TSTP Solution File: DAT232^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : DAT232^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 : Mon May 20 19:48:23 EDT 2024
% Result : Theorem 37.05s 13.13s
% Output : Refutation 38.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 323
% Syntax : Number of formulae : 583 ( 221 unt; 65 typ; 0 def)
% Number of atoms : 1952 ( 648 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 9371 ( 338 ~; 56 |; 223 &;8136 @)
% ( 0 <=>; 618 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 400 ( 400 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 27 con; 0-7 aty)
% Number of variables : 2311 ( 46 ^1990 !; 216 ?;2311 :)
% ( 59 !>; 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(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(inj_on_type,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(bind_type,type,
bind:
!>[TA: $tType,TB: $tType] : ( ( list @ TB ) > ( TB > ( list @ TA ) ) > ( list @ TA ) ) ).
thf(distinct_type,type,
distinct:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(extract_type,type,
extract:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > ( option @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) ) ) ).
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(listrel1_type,type,
listrel1:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ 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(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(sublists_type,type,
sublists:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(union_type,type,
union:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(dom_type,type,
dom:
!>[TA: $tType,TB: $tType] : ( ( TB > ( option @ TA ) ) > ( set @ TB ) ) ).
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(some_type,type,
some:
!>[TA: $tType] : ( TA > ( 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(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(rBT_Impl_Mirabelle_B_type,type,
rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
thf(rBT_Impl_Mirabelle_R_type,type,
rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
thf(rBT_Im1805589839lor_of_type,type,
rBT_Im1805589839lor_of:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > rBT_Im1923302023_color ) ).
thf(rBT_Im954575269ntries_type,type,
rBT_Im954575269ntries:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > ( list @ ( product_prod @ TB @ TA ) ) ) ).
thf(rBT_Im1040612427e_inv1_type,type,
rBT_Im1040612427e_inv1:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im1040612428e_inv2_type,type,
rBT_Im1040612428e_inv2:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > $o ) ).
thf(rBT_Im380146495e_keys_type,type,
rBT_Im380146495e_keys:
!>[TA: $tType,TB: $tType] : ( ( rBT_Im246033960le_rbt @ TB @ TA ) > ( list @ TB ) ) ).
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_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_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(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(set_greaterThan_type,type,
set_greaterThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_lessThan_type,type,
set_lessThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(transitive_acyclic_type,type,
transitive_acyclic:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(b2_type,type,
b2: rBT_Im246033960le_rbt @ a @ b ).
thf(c_type,type,
c: 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(s_type,type,
s: b ).
thf(t_type,type,
t: b ).
thf(va_type,type,
va: rBT_Im246033960le_rbt @ a @ b ).
thf(vb_type,type,
vb: a ).
thf(vc_type,type,
vc: rBT_Im246033960le_rbt @ a @ b ).
thf(vd_type,type,
vd: rBT_Im246033960le_rbt @ a @ b ).
thf(ve_type,type,
ve: a ).
thf(vf_type,type,
vf: rBT_Im246033960le_rbt @ a @ b ).
thf(vg_type,type,
vg: b ).
thf(vii_type,type,
vii: b ).
thf(x_type,type,
x: a ).
thf(y_type,type,
y: a ).
thf(z_type,type,
z: a ).
thf(106,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_240_ord_Orbt__lookup_Osimps_I1_J) ).
thf(645,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)],[106]) ).
thf(198,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(1036,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(29,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord_Olexordp__eq__refl) ).
thf(365,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ ( union @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_distinct__union) ).
thf(347,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ ( union @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_lessThan @ TA @ B @ C ) )
= ( B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_ord_OlessThan__iff) ).
thf(352,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_lessThan @ TA @ B @ C ) )
= ( B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(246,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_51_local_Olexordp__eq__antisym) ).
thf(1168,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)],[246]) ).
thf(134,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(760,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(216,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(1083,plain,
! [A: a,B: a] :
( ( A != B )
= ( ( less @ A @ B )
| ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(177,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_34_local_Ostrict__mono__eq) ).
thf(962,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)],[177]) ).
thf(140,axiom,
! [A: a,B: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_local_Olexordp_ONil) ).
thf(777,plain,
! [A: a,B: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(74,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ B ) @ ( append @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_ord_Olexordp__append__leftI) ).
thf(555,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ B ) @ ( append @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(253,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(1211,plain,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( ( less @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(8,axiom,
! [TA: $tType,A: TA > $o,B: list @ TA,C: list @ TA,D: TA,E: list @ TA] :
( ( ( extract @ TA @ A @ B )
= ( some @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) @ ( product_Pair @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) @ C @ ( product_Pair @ TA @ ( list @ TA ) @ D @ E ) ) ) )
=> ( ( B
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( A @ D )
& ~ ? [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ C ) )
& ( A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_extract__SomeE) ).
thf(276,plain,
! [TA: $tType,A: TA > $o,B: list @ TA,C: list @ TA,D: TA,E: list @ TA] :
( ( ( extract @ TA @ A @ B )
= ( some @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) @ ( product_Pair @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) @ C @ ( product_Pair @ TA @ ( list @ TA ) @ D @ E ) ) ) )
=> ( ( B
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( A @ D )
& ~ ? [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ C ) )
& ( A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(210,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp @ a @ less @ C @ D )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_local_Olexordp_OCons__eq) ).
thf(1068,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp @ a @ less @ C @ D )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(212,axiom,
! [A: a] :
( ( set_lessThan @ a @ less @ A )
= ( collect @ a
@ ^ [B: a] : ( less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_local_OlessThan__def) ).
thf(1073,plain,
! [A: a] :
( ( set_lessThan @ a @ less @ A )
= ( collect @ a
@ ^ [B: a] : ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(252,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_49_color_Oinduct) ).
thf(1205,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)],[252]) ).
thf(115,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_split__list__last__propE) ).
thf(677,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(248,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: a,D: list @ a] :
( B
!= ( cons @ a @ C @ D ) ) )
=> ( ! [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: list @ a] :
( ( A
= ( cons @ a @ C @ D ) )
=> ! [E: list @ a] :
( ( B
= ( cons @ a @ C @ E ) )
=> ~ ( lexordp @ a @ less @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_local_Olexordp__cases) ).
thf(1173,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: a,D: list @ a] :
( B
!= ( cons @ a @ C @ D ) ) )
=> ( ! [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: list @ a] :
( ( A
= ( cons @ a @ C @ D ) )
=> ! [E: list @ a] :
( ( B
= ( cons @ a @ C @ E ) )
=> ~ ( lexordp @ a @ less @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(64,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_241_ord_Orbt__lookup__rbt__less) ).
thf(523,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)],[64]) ).
thf(85,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_94_map__tailrec__rev_Oinduct) ).
thf(582,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)],[85]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_list_Oset__intros_I2_J) ).
thf(655,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(60,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_same__append__eq) ).
thf(511,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(35,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_108_ord_Olexordp__eq_OCons) ).
thf(384,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)],[35]) ).
thf(236,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_118_local_Olexordp__induct) ).
thf(1137,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)],[236]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_append1__eq__conv) ).
thf(533,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(208,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_52_local_Olexordp__eq__trans) ).
thf(1063,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)],[208]) ).
thf(68,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp @ TA @ A @ D @ E )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_ord_Olexordp_OCons__eq) ).
thf(538,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp @ TA @ A @ D @ E )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(154,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_local_Olexordp__eq__simps_I1_J) ).
thf(829,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(249,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_local_OlessThan__iff) ).
thf(1196,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(142,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(782,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_split__list__prop) ).
thf(288,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im380146495e_keys @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_keys__simps_I1_J) ).
thf(436,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im380146495e_keys @ TA @ TB @ ( rBT_Im418718756_Empty @ TA @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(259,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_36_local_Orbt__less__simps_I2_J) ).
thf(1228,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)],[259]) ).
thf(205,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_218_local_Oset__entries__inject) ).
thf(1055,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)],[205]) ).
thf(80,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_product__lists_Osimps_I1_J) ).
thf(570,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(58,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_82_ord_Olexordp__eq__simps_I2_J) ).
thf(504,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)],[58]) ).
thf(97,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_57_ord_Ois__rbt__rbt__sorted) ).
thf(619,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)],[97]) ).
thf(131,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_split__list__last__prop__iff) ).
thf(751,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(159,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_local_Oless__imp__neq) ).
thf(853,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(218,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_222_local_Oentries__eqI) ).
thf(1087,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)],[218]) ).
thf(238,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ? [C: a,D: list @ a] :
( B
= ( append @ a @ A @ ( cons @ a @ C @ D ) ) )
| ? [C: list @ a,D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
& ( A
= ( append @ a @ C @ ( cons @ a @ D @ F ) ) )
& ( B
= ( append @ a @ C @ ( cons @ a @ E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_local_Olexordp__iff) ).
thf(1147,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ? [C: a,D: list @ a] :
( B
= ( append @ a @ A @ ( cons @ a @ C @ D ) ) )
| ? [C: list @ a,D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
& ( A
= ( append @ a @ C @ ( cons @ a @ D @ F ) ) )
& ( B
= ( append @ a @ C @ ( cons @ a @ E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_list_Oset__cases) ).
thf(421,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(93,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp @ TA @ A @ ( nil @ TA ) @ B )
= ( B
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_ord_Olexordp__simps_I1_J) ).
thf(606,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp @ TA @ A @ ( nil @ TA ) @ B )
= ( B
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(156,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)],[156]) ).
thf(61,axiom,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_sublists_Osimps_I1_J) ).
thf(514,plain,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(192,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_43_ord_Orbt__less__simps_I2_J) ).
thf(1020,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)],[192]) ).
thf(148,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(806,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(199,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
= ( ! [C: a] :
( ( member @ a @ C @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ TA @ B ) ) )
=> ( less @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_local_Orbt__less__prop) ).
thf(1040,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im2075124343t_less @ a @ TA @ less @ A @ B )
= ( ! [C: a] :
( ( member @ a @ C @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ TA @ B ) ) )
=> ( less @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(227,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(1109,plain,
! [A: a,B: a] :
( ( less @ A @ B )
| ( A = B )
| ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(17,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_append__Nil2) ).
thf(321,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(136,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_33_local_Orbt__greater__simps_I2_J) ).
thf(766,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)],[136]) ).
thf(174,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_local_Olexordp_OCons) ).
thf(956,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(163,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ! [D: TA] :
( ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ C )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_local_Orbt__lookup__from__in__tree) ).
thf(866,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: rBT_Im246033960le_rbt @ a @ TA,C: a] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( rBT_Im759614907sorted @ a @ TA @ less @ B )
=> ( ! [D: TA] :
( ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ C @ D ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ B ) ) ) )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ C )
= ( rBT_Im35466040lookup @ a @ TA @ less @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(139,axiom,
! [A: list @ a] :
( ( lexordp @ a @ less @ ( nil @ a ) @ A )
= ( A
!= ( nil @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_local_Olexordp__simps_I1_J) ).
thf(774,plain,
! [A: list @ a] :
( ( lexordp @ a @ less @ ( nil @ a ) @ A )
= ( A
!= ( nil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(39,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 @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_rev__nonempty__induct) ).
thf(396,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 @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TB,B: rBT_Im246033960le_rbt @ TB @ TA] :
( ( member @ TB @ A @ ( set2 @ TB @ ( rBT_Im380146495e_keys @ TB @ TA @ B ) ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( set2 @ ( product_prod @ TB @ TA ) @ ( rBT_Im954575269ntries @ TB @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_keys__entries) ).
thf(660,plain,
! [TA: $tType,TB: $tType,A: TB,B: rBT_Im246033960le_rbt @ TB @ TA] :
( ( member @ TB @ A @ ( set2 @ TB @ ( rBT_Im380146495e_keys @ TB @ TA @ B ) ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ ( set2 @ ( product_prod @ TB @ TA ) @ ( rBT_Im954575269ntries @ TB @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_eq__Nil__appendI) ).
thf(507,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(225,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_61_local_Ostrict__mono__less) ).
thf(1104,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)],[225]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_list_Oset__intros_I1_J) ).
thf(265,plain,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,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_100_list__induct2_H) ).
thf(292,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)],[12]) ).
thf(48,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: TA,E: list @ TA] :
( C
!= ( cons @ TA @ D @ E ) ) )
=> ( ! [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 @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_ord_Olexordp_Ocases) ).
thf(439,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: TA,E: list @ TA] :
( C
!= ( cons @ TA @ D @ E ) ) )
=> ( ! [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 @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TB @ ( type2 @ TB ) )
=> ! [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less @ TB @ ( B @ D ) @ ( B @ C ) ) )
=> ( transitive_acyclic @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_order__class_OacyclicI__order) ).
thf(270,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TB @ ( type2 @ TB ) )
=> ! [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less @ TB @ ( B @ D ) @ ( B @ C ) ) )
=> ( transitive_acyclic @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(71,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_101_neq__Nil__conv) ).
thf(546,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)],[71]) ).
thf(250,axiom,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp @ a @ less @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_local_Olexordp__simps_I3_J) ).
thf(1199,plain,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp @ a @ less @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(240,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_39_local_Ois__rbt__rbt__sorted) ).
thf(1153,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)],[240]) ).
thf(244,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: set @ a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( inj_on @ a @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_local_Ostrict__mono__imp__inj__on) ).
thf(1163,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: a > TA,B: set @ a] :
( ( strict_mono @ a @ TA @ less @ A )
=> ( inj_on @ a @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(20,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_109_ord_Olexordp__eq_Oinducts) ).
thf(334,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)],[20]) ).
thf(129,axiom,
! [TA: $tType,A: TA > $o,B: list @ TA] :
( ( ( extract @ TA @ A @ B )
= ( none @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) ) )
= ( ~ ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_extract__None__iff) ).
thf(746,plain,
! [TA: $tType,A: TA > $o,B: list @ TA] :
( ( ( extract @ TA @ A @ B )
= ( none @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) ) )
= ( ~ ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(152,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp_eq @ a @ less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_local_Olexordp__into__lexordp__eq) ).
thf(820,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp_eq @ a @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel1 @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Cons__listrel1__Cons) ).
thf(630,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel1 @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TA,C: TA > ( list @ TB ),D: TA > ( list @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ A ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( bind @ TA @ TB @ A @ C )
= ( bind @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_list__bind__cong) ).
thf(429,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TA,C: TA > ( list @ TB ),D: TA > ( list @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ A ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( bind @ TA @ TB @ A @ C )
= ( bind @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(145,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_84_local_Olexordp__eq_Oinducts) ).
thf(788,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)],[145]) ).
thf(1,conjecture,
( ( less @ y @ z )
& ( rBT_Im1259024060reater @ a @ b @ less @ z @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( less @ y @ z )
& ( rBT_Im1259024060reater @ a @ b @ less @ z @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(260,plain,
~ ( ( less @ y @ z )
& ( rBT_Im1259024060reater @ a @ b @ less @ z @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(232,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_88_local_Olexordp__eq_OCons__eq) ).
thf(1123,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)],[232]) ).
thf(255,axiom,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( lexordp @ a @ less @ B @ C )
=> ( lexordp @ a @ less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_local_Olexordp__trans) ).
thf(1217,plain,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( lexordp @ a @ less @ B @ C )
=> ( lexordp @ a @ less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_not__Cons__self2) ).
thf(598,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(78,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA,F: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ ( cons @ TA @ B @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_ord_Olexordp__append__left__rightI) ).
thf(566,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA,F: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ ( cons @ TA @ B @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(196,axiom,
rBT_Im1259024060reater @ a @ b @ less @ k @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_assms_I4_J) ).
thf(1032,plain,
rBT_Im1259024060reater @ a @ b @ less @ k @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(27,axiom,
! [TA: $tType,A: TA > $o] :
( ( extract @ TA @ A @ ( nil @ TA ) )
= ( none @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_extract__Nil__code) ).
thf(361,plain,
! [TA: $tType,A: TA > $o] :
( ( extract @ TA @ A @ ( nil @ TA ) )
= ( none @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(168,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_29_rbt_Oinject) ).
thf(879,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)],[168]) ).
thf(113,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_102_list_Oinducts) ).
thf(665,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)],[113]) ).
thf(242,axiom,
rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40__C5__4_Oprems_C_I4_J) ).
thf(1159,plain,
rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(116,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_append__Nil) ).
thf(682,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(18,axiom,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: TA,C: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_splice_Ocases) ).
thf(324,plain,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: TA,C: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(181,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_78_ord_Orbt__greater__simps_I1_J) ).
thf(974,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)],[181]) ).
thf(171,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_local_Olexordp__eq__refl) ).
thf(948,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(191,axiom,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_color_Odistinct_I1_J) ).
thf(1017,plain,
rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(121,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_98_transpose_Ocases) ).
thf(725,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)],[121]) ).
thf(40,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_90_ord_Olexordp__eq__simps_I4_J) ).
thf(403,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)],[40]) ).
thf(221,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_119_local_Olexordp__antisym) ).
thf(1096,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)],[221]) ).
thf(164,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(869,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( A != B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Cons__eq__append__conv) ).
thf(499,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(160,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_238_local_Orbt__lookup__rbt__greater) ).
thf(857,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)],[160]) ).
thf(49,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(471,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(243,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ? [C: a,D: list @ a] :
( ( A
= ( nil @ a ) )
& ( B
= ( cons @ a @ 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 ) )
| ? [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 @ a @ less @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_local_Olexordp_Osimps) ).
thf(1160,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ? [C: a,D: list @ a] :
( ( A
= ( nil @ a ) )
& ( B
= ( cons @ a @ 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 ) )
| ? [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 @ a @ less @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(51,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ! [E: TA,F: list @ TA] : ( D @ ( nil @ TA ) @ ( cons @ TA @ E @ F ) )
=> ( ! [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 @ 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_142_ord_Olexordp_Oinducts) ).
thf(476,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ! [E: TA,F: list @ TA] : ( D @ ( nil @ TA ) @ ( cons @ TA @ E @ F ) )
=> ( ! [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 @ 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)],[51]) ).
thf(105,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ! [B: list @ TA] :
( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
=> ( distinct @ TA @ B ) )
=> ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_distinct__product__lists) ).
thf(642,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ! [B: list @ TA] :
( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
=> ( distinct @ TA @ B ) )
=> ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(65,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_95_list__nonempty__induct) ).
thf(526,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)],[65]) ).
thf(254,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_Im954575269ntries @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( append @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ B ) @ ( cons @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( rBT_Im954575269ntries @ TA @ TB @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_entries_Osimps_I2_J) ).
thf(1214,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_Im954575269ntries @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( append @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ B ) @ ( cons @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ ( rBT_Im954575269ntries @ TA @ TB @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(241,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(1155,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(157,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)],[157]) ).
thf(186,axiom,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_local_Olexordp__irreflexive_H) ).
thf(997,plain,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(239,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1259024060reater @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB] :
! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ C ) ) )
=> ( A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_ord_Orbt__greater__prop) ).
thf(1150,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im1259024060reater @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB] :
! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ C ) ) )
=> ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(234,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Oorder_Oirrefl) ).
thf(1131,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(207,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(1060,plain,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(141,axiom,
! [A: a,B: list @ a] :
~ ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( nil @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_local_Olexordp__eq__simps_I3_J) ).
thf(779,plain,
! [A: a,B: list @ a] :
~ ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(38,axiom,
! [TA: $tType,A: list @ TA,B: TA > TA > $o,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( lexordp @ TA @ B @ C @ ( append @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_ord_Olexordp__append__rightI) ).
thf(393,plain,
! [TA: $tType,A: list @ TA,B: TA > TA > $o,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( lexordp @ TA @ B @ C @ ( append @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(229,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( dom @ a @ TA @ ( rBT_Im35466040lookup @ a @ TA @ less @ A ) )
= ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_local_Orbt__lookup__keys) ).
thf(1114,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( dom @ a @ TA @ ( rBT_Im35466040lookup @ a @ TA @ less @ A ) )
= ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(223,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_54_local_Olexordp__eq__linear) ).
thf(1099,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)],[223]) ).
thf(185,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: 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 @ 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_115_local_Olexordp_Oinducts) ).
thf(985,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: 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 @ 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)],[185]) ).
thf(251,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_80_rbt__cases) ).
thf(1202,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)],[251]) ).
thf(217,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56__C5__4_Oprems_C_I3_J) ).
thf(1086,plain,
rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(102,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_self__append__conv2) ).
thf(633,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(110,axiom,
! [TA: $tType,A: list @ TA] :
( ( ~ ( distinct @ TA @ A ) )
= ( ? [B: list @ TA,C: TA,D: list @ TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B )
& ( A
= ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_not__distinct__conv__prefix) ).
thf(657,plain,
! [TA: $tType,A: list @ TA] :
( ( ~ ( distinct @ TA @ A ) )
= ( ? [B: list @ TA,C: TA,D: list @ TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B )
& ( A
= ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(211,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_local_Olexordp__eq_ONil) ).
thf(1071,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(114,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_append__eq__append__conv2) ).
thf(674,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(194,axiom,
( ( less @ x @ y )
& ( rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38__092_060open_062x_A_060_Ay_A_092_060and_062_ABranch_AB_Ava_Avb_Avg_Avc_A_124_092_060guillemotleft_062_Ax_092_060close_062) ).
thf(1026,plain,
( ( less @ x @ y )
& ( rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(173,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_221_local_Oentries__rbt__lookup) ).
thf(953,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)],[173]) ).
thf(43,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_rev__induct) ).
thf(412,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(178,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ B )
= ( some @ TA @ C ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ B @ C ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_local_Orbt__lookup__in__tree) ).
thf(965,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA,B: a,C: TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( ( ( rBT_Im35466040lookup @ a @ TA @ less @ A @ B )
= ( some @ TA @ C ) )
= ( member @ ( product_prod @ a @ TA ) @ ( product_Pair @ a @ TA @ B @ C ) @ ( set2 @ ( product_prod @ a @ TA ) @ ( rBT_Im954575269ntries @ a @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(81,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) )
=> ( ! [E: TA] :
~ ( A @ E @ E )
=> ( lexordp @ TA @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_ord_Olexordp__append__leftD) ).
thf(573,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) )
=> ( ! [E: TA] :
~ ( A @ E @ E )
=> ( lexordp @ TA @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(124,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_107_ord_Olexordp__eq_OCons__eq) ).
thf(733,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)],[124]) ).
thf(91,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_append__same__eq) ).
thf(601,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(189,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_87_local_Olexordp__eq_OCons) ).
thf(1007,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)],[189]) ).
thf(138,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_27_local_Orbt__less__trans) ).
thf(772,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)],[138]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_listrel1I2) ).
thf(286,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(128,axiom,
! [TA: $tType,A: list @ TA] :
( ~ ( distinct @ TA @ A )
=> ? [B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( A
= ( append @ TA @ B @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_not__distinct__decomp) ).
thf(743,plain,
! [TA: $tType,A: list @ TA] :
( ~ ( distinct @ TA @ A )
=> ? [B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( A
= ( append @ TA @ B @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(84,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_99_splice_Oinduct) ).
thf(579,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)],[84]) ).
thf(166,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37__C1_C) ).
thf(875,plain,
rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(83,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp_eq @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_ord_Olexordp__into__lexordp__eq) ).
thf(577,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp_eq @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(37,axiom,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_distinct_Osimps_I1_J) ).
thf(391,plain,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(34,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] : ( lexordp @ TA @ A @ ( nil @ TA ) @ ( cons @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_ord_Olexordp_ONil) ).
thf(382,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] : ( lexordp @ TA @ A @ ( nil @ TA ) @ ( cons @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(219,axiom,
! [A: a,B: a,C: list @ a,D: list @ a,E: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ ( cons @ a @ A @ D ) ) @ ( append @ a @ C @ ( cons @ a @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_local_Olexordp__append__left__rightI) ).
thf(1090,plain,
! [A: a,B: a,C: list @ a,D: list @ a,E: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ ( cons @ a @ A @ D ) ) @ ( append @ a @ C @ ( cons @ a @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(258,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(1224,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(23,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_76_ord_Orbt__sorted_Osimps_I1_J) ).
thf(350,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)],[23]) ).
thf(69,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev__exhaust) ).
thf(540,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(206,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( distinct @ a @ ( rBT_Im380146495e_keys @ a @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_local_Odistinct__keys) ).
thf(1058,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im759614907sorted @ a @ TA @ less @ A )
=> ( distinct @ a @ ( rBT_Im380146495e_keys @ a @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(226,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_64_local_Ostrict__monoD) ).
thf(1107,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)],[226]) ).
thf(41,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_97_remdups__adj_Ocases) ).
thf(406,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)],[41]) ).
thf(155,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_local_OgreaterThan__iff) ).
thf(831,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(202,axiom,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41__C5__4_Oprems_C_I2_J) ).
thf(1048,plain,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(33,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_split__list__first__prop) ).
thf(377,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(200,axiom,
! [TA: $tType,A: a] : ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_local_Orbt__greater__simps_I1_J) ).
thf(1043,plain,
! [TA: $tType,A: a] : ( rBT_Im1259024060reater @ a @ TA @ less @ A @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_map__tailrec__rev_Ocases) ).
thf(616,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(162,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_35_ord_Orbt__greater__simps_I2_J) ).
thf(863,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)],[162]) ).
thf(183,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_Im380146495e_keys @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( append @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ B ) @ ( cons @ TA @ C @ ( rBT_Im380146495e_keys @ TA @ TB @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_keys__simps_I2_J) ).
thf(979,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_Im380146495e_keys @ TA @ TB @ ( rBT_Im480247531Branch @ TA @ TB @ A @ B @ C @ D @ E ) )
= ( append @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ B ) @ ( cons @ TA @ C @ ( rBT_Im380146495e_keys @ TA @ TB @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ C ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_entry__in__tree__keys) ).
thf(604,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: rBT_Im246033960le_rbt @ TA @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( set2 @ ( product_prod @ TA @ TB ) @ ( rBT_Im954575269ntries @ TA @ TB @ C ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(143,axiom,
! [TA: $tType] : ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_local_OEmpty__is__rbt) ).
thf(784,plain,
! [TA: $tType] : ( rBT_Im862805236is_rbt @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(230,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(1117,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( ~ ( less @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(126,axiom,
! [TA: $tType] :
( ( set_lessThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA] :
( collect @ TA
@ ^ [C: TA] : ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_ord_OlessThan__def) ).
thf(737,plain,
! [TA: $tType] :
( ( set_lessThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA] :
( collect @ TA
@ ^ [C: TA] : ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_list_Odistinct_I1_J) ).
thf(318,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(150,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)],[150]) ).
thf(133,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_28_local_Orbt__greater__trans) ).
thf(758,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)],[133]) ).
thf(151,axiom,
! [A: list @ a,B: list @ a] :
( ( A
!= ( nil @ a ) )
=> ( lexordp @ a @ less @ B @ ( append @ a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_local_Olexordp__append__rightI) ).
thf(816,plain,
! [A: list @ a,B: list @ a] :
( ( A
!= ( nil @ a ) )
=> ( lexordp @ a @ less @ B @ ( append @ a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(94,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_append__eq__appendI) ).
thf(609,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(98,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_103_list_Oexhaust) ).
thf(621,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)],[98]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_distinct__length__2__or__more) ).
thf(520,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(195,axiom,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ ( nil @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_local_Olexordp__simps_I2_J) ).
thf(1029,plain,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(170,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: a,D: list @ a] :
( B
!= ( cons @ a @ C @ D ) ) )
=> ( ! [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 @ a @ less @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_local_Olexordp_Ocases) ).
thf(915,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: a,D: list @ a] :
( B
!= ( cons @ a @ C @ D ) ) )
=> ( ! [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 @ a @ less @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(137,axiom,
! [A: list @ a] :
( ( lexordp_eq @ a @ less @ A @ ( nil @ a ) )
= ( A
= ( nil @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_local_Olexordp__eq__simps_I2_J) ).
thf(769,plain,
! [A: list @ a] :
( ( lexordp_eq @ a @ less @ A @ ( nil @ a ) )
= ( A
= ( nil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(228,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_local_Oorder_Oasym) ).
thf(1112,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_greaterThan @ TA @ B @ C ) )
= ( B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_ord_OgreaterThan__iff) ).
thf(494,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_greaterThan @ TA @ B @ C ) )
= ( B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(215,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_85_local_Olexordp__eq_Osimps) ).
thf(1080,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)],[215]) ).
thf(21,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_81_ord_Olexordp__eq__simps_I1_J) ).
thf(345,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)],[21]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_in__set__conv__decomp__last) ).
thf(367,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType] :
( ( rBT_Im2075124343t_less @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB] :
! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ C ) ) )
=> ( A @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_ord_Orbt__less__prop) ).
thf(552,plain,
! [TA: $tType,TB: $tType] :
( ( rBT_Im2075124343t_less @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA,C: rBT_Im246033960le_rbt @ TA @ TB] :
! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ ( rBT_Im380146495e_keys @ TA @ TB @ C ) ) )
=> ( A @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(175,axiom,
rBT_Im759614907sorted @ a @ b @ less @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_assms_I2_J) ).
thf(959,plain,
rBT_Im759614907sorted @ a @ b @ less @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(103,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_89_list_Oinject) ).
thf(636,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)],[103]) ).
thf(209,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_71_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)],[209]) ).
thf(77,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_in__set__conv__decomp__first) ).
thf(563,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(187,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(1000,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(5,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(267,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType] :
( ( dom @ TA @ TB )
= ( ^ [A: TA > ( option @ TB )] :
( collect @ TA
@ ^ [B: TA] :
( ( A @ B )
!= ( none @ TB ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_dom__def) ).
thf(685,plain,
! [TA: $tType,TB: $tType] :
( ( dom @ TA @ TB )
= ( ^ [A: TA > ( option @ TB )] :
( collect @ TA
@ ^ [B: TA] :
( ( A @ B )
!= ( none @ TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(247,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(1171,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(120,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(722,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)],[120]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_distinct_Osimps_I2_J) ).
thf(426,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(87,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp @ TA @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_ord_Olexordp__simps_I3_J) ).
thf(589,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp @ TA @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(112,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
~ ( lexordp @ TA @ A @ B @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_ord_Olexordp__simps_I2_J) ).
thf(663,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
~ ( lexordp @ TA @ A @ B @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_bind__simps_I1_J) ).
thf(374,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(130,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_86_ord_Olexordp__eq_ONil) ).
thf(749,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)],[130]) ).
thf(237,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(1145,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(25,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( listrel1 @ TA @ E ) )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_snoc__listrel1__snoc__iff) ).
thf(355,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( listrel1 @ TA @ E ) )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(132,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_split__list__last) ).
thf(754,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(179,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_236_local_Orbt__lookup__Empty) ).
thf(968,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)],[179]) ).
thf(203,axiom,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ ( append @ a @ A @ B ) @ ( append @ a @ A @ C ) )
=> ( ! [D: a] :
~ ( less @ D @ D )
=> ( lexordp @ a @ less @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_local_Olexordp__append__leftD) ).
thf(1049,plain,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ ( append @ a @ A @ B ) @ ( append @ a @ A @ C ) )
=> ( ! [D: a] :
~ ( less @ D @ D )
=> ( lexordp @ a @ less @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(50,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_append__is__Nil__conv) ).
thf(473,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(213,axiom,
rBT_Im2075124343t_less @ a @ b @ less @ k @ l,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_assms_I3_J) ).
thf(1076,plain,
rBT_Im2075124343t_less @ a @ b @ less @ k @ l,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(235,axiom,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_color_Oexhaust) ).
thf(1134,plain,
! [A: rBT_Im1923302023_color] :
( ( A != rBT_Impl_Mirabelle_R )
=> ( A = rBT_Impl_Mirabelle_B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(107,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_104_list_OdiscI) ).
thf(648,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)],[107]) ).
thf(52,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_split__list__propE) ).
thf(487,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(75,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_append__eq__Cons__conv) ).
thf(557,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(119,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_111_ord_Olexordp__eq_Ocases) ).
thf(690,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)],[119]) ).
thf(13,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_split__list__first__propE) ).
thf(295,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(165,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(872,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( less @ A @ B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(180,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_32_local_Orbt__sorted_Osimps_I2_J) ).
thf(971,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)],[180]) ).
thf(19,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
& ( D = E ) )
| ( ( A = B )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( listrel1 @ TA @ C ) ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_append__listrel1I) ).
thf(327,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
& ( D = E ) )
| ( ( A = B )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( listrel1 @ TA @ C ) ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ( rBT_Im380146495e_keys @ TA @ TB @ A )
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_non__empty__rbt__keys) ).
thf(409,plain,
! [TA: $tType,TB: $tType,A: rBT_Im246033960le_rbt @ TA @ TB] :
( ( A
!= ( rBT_Im418718756_Empty @ TA @ TB ) )
=> ( ( rBT_Im380146495e_keys @ TA @ TB @ A )
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(222,axiom,
rBT_Im759614907sorted @ a @ b @ less @ l,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_assms_I1_J) ).
thf(1098,plain,
rBT_Im759614907sorted @ a @ b @ less @ l,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(57,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_1) ).
thf(502,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(158,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_74_rbt_Oinduct) ).
thf(840,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)],[158]) ).
thf(149,axiom,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
= ( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
& ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
& ( ( rBT_Im1805589839lor_of @ a @ TA @ A )
= rBT_Impl_Mirabelle_B )
& ( rBT_Im759614907sorted @ a @ TA @ less @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_local_Ois__rbt__def) ).
thf(808,plain,
! [TA: $tType,A: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im862805236is_rbt @ a @ TA @ less @ A )
= ( ( rBT_Im1040612427e_inv1 @ a @ TA @ A )
& ( rBT_Im1040612428e_inv2 @ a @ TA @ A )
& ( ( rBT_Im1805589839lor_of @ a @ TA @ A )
= rBT_Impl_Mirabelle_B )
& ( rBT_Im759614907sorted @ a @ TA @ less @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(256,axiom,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55__C5__4_Oprems_C_I1_J) ).
thf(1220,plain,
rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Cons__eq__appendI) ).
thf(585,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_split__list__first) ).
thf(370,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(193,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_237_local_Orbt__lookup__rbt__less) ).
thf(1023,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)],[193]) ).
thf(95,axiom,
! [TA: $tType,A: TA > $o,B: list @ TA,C: list @ TA,D: TA,E: list @ TA] :
( ( ( extract @ TA @ A @ B )
= ( some @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) @ ( product_Pair @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) @ C @ ( product_Pair @ TA @ ( list @ TA ) @ D @ E ) ) ) )
= ( ( B
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( A @ D )
& ~ ? [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ C ) )
& ( A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_extract__Some__iff) ).
thf(613,plain,
! [TA: $tType,A: TA > $o,B: list @ TA,C: list @ TA,D: TA,E: list @ TA] :
( ( ( extract @ TA @ A @ B )
= ( some @ ( product_prod @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) ) @ ( product_Pair @ ( list @ TA ) @ ( product_prod @ TA @ ( list @ TA ) ) @ C @ ( product_Pair @ TA @ ( list @ TA ) @ D @ E ) ) ) )
= ( ( B
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( A @ D )
& ~ ? [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ C ) )
& ( A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(257,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > a] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( less @ ( B @ D ) @ ( B @ C ) ) )
=> ( transitive_acyclic @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_local_OacyclicI__order) ).
thf(1221,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > a] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( less @ ( B @ D ) @ ( B @ C ) ) )
=> ( transitive_acyclic @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(204,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_local_Oless__irrefl) ).
thf(1052,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(36,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_split__list__last__prop) ).
thf(386,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(89,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_set__ConsD) ).
thf(595,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(55,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_77_ord_Orbt__less__simps_I1_J) ).
thf(497,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)],[55]) ).
thf(167,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_242_ord_Orbt__lookup__rbt__greater) ).
thf(876,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)],[167]) ).
thf(100,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_split__list__first__prop__iff) ).
thf(627,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(233,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(1126,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(190,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: TB,D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TB @ TA,F: TA,G: rBT_Im246033960le_rbt @ TB @ TA] :
( ( ( A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ E @ B ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ G @ B ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( some @ TA @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_ord_Orbt__lookup_Osimps_I2_J) ).
thf(1010,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB,C: TB,D: rBT_Im1923302023_color,E: rBT_Im246033960le_rbt @ TB @ TA,F: TA,G: rBT_Im246033960le_rbt @ TB @ TA] :
( ( ( A @ B @ C )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ E @ B ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( rBT_Im35466040lookup @ TB @ TA @ A @ G @ B ) ) )
& ( ~ ( A @ C @ B )
=> ( ( rBT_Im35466040lookup @ TB @ TA @ A @ ( rBT_Im480247531Branch @ TB @ TA @ D @ E @ C @ F @ G ) @ B )
= ( some @ TA @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(182,axiom,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ A ) @ ( append @ a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_local_Olexordp__append__leftI) ).
thf(976,plain,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ A ) @ ( append @ a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(118,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ! [C: TA] :
~ ( A @ C @ C )
=> ~ ( lexordp @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ord_Olexordp__irreflexive) ).
thf(688,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ! [C: TA] :
~ ( A @ C @ C )
=> ~ ( lexordp @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(62,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_self__append__conv) ).
thf(517,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(224,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_63_local_Ostrict__monoI) ).
thf(1101,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)],[224]) ).
thf(108,axiom,
! [TA: $tType] :
( ( set_greaterThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA] : ( collect @ TA @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ord_OgreaterThan__def) ).
thf(652,plain,
! [TA: $tType] :
( ( set_greaterThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA] : ( collect @ TA @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(123,axiom,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_distinct__singleton) ).
thf(731,plain,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(144,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_local_Oless__asym) ).
thf(786,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(79,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_ord_Olexordp_OCons) ).
thf(568,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(214,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ( lexordp_eq @ a @ less @ A @ B )
& ~ ( lexordp_eq @ a @ less @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_local_Olexordp__conv__lexordp__eq) ).
thf(1077,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ( lexordp_eq @ a @ less @ A @ B )
& ~ ( lexordp_eq @ a @ less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(135,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_62_local_Ostrict__mono__def) ).
thf(763,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)],[135]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_in__set__conv__decomp) ).
thf(549,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(67,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_79_ord_OEmpty__is__rbt) ).
thf(536,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)],[67]) ).
thf(201,axiom,
! [A: list @ a] :
( ! [B: a] :
~ ( less @ B @ B )
=> ~ ( lexordp @ a @ less @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_local_Olexordp__irreflexive) ).
thf(1045,plain,
! [A: list @ a] :
( ! [B: a] :
~ ( less @ B @ B )
=> ~ ( lexordp @ a @ less @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(146,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_73_rbt_Odistinct_I1_J) ).
thf(800,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)],[146]) ).
thf(14,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_96_remdups__adj_Oinduct) ).
thf(300,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)],[14]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_split__list) ).
thf(315,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_append__self__conv) ).
thf(273,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(125,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_91_ord_Olexordp__eq__simps_I3_J) ).
thf(735,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)],[125]) ).
thf(172,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_235_local_Orbt__lookup_Osimps_I1_J) ).
thf(950,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)],[172]) ).
thf(3,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_append__self__conv2) ).
thf(262,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Nil__is__append__conv) ).
thf(358,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(197,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_122_local_Olexordp__linear) ).
thf(1033,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)],[197]) ).
thf(176,axiom,
! [TA: $tType] : ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_local_Orbt__sorted_Osimps_I1_J) ).
thf(960,plain,
! [TA: $tType] : ( rBT_Im759614907sorted @ a @ TA @ less @ ( rBT_Im418718756_Empty @ a @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(245,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_92_local_Olexordp__eq__simps_I4_J) ).
thf(1165,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)],[245]) ).
thf(9,axiom,
! [TA: $tType] :
( ( lexordp @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: TA,E: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ 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 ) )
| ? [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 @ TA @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_ord_Olexordp_Osimps) ).
thf(283,plain,
! [TA: $tType] :
( ( lexordp @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: TA,E: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ 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 ) )
| ? [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 @ TA @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( listrel1 @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_not__listrel1__Nil) ).
thf(575,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( listrel1 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(161,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_42_ord_Orbt__sorted_Osimps_I2_J) ).
thf(860,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)],[161]) ).
thf(153,axiom,
! [TA: $tType,A: a,B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ D @ A ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ F @ A ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( some @ TA @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_local_Orbt__lookup_Osimps_I2_J) ).
thf(822,plain,
! [TA: $tType,A: a,B: a,C: rBT_Im1923302023_color,D: rBT_Im246033960le_rbt @ a @ TA,E: TA,F: rBT_Im246033960le_rbt @ a @ TA] :
( ( ( less @ A @ B )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ D @ A ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( rBT_Im35466040lookup @ a @ TA @ less @ F @ A ) ) )
& ( ~ ( less @ B @ A )
=> ( ( rBT_Im35466040lookup @ a @ TA @ less @ ( rBT_Im480247531Branch @ a @ TA @ C @ D @ B @ E @ F ) @ A )
= ( some @ TA @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(231,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
= ( ( A = B )
| ( lexordp @ a @ less @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_local_Olexordp__eq__conv__lexord) ).
thf(1120,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
= ( ( A = B )
| ( lexordp @ a @ less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(220,axiom,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
= ( ! [C: a] :
( ( member @ a @ C @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ TA @ B ) ) )
=> ( less @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_local_Orbt__greater__prop) ).
thf(1093,plain,
! [TA: $tType,A: a,B: rBT_Im246033960le_rbt @ a @ TA] :
( ( rBT_Im1259024060reater @ a @ TA @ less @ A @ B )
= ( ! [C: a] :
( ( member @ a @ C @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ TA @ B ) ) )
=> ( less @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_append__assoc) ).
thf(624,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(122,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_append__Cons) ).
thf(728,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(127,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_the__elem__set) ).
thf(740,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(184,axiom,
! [A: a] :
( ( set_greaterThan @ a @ less @ A )
= ( collect @ a @ ( less @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_local_OgreaterThan__def) ).
thf(982,plain,
! [A: a] :
( ( set_greaterThan @ a @ less @ A )
= ( collect @ a @ ( less @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(188,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_234_local_Omap__of__entries) ).
thf(1004,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)],[188]) ).
thf(147,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_75_rbt_Oexhaust) ).
thf(803,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)],[147]) ).
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(543,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(76,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_bind__simps_I2_J) ).
thf(560,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(104,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_239_ord_Orbt__lookup__Empty) ).
thf(639,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)],[104]) ).
thf(53,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_220_entries_Osimps_I1_J) ).
thf(491,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)],[53]) ).
thf(88,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_110_ord_Olexordp__eq_Osimps) ).
thf(592,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)],[88]) ).
thf(28,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_2) ).
thf(364,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(169,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_83_local_Olexordp__eq_Ocases) ).
thf(882,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)],[169]) ).
thf(1357,plain,
$false,
inference(e,[status(thm)],[645,1036,365,347,352,1168,760,1083,962,777,555,1211,276,1068,1073,1205,677,1173,523,582,655,511,384,1137,533,1063,538,829,1196,782,288,436,1228,1055,570,504,619,751,853,1087,1147,421,606,834,514,1020,806,1040,1109,321,766,956,866,774,396,660,507,1104,265,292,439,270,546,1199,1153,1163,334,746,820,630,429,788,260,1123,1217,598,566,1032,361,879,665,1159,682,324,974,948,1017,725,403,1096,869,499,857,471,1160,476,642,526,1214,1155,837,997,1150,1131,1060,779,393,1114,1099,985,1202,1086,633,657,1071,674,1026,953,412,965,573,733,601,1007,772,286,743,579,875,577,391,382,1090,1224,350,540,1058,1107,406,831,1048,377,1043,616,863,979,604,784,1117,737,318,811,758,816,609,621,520,1029,915,769,1112,494,1080,345,367,552,959,636,1066,563,1000,267,685,1171,722,426,589,663,374,749,1145,355,754,968,1049,473,1076,1134,648,487,557,690,295,872,971,327,409,1098,502,840,808,1220,585,370,1023,613,1221,1052,386,595,497,876,627,1126,1010,976,688,517,1101,652,731,786,568,1077,763,549,536,1045,800,300,315,273,735,950,262,358,1033,960,1165,283,575,860,822,1120,1093,624,728,740,982,1004,803,543,560,639,491,592,364,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : DAT232^1 : TPTP v8.2.0. Released v7.0.0.
% 0.09/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n004.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sun May 19 23:12:54 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.96/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/1.14 % [INFO] Parsing done (242ms).
% 1.75/1.15 % [INFO] Running in sequential loop mode.
% 2.71/1.40 % [INFO] eprover registered as external prover.
% 2.71/1.40 % [INFO] cvc4 registered as external prover.
% 2.71/1.40 % [INFO] Scanning for conjecture ...
% 3.00/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 258 axioms. Running axiom selection ...
% 3.44/1.64 % [INFO] Axiom selection finished. Selected 257 axioms (removed 1 axioms).
% 4.25/1.90 % [INFO] Problem is higher-order (TPTP THF).
% 4.25/1.92 % [INFO] Type checking passed.
% 4.65/1.92 % [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 ...
% 17.19/6.30 % [INFO] [Domain constraints] Detected constraint on rBT_Im1923302023_color
% 17.19/6.30 % [INFO] [Domain constraints] dom(rBT_Im1923302023_color) ⊆ {rBT_Impl_Mirabelle_R,rBT_Impl_Mirabelle_B}
% 37.05/13.12 % External prover 'e' found a proof!
% 37.05/13.12 % [INFO] Killing All external provers ...
% 37.05/13.12 % Time passed: 12573ms (effective reasoning time: 11968ms)
% 37.05/13.12 % 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)>
% 37.05/13.12 % Axioms used in derivation (257): fact_66_local_Orbt__sorted_Osimps_I1_J, fact_25_assms_I2_J, fact_235_local_Orbt__lookup_Osimps_I1_J, fact_1_local_Odual__order_Oasym, fact_99_splice_Oinduct, fact_113_local_Olexordp_ONil, fact_34_local_Ostrict__mono__eq, fact_226_entry__in__tree__keys, fact_43_ord_Orbt__less__simps_I2_J, fact_14_local_Oless__trans, fact_132_local_Olexordp__simps_I3_J, fact_114_local_Olexordp_Ocases, fact_243_order__class_OacyclicI__order, fact_240_ord_Orbt__lookup_Osimps_I1_J, fact_115_local_Olexordp_Oinducts, fact_59_local_OlessThan__def, fact_144_local_Olexordp__iff, fact_253_append__listrel1I, fact_209_distinct_Osimps_I2_J, fact_164_eq__Nil__appendI, fact_37__C1_C, fact_81_ord_Olexordp__eq__simps_I1_J, fact_213_not__distinct__decomp, fact_90_ord_Olexordp__eq__simps_I4_J, fact_8_local_Oless__imp__not__eq2, fact_227_keys__entries, fact_109_ord_Olexordp__eq_Oinducts, fact_210_distinct_Osimps_I1_J, fact_246_extract__SomeE, fact_49_color_Oinduct, fact_242_ord_Orbt__lookup__rbt__greater, fact_172_rev__induct, fact_159_append1__eq__conv, fact_135_ord_Olexordp__irreflexive, fact_220_entries_Osimps_I1_J, fact_202_list_Oset__intros_I2_J, fact_189_split__list__first__propE, fact_128_local_Olexordp__into__lexordp__eq, fact_238_local_Orbt__lookup__rbt__greater, fact_54_local_Olexordp__eq__linear, fact_98_transpose_Ocases, fact_149_same__append__eq, fact_82_ord_Olexordp__eq__simps_I2_J, fact_215_ord_OlessThan__iff, fact_18_local_Onot__less__iff__gr__or__eq, fact_252_listrel1I2, fact_89_list_Oinject, fact_196_split__list__prop, fact_104_list_OdiscI, fact_87_local_Olexordp__eq_OCons, fact_244_dom__def, fact_158_append__is__Nil__conv, fact_77_ord_Orbt__less__simps_I1_J, fact_175_keys__simps_I2_J, fact_19_local_Oord__eq__less__trans, fact_207_ord_OgreaterThan__def, fact_139_ord_Olexordp_ONil, fact_17_local_Oneq__iff, fact_179_keys__simps_I1_J, fact_184_list__bind__cong, fact_2_local_Odual__order_Ostrict__implies__not__eq, fact_166_append__eq__append__conv2, fact_247_extract__Nil__code, fact_102_list_Oinducts, fact_212_distinct__singleton, fact_234_local_Omap__of__entries, fact_236_local_Orbt__lookup__Empty, fact_67_local_OlessThan__iff, fact_165_append__Nil, fact_174_ord_Olexordp__append__rightI, fact_22_local_Oorder_Oirrefl, fact_217_ord_OlessThan__def, fact_13_local_Oless__not__sym, fact_161_ord_Olexordp__append__leftI, fact_58_local_OgreaterThan__def, fact_101_neq__Nil__conv, fact_92_local_Olexordp__eq__simps_I4_J, fact_110_ord_Olexordp__eq_Osimps, fact_156_self__append__conv2, fact_12_local_Oless__linear, fact_254_not__listrel1__Nil, fact_193_in__set__conv__decomp, fact_145_local_Olexordp__append__left__rightI, fact_136_ord_Olexordp_OCons__eq, fact_95_list__nonempty__induct, fact_222_local_Oentries__eqI, fact_154_self__append__conv, fact_186_split__list__last__prop__iff, fact_79_ord_OEmpty__is__rbt, fact_46_Collect__mem__eq, fact_199_list_Oset__cases, fact_214_not__distinct__conv__prefix, fact_148_local_Olexordp__append__leftD, fact_93_local_Olexordp__eq__simps_I3_J, fact_178_bind__simps_I1_J, fact_142_ord_Olexordp_Oinducts, fact_78_ord_Orbt__greater__simps_I1_J, fact_83_local_Olexordp__eq_Ocases, fact_233_ord_Orbt__lookup_Osimps_I2_J, fact_231_splice_Ocases, fact_185_split__list__first__prop__iff, fact_181_local_Orbt__greater__prop, fact_251_Cons__listrel1__Cons, fact_40__C5__4_Oprems_C_I4_J, fact_68_local_OgreaterThan__iff, fact_133_local_Olexordp__simps_I2_J, fact_73_rbt_Odistinct_I1_J, fact_137_ord_Olexordp_OCons, fact_9_local_Oless__imp__not__less, fact_173_ord_Olexordp__append__left__rightI, fact_127_local_Olexordp__eq__conv__lexord, fact_153_append__self__conv, fact_151_append__assoc, fact_249_snoc__listrel1__snoc__iff, fact_169_append__eq__Cons__conv, fact_5_local_Oless__asym_H, fact_150_append__same__eq, fact_64_local_Ostrict__monoD, fact_126_local_Olexordp__conv__lexordp__eq, fact_118_local_Olexordp__induct, fact_167_append__eq__appendI, fact_232_map__tailrec__rev_Ocases, fact_219_distinct__union, fact_200_set__ConsD, fact_168_rev__nonempty__induct, fact_141_ord_Olexordp_Osimps, fact_121_local_Olexordp__irreflexive_H, fact_138_ord_Olexordp__into__lexordp__eq, fact_223_local_Orbt__lookup__from__in__tree, tcon_HOL_Obool___Orderings_Oorder_2, fact_76_ord_Orbt__sorted_Osimps_I1_J, fact_4_local_Oless__asym, fact_105_list_Odistinct_I1_J, fact_147_local_Olexordp__append__leftI, fact_218_local_Oset__entries__inject, fact_45_mem__Collect__eq, fact_31_assms_I4_J, fact_7_local_Oless__imp__not__eq, fact_194_split__list__propE, tcon_Set_Oset___Orderings_Oorder_1, fact_100_list__induct2_H, fact_239_ord_Orbt__lookup__Empty, fact_94_map__tailrec__rev_Oinduct, fact_28_local_Orbt__greater__trans, fact_116_local_Olexordp_Osimps, fact_70_local_Olexordp__eq__simps_I1_J, fact_245_extract__Some__iff, fact_122_local_Olexordp__linear, fact_55__C5__4_Oprems_C_I1_J, fact_88_local_Olexordp__eq_OCons__eq, fact_50_color_Oexhaust, fact_241_ord_Orbt__lookup__rbt__less, fact_177_bind__simps_I2_J, fact_107_ord_Olexordp__eq_OCons__eq, fact_140_ord_Olexordp_Ocases, fact_112_ord_Olexordp__eq__refl, fact_33_local_Orbt__greater__simps_I2_J, fact_6_local_Oless__imp__neq, fact_146_sublists_Osimps_I1_J, fact_225_entries_Osimps_I2_J, fact_11_local_Oless__irrefl, fact_47_Collect__cong, fact_160_ord_Olexordp__append__leftD, fact_188_in__set__conv__decomp__last, fact_56__C5__4_Oprems_C_I3_J, fact_224_local_Orbt__lookup__keys, fact_53_local_Olexordp__eq__refl, fact_74_rbt_Oinduct, fact_190_split__list__last__propE, fact_237_local_Orbt__lookup__rbt__less, fact_201_list_Oset__intros_I1_J, fact_131_ord_Olexordp__simps_I2_J, fact_170_Cons__eq__append__conv, fact_15_local_Olinorder__cases, fact_229_local_Orbt__lookup__in__tree, fact_86_ord_Olexordp__eq_ONil, fact_52_local_Olexordp__eq__trans, fact_171_rev__exhaust, fact_3_local_Odual__order_Ostrict__trans, fact_51_local_Olexordp__eq__antisym, fact_26_assms_I1_J, fact_198_split__list, fact_208_distinct__product__lists, fact_125_local_Olexordp_OCons__eq, fact_60_local_OEmpty__is__rbt, fact_163_Cons__eq__appendI, fact_130_ord_Olexordp__simps_I1_J, fact_75_rbt_Oexhaust, fact_21_local_Oorder_Oasym, fact_192_split__list__last__prop, fact_230_local_Orbt__lookup_Osimps_I2_J, fact_157_Nil__is__append__conv, fact_106_not__Cons__self2, fact_20_local_Oord__less__eq__trans, fact_123_local_Olexordp__trans, fact_63_local_Ostrict__monoI, fact_85_local_Olexordp__eq_Osimps, fact_62_local_Ostrict__mono__def, fact_0_local_Oantisym__conv3, fact_221_local_Oentries__rbt__lookup, fact_176_product__lists_Osimps_I1_J, fact_182_local_Orbt__less__prop, tcon_fun___Orderings_Oorder, fact_250_local_Ois__rbt__def, fact_206_the__elem__set, fact_32_local_Orbt__sorted_Osimps_I2_J, fact_91_ord_Olexordp__eq__simps_I3_J, fact_16_local_OneqE, fact_134_local_Olexordp__simps_I1_J, fact_111_ord_Olexordp__eq_Ocases, fact_191_split__list__first__prop, fact_228_local_OacyclicI__order, fact_155_append__self__conv2, fact_216_ord_OgreaterThan__iff, fact_162_append__Cons, fact_97_remdups__adj_Ocases, fact_36_local_Orbt__less__simps_I2_J, fact_24_local_Oorder_Ostrict__trans, fact_117_local_Olexordp__cases, fact_152_append__Nil2, fact_10_local_Oless__imp__triv, fact_119_local_Olexordp__antisym, fact_205_local_Odistinct__keys, fact_41__C5__4_Oprems_C_I2_J, fact_65_local_Olexordp__eq_ONil, fact_108_ord_Olexordp__eq_OCons, fact_197_split__list__last, fact_124_local_Olexordp_OCons, fact_38__092_060open_062x_A_060_Ay_A_092_060and_062_ABranch_AB_Ava_Avb_Avg_Avc_A_124_092_060guillemotleft_062_Ax_092_060close_062, fact_103_list_Oexhaust, fact_248_extract__None__iff, fact_183_local_Ostrict__mono__imp__inj__on, fact_204_ord_Orbt__greater__prop, fact_61_local_Ostrict__mono__less, fact_203_ord_Orbt__less__prop, fact_96_remdups__adj_Oinduct, fact_29_rbt_Oinject, fact_23_local_Oorder_Ostrict__implies__not__eq, fact_44_color_Odistinct_I1_J, fact_42_ord_Orbt__sorted_Osimps_I2_J, fact_80_rbt__cases, fact_143_local_Olexordp__append__rightI, fact_69_local_Olexordp__eq__simps_I2_J, fact_180_non__empty__rbt__keys, fact_35_ord_Orbt__greater__simps_I2_J, fact_27_local_Orbt__less__trans, fact_211_distinct__length__2__or__more, fact_57_ord_Ois__rbt__rbt__sorted, fact_39_local_Ois__rbt__rbt__sorted, fact_187_in__set__conv__decomp__first, fact_71_local_Orbt__less__simps_I1_J, fact_195_split__list__first, fact_30_assms_I3_J, fact_120_local_Olexordp__irreflexive, fact_129_ord_Olexordp__simps_I3_J, fact_84_local_Olexordp__eq_Oinducts, fact_72_local_Orbt__greater__simps_I1_J
% 37.05/13.12 % No. of inferences in proof: 518
% 37.05/13.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12573 ms resp. 11968 ms w/o parsing
% 38.12/13.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.12/13.34 % [INFO] Killing All external provers ...
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