,334,910,825,862,561,392,746,1091,1042,952,407,693,275,788,916,847,879,710,742,874,317,615,1121,1111,356,869,1118,989,650,948,328,1028,488,753,669,1016,970,837,1114,647,701,1060,1002,569,371,266,311,657,398,1026,662,1086,938,558,1071,298,618,1103,264,856,733,819,743,958,281,413,641,572,713,466,804,704,947,350,672,979,900,831,681,1048,736,377,996,362,451,567,890,477,811,494,816,609,594,799,621,483,895,964,626,1112,521,983,883,986,267,922,1066,278,1034,675,944,795,749,1018,553,927,374,690,295,872,707,887,954,739,263,1053,331,840,463,359,907,1023,600,386,1008,314,612,859,991,497,876,556,1010,976,903,368,844,588,304,632,401,418,963,517,1030,510,272,383,684,1045,716,287,999,790,410,967,564,1033,828,696,955,283,918,801,897,474,960,635,928,415,575,644,822,850,982,442,1093,395,322,486,337,469,935,755,454,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : DAT234^1 : TPTP v8.1.2. Released v7.0.0.
% 0.16/0.18 % Command : run_Leo-III %s %d
% 0.18/0.39 % Computer : n023.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Mon May 6 11:29:24 EDT 2024
% 0.18/0.39 % CPUTime :
% 0.96/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.19 % [INFO] Parsing done (296ms).
% 1.96/1.20 % [INFO] Running in sequential loop mode.
% 2.85/1.44 % [INFO] eprover registered as external prover.
% 2.85/1.44 % [INFO] cvc4 registered as external prover.
% 2.85/1.45 % [INFO] Scanning for conjecture ...
% 3.11/1.55 % [INFO] Found a conjecture and 261 axioms. Running axiom selection ...
% 3.54/1.67 % [INFO] Axiom selection finished. Selected 260 axioms (removed 1 axioms).
% 4.63/2.02 % [INFO] Problem is higher-order (TPTP THF).
% 4.97/2.05 % [INFO] Type checking passed.
% 4.97/2.05 % [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 ...
% 11.91/4.51 % [INFO] [Domain constraints] Detected constraint on rBT_Im1923302023_color
% 11.91/4.51 % [INFO] [Domain constraints] dom(rBT_Im1923302023_color) ⊆ {rBT_Impl_Mirabelle_R,rBT_Impl_Mirabelle_B}
% 30.90/10.43 % External prover 'e' found a proof!
% 30.90/10.43 % [INFO] Killing All external provers ...
% 31.19/10.43 % Time passed: 9871ms (effective reasoning time: 9225ms)
% 31.19/10.43 % 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)>
% 31.19/10.44 % Axioms used in derivation (260): fact_153_balance__left_Osimps_I9_J, fact_211_local_Orbt__lookup_Osimps_I1_J, fact_241_transpose_Ocases, fact_205_balance__left_Osimps_I5_J, fact_1_local_Odual__order_Oasym, fact_14_local_Oless__trans, fact_182_balance__left_Osimps_I8_J, fact_138_balance_Osimps_I22_J, fact_137_balance_Osimps_I21_J, fact_68_local_Obalance__rbt__greater, fact_240_splice_Oinduct, fact_87_local_Ostrict__mono__def, fact_136_balance_Osimps_I20_J, fact_179_balance__left_Osimps_I1_J, fact_177_balance_Osimps_I9_J, fact_90_local_Orbt__sorted_Osimps_I1_J, fact_216_ord_Orbt__lookup__Empty, fact_103_ord_Orbt__sorted_Osimps_I1_J, fact_175_balance_Osimps_I3_J, fact_8_local_Oless__imp__not__eq2, fact_117_ord_Olexordp__eq__simps_I2_J, fact_249_local_Oset__entries__inject, fact_232_ord_Olexordp__eq_Osimps, fact_151_balance_Osimps_I42_J, fact_219_ord_Orbt__lookup__rbt__less, fact_166_color_Oexhaust, fact_35__092_060open_062x_A_060_Ak_A_092_060and_062_Ak_A_092_060guillemotleft_062_124_Ac_092_060close_062, fact_114__C4_Oprems_C_I4_J, fact_156_ord_Olexordp__eq__refl, tcon_HOL_Obool___Orderings_Oord_4, fact_64_local_Orbt__insertw__is__rbt, fact_234_list_Odistinct_I1_J, fact_178_balance_Osimps_I13_J, fact_157_ord_Orbt__insert__with__key__def, fact_130_balance_Osimps_I14_J, fact_116_local_OgreaterThan__def, fact_142_balance_Osimps_I28_J, fact_63_local_Orbt__insert__is__rbt, fact_18_local_Onot__less__iff__gr__or__eq, fact_165_local_Opaint__rbt__lookup, fact_43_local_Obalance__left__rbt__less, fact_120_local_Orbt__ins_Osimps_I2_J, fact_195_balance_Osimps_I11_J, fact_237_list_Oinducts, fact_88_local_Ostrict__mono__less, fact_218_ord_Orbt__lookup__rbt__greater, fact_176_balance_Osimps_I7_J, fact_19_local_Oord__eq__less__trans, fact_31_local_Obalance__right__rbt__greater, fact_122__C4_Oprems_C_I1_J, fact_173_ord_Orbt__ins_Oinduct, tcon_fun___Orderings_Oord, fact_29_combine__rbt__greater, fact_181_balance__left_Osimps_I7_J, fact_251_local_Olexordp__antisym, fact_17_local_Oneq__iff, fact_185_combine_Osimps_I6_J, fact_89_local_Olexordp__eq_ONil, fact_98_local_Orbt__greater__simps_I1_J, fact_40_local_Olexordp__eq__trans, fact_140_balance_Osimps_I25_J, fact_34_assms_I1_J, fact_50_local_Obalance__right__rbt__sorted, fact_30__092_060open_062x_A_092_060guillemotleft_062_124_Ac_092_060close_062, fact_49_local_Obalance__left__rbt__sorted, fact_22_local_Oorder_Oirrefl, fact_2_local_Odual__order_Ostrict__implies__not__eq, fact_201_balance__left_Osimps_I3_J, fact_149_balance_Osimps_I40_J, fact_12_local_Oless__linear, fact_13_local_Oless__not__sym, fact_39_local_Olexordp__eq__refl, fact_79_ord_Opaint__rbt__greater, fact_200_balance__right_Osimps_I10_J, fact_97_local_Oins__rbt__less, fact_105_ord_Orbt__less__simps_I1_J, fact_197_balance__left_Osimps_I11_J, fact_99_local_Orbt__less__simps_I1_J, fact_135_balance_Osimps_I19_J, fact_217_ord_Orbt__lookup_Osimps_I1_J, fact_183_balance__right_Osimps_I1_J, fact_74_ord_Orbt__greater__simps_I2_J, fact_192_balance_Osimps_I6_J, fact_123_local_OgreaterThan__iff, fact_110_combine_Osimps_I1_J, fact_66_local_Orbt__greater__simps_I2_J, fact_194_balance_Osimps_I10_J, fact_46_Collect__mem__eq, fact_220_local_Omap__of__entries, fact_223_local_Olexordp__eq_OCons, fact_106_ord_Orbt__insert__def, fact_41_assms_I3_J, tcon_Set_Oset___Orderings_Oord_2, fact_73_paint_Osimps_I2_J, fact_207_balance__left_Osimps_I4_J, fact_226_local_Olexordp__eq_Oinducts, fact_53_local_Orbt__insertwk__rbt__sorted, fact_102_rbt_Oexhaust, fact_75_ord_Orbt__less__simps_I2_J, fact_104_ord_Orbt__greater__simps_I1_J, fact_9_local_Oless__imp__not__less, fact_133_balance_Osimps_I17_J, fact_171_rbt__cases, fact_101_rbt_Oinduct, fact_236_list_Oexhaust, fact_77_ord_Obalance__rbt__less, fact_36_local_Orbt__less__trans, fact_112_ord_OEmpty__is__rbt, fact_208_balance__right_Osimps_I4_J, fact_145_balance_Osimps_I34_J, fact_91_local_OEmpty__is__rbt, fact_5_local_Oless__asym_H, fact_80_ord_Opaint__rbt__less, fact_52_local_Orbt__insert__rbt__sorted, fact_28_assms_I4_J, fact_244_list__nonempty__induct, fact_214_local_Orbt__lookup__rbt__less, fact_4_local_Oless__asym, fact_85_local_Ostrict__monoD, fact_233_ord_Olexordp__eq_Oinducts, fact_198_balance__left_Osimps_I10_J, fact_60_local_Orbt__sorted_Osimps_I2_J, fact_125_balance_Osimps_I27_J, fact_167_color_Oinduct, fact_27_local_Ostrict__mono__eq, fact_162_local_Orbt__lookup__balance, fact_239_list__induct2_H, fact_45_mem__Collect__eq, fact_7_local_Oless__imp__not__eq, fact_81_ord_Orbt__sorted_Osimps_I2_J, fact_67_local_Orbt__less__simps_I2_J, fact_93_local_Orbt__insertw__def, fact_26__092_060open_062x_A_060_Ay_A_092_060and_062_Ay_A_092_060guillemotleft_062_124_Ad_092_060close_062, fact_206_balance__right_Osimps_I5_J, fact_37_local_Olexordp__eq__antisym, fact_32_local_Obalance__left__rbt__greater, tcon_Set_Oset___Orderings_Oorder_1, fact_54_local_Ois__rbt__rbt__sorted, fact_82_ord_Ois__rbt__rbt__sorted, fact_188_ord__class_Orbt__ins_Oinduct, fact_189_balance_Osimps_I2_J, fact_141_balance_Osimps_I26_J, fact_164_local_OlessThan__iff, fact_154_balance__right_Osimps_I9_J, fact_150_balance_Osimps_I41_J, fact_42_combine__rbt__less, fact_248_ord_Olexordp__eq_OCons__eq, fact_62_local_Orbt__insertwk__is__rbt, fact_96_local_Oins__rbt__greater, fact_247_ord_Olexordp__eq_OCons, fact_246_not__Cons__self2, fact_245_map__tailrec__rev_Oinduct, fact_134_balance_Osimps_I18_J, fact_190_balance_Osimps_I4_J, fact_191_balance_Osimps_I5_J, fact_6_local_Oless__imp__neq, fact_78_ord_Opaint__rbt__sorted, fact_47_Collect__cong, fact_111_balance__right_Osimps_I6_J, fact_108_paint_Osimps_I1_J, fact_163_local_Orbt__ins_Osimps_I3_J, fact_11_local_Oless__irrefl, fact_186_balance__right_Osimps_I7_J, fact_161_local_Orbt__ins_Oinduct, fact_225_local_Olexordp__eq_Osimps, fact_124_balance_Osimps_I23_J, fact_61_local_Obalance__rbt__sorted, fact_187_balance__right_Osimps_I8_J, fact_231_ord_Olexordp__eq_Ocases, fact_113_combine_Osimps_I2_J, fact_70_local_Opaint__rbt__greater, fact_152_balance_Osimps_I44_J, fact_184_combine_Osimps_I5_J, fact_169_ord_Orbt__ins_Osimps_I3_J, fact_38_local_Olexordp__eq__linear, fact_170_ord_Opaint__rbt__lookup, fact_131_balance_Osimps_I15_J, fact_144_balance_Osimps_I33_J, fact_92_local_Orbt__insert__def, fact_15_local_Olinorder__cases, fact_253_local_Olexordp__irreflexive_H, fact_83__C4_Ohyps_C, fact_221_local_Olexordp__eq_Ocases, fact_76_ord_Obalance__rbt__greater, fact_126_balance_Osimps_I29_J, fact_3_local_Odual__order_Ostrict__trans, fact_210_local_Oentries__eqI, fact_115__C4_Oprems_C_I2_J, fact_21_local_Oorder_Oasym, fact_230_local_Olexordp__eq__simps_I3_J, fact_227_ord_Olexordp__eq__simps_I4_J, fact_148_balance_Osimps_I37_J, fact_199_balance__right_Osimps_I11_J, tcon_HOL_Obool___Orderings_Oorder_3, fact_158_ord_Olexordp__eq_ONil, fact_250_local_Olexordp__induct, fact_118_ord_Olexordp__eq__simps_I1_J, fact_51_local_Orbt__insertw__rbt__sorted, fact_100_rbt_Odistinct_I1_J, fact_128_balance_Osimps_I43_J, fact_174_balance_Osimps_I1_J, fact_129_balance_Osimps_I45_J, fact_69_local_Obalance__rbt__less, fact_109_balance__left_Osimps_I6_J, fact_193_balance_Osimps_I8_J, fact_20_local_Oord__less__eq__trans, fact_202_balance__right_Osimps_I3_J, fact_229_local_Olexordp__eq__simps_I4_J, fact_238_neq__Nil__conv, fact_56__C3_C, fact_0_local_Oantisym__conv3, fact_203_balance__left_Osimps_I2_J, fact_215_entries_Osimps_I1_J, fact_196_balance_Osimps_I12_J, fact_235_list_OdiscI, tcon_fun___Orderings_Oorder, fact_119__C4_Oprems_C_I3_J, fact_16_local_OneqE, fact_71_local_Opaint__rbt__less, fact_55__C2_C, fact_143_balance_Osimps_I32_J, fact_159_local_OlessThan__def, fact_24_local_Oorder_Ostrict__trans, fact_10_local_Oless__imp__triv, fact_243_remdups__adj_Oinduct, fact_212_local_Orbt__lookup__Empty, fact_25_local_Orbt__greater__trans, fact_94_local_Olexordp__eq__simps_I1_J, fact_160_local_Orbt__ins_Osimps_I1_J, fact_121_local_Orbt__insert__with__key__def, fact_172_combine_Oinduct, fact_33_assms_I2_J, fact_72_Empty, fact_59_local_Opaint__rbt__sorted, fact_23_local_Oorder_Ostrict__implies__not__eq, fact_180_ord_Orbt__ins_Osimps_I1_J, fact_147_balance_Osimps_I36_J, fact_146_balance_Osimps_I35_J, fact_86_local_Ostrict__monoI, fact_254_local_Olexordp__linear, fact_139_balance_Osimps_I24_J, fact_224_list_Oinject, fact_58__092_060open_062b_A_124_092_060guillemotleft_062_Ay_092_060close_062, fact_228_ord_Olexordp__eq__simps_I3_J, fact_57__092_060open_062k_A_060_Ay_A_092_060and_062_Ab_A_124_092_060guillemotleft_062_Ak_092_060close_062, fact_204_balance__right_Osimps_I2_J, fact_132_balance_Osimps_I16_J, fact_65_rbt_Oinject, fact_213_local_Orbt__lookup__rbt__greater, fact_84_local_Oins__rbt__sorted, fact_209_local_Oentries__rbt__lookup, fact_95_local_Olexordp__eq__simps_I2_J, fact_252_local_Olexordp__irreflexive, fact_155_ord_Orbt__ins_Osimps_I2_J, fact_127_balance_Osimps_I39_J, fact_168_color_Odistinct_I1_J, fact_107_ord_Orbt__insertw__def, fact_242_remdups__adj_Ocases, fact_44_local_Obalance__right__rbt__less, fact_222_local_Olexordp__eq_OCons__eq
% 31.19/10.44 % No. of inferences in proof: 524
% 31.19/10.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9871 ms resp. 9225 ms w/o parsing
% 32.09/10.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.09/10.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------