TSTP Solution File: DAT214^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT214^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:46 EDT 2024
% Result : Theorem 19.62s 5.79s
% Output : Refutation 20.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 410
% Syntax : Number of formulae : 747 ( 287 unt; 75 typ; 0 def)
% Number of atoms : 1698 ( 633 equ; 0 cnn)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 7755 ( 178 ~; 7 |; 48 &;6802 @)
% ( 0 <=>; 720 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 76 usr; 15 con; 0-5 aty)
% Number of variables : 1632 ( 30 ^1507 !; 34 ?;1632 :)
% ( 61 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(code_natural_type,type,
code_natural: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(type_type,type,
type:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(size_type,type,
size:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(one_type,type,
one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_type,type,
zero:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ln_type,type,
ln:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_less_one_type,type,
zero_less_one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_add_type,type,
semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere216010020id_add_type,type,
ordere216010020id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(strict797366125id_add_type,type,
strict797366125id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(strict2144017051up_add_type,type,
strict2144017051up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere516151231imp_le_type,type,
ordere516151231imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(code_case_natural_type,type,
code_case_natural:
!>[TA: $tType] : ( TA > ( code_natural > TA ) > code_natural > TA ) ).
thf(code_rec_natural_type,type,
code_rec_natural:
!>[TA: $tType] : ( TA > ( code_natural > TA > TA ) > code_natural > TA ) ).
thf(code_size_natural_type,type,
code_size_natural: code_natural > nat ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(size_bool_type,type,
size_bool: $o > nat ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(neg_numeral_dbl_dec_type,type,
neg_numeral_dbl_dec:
!>[TA: $tType] : ( TA > TA ) ).
thf(neg_numeral_dbl_inc_type,type,
neg_numeral_dbl_inc:
!>[TA: $tType] : ( TA > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_rec_bool_type,type,
product_rec_bool:
!>[TA: $tType] : ( TA > TA > $o > TA ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(set_fo292404081st_nat_type,type,
set_fo292404081st_nat:
!>[TA: $tType] : ( ( nat > TA > TA ) > nat > nat > TA > TA ) ).
thf(splay_splay_type,type,
splay_splay:
!>[TA: $tType] : ( TA > ( tree @ TA ) > ( tree @ TA ) ) ).
thf(splay_splay_max_type,type,
splay_splay_max:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(splay_914434265_splay_type,type,
splay_914434265_splay:
!>[TA: $tType] : ( TA > ( tree @ TA ) > nat ) ).
thf(splay_878424299ay_max_type,type,
splay_878424299ay_max:
!>[TA: $tType] : ( ( tree @ TA ) > nat ) ).
thf(splay_1816415694ax_rel_type,type,
splay_1816415694ax_rel:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) > $o ) ).
thf(splay_266122055elle_A_type,type,
splay_266122055elle_A:
!>[TA: $tType] : ( TA > ( tree @ TA ) > real ) ).
thf(ln_ln_type,type,
ln_ln:
!>[TA: $tType] : ( TA > TA ) ).
thf(powr_type,type,
powr:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(linorder_bst_type,type,
linorder_bst:
!>[TA: $tType] : ( ( tree @ TA ) > $o ) ).
thf(path_len_type,type,
path_len:
!>[TA: $tType] : ( ( tree @ TA ) > nat ) ).
thf(path_len_rel_type,type,
path_len_rel:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) > $o ) ).
thf(size1_type,type,
size1:
!>[TA: $tType] : ( ( tree @ TA ) > nat ) ).
thf(leaf_type,type,
leaf:
!>[TA: $tType] : ( tree @ TA ) ).
thf(node_type,type,
node:
!>[TA: $tType] : ( ( tree @ TA ) > TA > ( tree @ TA ) > ( tree @ TA ) ) ).
thf(size_tree_type,type,
size_tree:
!>[TA: $tType] : ( ( TA > nat ) > ( tree @ TA ) > nat ) ).
thf(accp_type,type,
accp:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > $o ) ).
thf(b_type,type,
b: a ).
thf(c_type,type,
c: a ).
thf(l_type,type,
l: tree @ a ).
thf(l2_type,type,
l2: tree @ a ).
thf(r_type,type,
r: tree @ a ).
thf(rl_type,type,
rl: tree @ a ).
thf(rr_type,type,
rr: tree @ a ).
thf(u_type,type,
u: a ).
thf(203,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__cancel__right__left) ).
thf(892,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(174,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_add__right__imp__eq) ).
thf(809,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(292,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ C @ A @ ( leaf @ TA ) ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_t__splay__simps_I6_J) ).
thf(1179,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ C @ A @ ( leaf @ TA ) ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(325,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_add__less__imp__less__left) ).
thf(1295,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(10,axiom,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_tree_Oinduct) ).
thf(352,plain,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: code_natural > TA > TA] :
( ( code_rec_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_natural_Osimps_I6_J) ).
thf(365,plain,
! [TA: $tType,A: TA,B: code_natural > TA > TA] :
( ( code_rec_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(296,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
& ( ( plus_plus @ nat @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_less__imp__add__positive) ).
thf(1190,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
& ( ( plus_plus @ nat @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(225,axiom,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( powr @ real @ A @ B ) @ ( powr @ real @ A @ C ) )
=> ( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ord_less @ real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_powr__less__cancel) ).
thf(977,plain,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( powr @ real @ A @ B ) @ ( powr @ real @ A @ C ) )
=> ( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ord_less @ real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(103,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ D @ C @ ( leaf @ TA ) ) @ B @ E ) )
= ( node @ TA @ D @ C @ ( node @ TA @ ( leaf @ TA ) @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_splay_Osimps_I7_J) ).
thf(582,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ D @ C @ ( leaf @ TA ) ) @ B @ E ) )
= ( node @ TA @ D @ C @ ( node @ TA @ ( leaf @ TA ) @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(235,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_measure__induct__rule) ).
thf(1005,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(148,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA] :
( ( ( splay_splay @ TA @ A @ B )
= ( node @ TA @ C @ D @ E ) )
=> ( ( size_size @ ( tree @ TA ) @ B )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ TA ) @ C ) @ ( size_size @ ( tree @ TA ) @ E ) ) @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_size__if__splay) ).
thf(730,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA] :
( ( ( splay_splay @ TA @ A @ B )
= ( node @ TA @ C @ D @ E ) )
=> ( ( size_size @ ( tree @ TA ) @ B )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ TA ) @ C ) @ ( size_size @ ( tree @ TA ) @ E ) ) @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(254,axiom,
comm_monoid_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(1068,plain,
comm_monoid_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(330,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_nat__add__left__cancel__less) ).
thf(1305,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(290,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_semiring__normalization__rules_I6_J) ).
thf(1173,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(302,axiom,
! [TA: $tType] :
( ( set_fo292404081st_nat @ TA )
= ( ^ [A: nat > TA > TA,B: nat,C: nat,D: TA] : ( if @ TA @ ( ord_less @ nat @ C @ B ) @ D @ ( set_fo292404081st_nat @ TA @ A @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) @ C @ ( A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_fold__atLeastAtMost__nat_Osimps) ).
thf(1205,plain,
! [TA: $tType] :
( ( set_fo292404081st_nat @ TA )
= ( ^ [A: nat > TA > TA,B: nat,C: nat,D: TA] : ( if @ TA @ ( ord_less @ nat @ C @ B ) @ D @ ( set_fo292404081st_nat @ TA @ A @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) @ C @ ( A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(50,axiom,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ E )
=> ( ( A @ C )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_mirror_Oinduct) ).
thf(449,plain,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ E )
=> ( ( A @ C )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(278,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_semiring__normalization__rules_I24_J) ).
thf(1142,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(18,axiom,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less_eq @ real @ ( ln_ln @ real @ A ) @ ( ln_ln @ real @ B ) )
= ( ord_less_eq @ real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_ln__le__cancel__iff) ).
thf(379,plain,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less_eq @ real @ ( ln_ln @ real @ A ) @ ( ln_ln @ real @ B ) )
= ( ord_less_eq @ real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(197,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_add__mono__thms__linordered__field_I5_J) ).
thf(878,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(511,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(114,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ D @ A @ ( node @ TA @ ( leaf @ TA ) @ C @ E ) ) )
= ( node @ TA @ ( node @ TA @ D @ A @ ( leaf @ TA ) ) @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_splay_Osimps_I12_J) ).
thf(614,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ D @ A @ ( node @ TA @ ( leaf @ TA ) @ C @ E ) ) )
= ( node @ TA @ ( node @ TA @ D @ A @ ( leaf @ TA ) ) @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
( ( size_size @ ( product_prod @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_prod_Osize__neq) ).
thf(677,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
( ( size_size @ ( product_prod @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(78,axiom,
semigroup_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Osemigroup__add_18) ).
thf(533,plain,
semigroup_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(212,axiom,
( ( size_bool @ $true )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_bool_Osize_I1_J) ).
thf(913,plain,
( ( size_bool @ $true )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(251,axiom,
semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).
thf(1063,plain,
semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(287,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_infinite__descent__measure) ).
thf(1164,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(170,axiom,
! [TA: $tType] : ( size @ ( tree @ TA ) @ ( type2 @ ( tree @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Tree_Otree___Nat_Osize_25) ).
thf(797,plain,
! [TA: $tType] : ( size @ ( tree @ TA ) @ ( type2 @ ( tree @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(205,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_double__zero) ).
thf(898,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(186,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_less__not__refl) ).
thf(841,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(246,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq @ real @ A @ B )
=> ( ( ord_less_eq @ real @ ( one_one @ real ) @ C )
=> ( ord_less_eq @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_powr__mono) ).
thf(1046,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq @ real @ A @ B )
=> ( ( ord_less_eq @ real @ ( one_one @ real ) @ C )
=> ( ord_less_eq @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(43,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_1) ).
thf(436,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(327,axiom,
linordered_semidom @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom) ).
thf(1298,plain,
linordered_semidom @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(14,axiom,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ ( ln_ln @ real @ A ) @ ( ln_ln @ real @ B ) )
= ( ord_less @ real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_ln__less__cancel__iff) ).
thf(372,plain,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ ( ln_ln @ real @ A ) @ ( ln_ln @ real @ B ) )
= ( ord_less @ real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(185,axiom,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA] :
( ( path_len @ TA @ ( node @ TA @ A @ B @ C ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ TA @ A ) @ ( size_size @ ( tree @ TA ) @ A ) ) @ ( path_len @ TA @ C ) ) @ ( size_size @ ( tree @ TA ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_path__len_Osimps_I2_J) ).
thf(838,plain,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA] :
( ( path_len @ TA @ ( node @ TA @ A @ B @ C ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ TA @ A ) @ ( size_size @ ( tree @ TA ) @ A ) ) @ ( path_len @ TA @ C ) ) @ ( size_size @ ( tree @ TA ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(153,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ord_less @ real @ ( one_one @ real ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_ln__gt__zero__imp__gt__one) ).
thf(751,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ord_less @ real @ ( one_one @ real ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(85,axiom,
ab_semigroup_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_37) ).
thf(542,plain,
ab_semigroup_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(91,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_not__gr__zero) ).
thf(559,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(190,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__less__same__cancel1) ).
thf(853,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(262,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_zero__le__double__add__iff__zero__le__single__add) ).
thf(1087,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(239,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_infinite__descent0) ).
thf(1013,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(272,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_add__mono__thms__linordered__field_I2_J) ).
thf(1115,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(310,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_add_Ogroup__left__neutral) ).
thf(1232,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(166,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__cancel__left__left) ).
thf(789,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(108,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_gr__zeroI) ).
thf(591,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(47,axiom,
ordere216010020id_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_11) ).
thf(443,plain,
ordere216010020id_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(15,axiom,
linorder @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Orderings_Olinorder_42) ).
thf(376,plain,
linorder @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(127,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ B )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ F @ C @ D ) ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ F @ C @ D ) ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ B @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_t__splay__simps_I9_J) ).
thf(646,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ B )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ F @ C @ D ) ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ F @ C @ D ) ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ B @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(276,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_neq0__conv) ).
thf(1136,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA] : ( A @ ( node @ TA @ C @ D @ ( leaf @ TA ) ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA,F: TA,G: tree @ TA] :
( ( ( G
!= ( leaf @ TA ) )
=> ( A @ G ) )
=> ( A @ ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_t__splay__max_Oinduct) ).
thf(514,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA] : ( A @ ( node @ TA @ C @ D @ ( leaf @ TA ) ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA,F: TA,G: tree @ TA] :
( ( ( G
!= ( leaf @ TA ) )
=> ( A @ G ) )
=> ( A @ ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(222,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_infinite__descent) ).
thf(966,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(322,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_add__less__mono1) ).
thf(1283,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(248,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_add_Ocommute) ).
thf(1051,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(55,axiom,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ B @ C )
=> ( ord_less @ real @ ( powr @ real @ B @ A ) @ ( powr @ real @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_powr__less__mono2) ).
thf(480,plain,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ B @ C )
=> ( ord_less @ real @ ( powr @ real @ B @ A ) @ ( powr @ real @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(329,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_linorder__neqE__nat) ).
thf(1302,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(156,axiom,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_one__reorient) ).
thf(756,plain,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(244,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__gr__0) ).
thf(1040,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(270,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( splay_878424299ay_max @ TA @ ( node @ TA @ A @ B @ ( leaf @ TA ) ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_t__splay__max_Osimps_I2_J) ).
thf(1109,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( splay_878424299ay_max @ TA @ ( node @ TA @ A @ B @ ( leaf @ TA ) ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(8,axiom,
one @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oone_24) ).
thf(348,plain,
one @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(98,axiom,
linorder @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_21) ).
thf(574,plain,
linorder @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(143,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type2 @ TA ) )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_zero__neq__one) ).
thf(687,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type2 @ TA ) )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(305,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__add__same__cancel2) ).
thf(1215,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(256,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ B @ A @ C ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_t__splay__simps_I1_J) ).
thf(1072,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ B @ A @ C ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(273,axiom,
zero_less_one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one) ).
thf(1119,plain,
zero_less_one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(132,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__right__cancel) ).
thf(660,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(229,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_add__strict__right__mono) ).
thf(988,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(39,axiom,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39__092_060Phi_062_Ocases) ).
thf(428,plain,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(70,axiom,
ordere236663937imp_le @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add__imp__le_31) ).
thf(507,plain,
ordere236663937imp_le @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(45,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( splay_splay_max @ TA @ ( node @ TA @ A @ B @ ( leaf @ TA ) ) )
= ( node @ TA @ A @ B @ ( leaf @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_splay__max_Osimps_I2_J) ).
thf(439,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( splay_splay_max @ TA @ ( node @ TA @ A @ B @ ( leaf @ TA ) ) )
= ( node @ TA @ A @ B @ ( leaf @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(76,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( splay_splay @ TA @ A @ ( node @ TA @ B @ A @ C ) )
= ( node @ TA @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_splay_Osimps_I2_J) ).
thf(529,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( splay_splay @ TA @ A @ ( node @ TA @ B @ A @ C ) )
= ( node @ TA @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(87,axiom,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA] :
( ( leaf @ TA )
!= ( node @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_tree_Odistinct_I1_J) ).
thf(546,plain,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA] :
( ( leaf @ TA )
!= ( node @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(216,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add_Oassoc) ).
thf(925,plain,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(299,axiom,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add_Oright__neutral) ).
thf(1199,plain,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(283,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_semiring__normalization__rules_I21_J) ).
thf(1153,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_add__less__mono) ).
thf(761,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(332,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_measure__induct) ).
thf(1311,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(79,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(534,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(210,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_add__strict__mono) ).
thf(910,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(152,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_nat__less__induct) ).
thf(746,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(179,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_le__add__same__cancel2) ).
thf(825,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(163,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_nat__add__right__cancel) ).
thf(778,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(312,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_add__le__cancel__left) ).
thf(1238,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(193,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_trans__less__add1) ).
thf(862,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(9,axiom,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( powr @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_powr__eq__0__iff) ).
thf(349,plain,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( powr @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( A
!= ( leaf @ TA ) )
=> ? [C: tree @ TA,D: TA,E: tree @ TA] :
( ( splay_splay @ TA @ B @ A )
= ( node @ TA @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_splay__not__Leaf) ).
thf(407,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( A
!= ( leaf @ TA ) )
=> ? [C: tree @ TA,D: TA,E: tree @ TA] :
( ( splay_splay @ TA @ B @ A )
= ( node @ TA @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(145,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( splay_266122055elle_A @ TA @ A @ ( node @ TA @ B @ A @ C ) )
= ( one_one @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_A__simps_I1_J) ).
thf(693,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA,C: tree @ TA] :
( ( splay_266122055elle_A @ TA @ A @ ( node @ TA @ B @ A @ C ) )
= ( one_one @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(121,axiom,
! [A: real] :
( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_ln__gt__zero) ).
thf(630,plain,
! [A: real] :
( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(241,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ( ln_ln @ real @ A )
= ( zero_zero @ real ) )
= ( A
= ( one_one @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_ln__eq__zero__iff) ).
thf(1032,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ( ln_ln @ real @ A )
= ( zero_zero @ real ) )
= ( A
= ( one_one @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(119,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( linorder_bst @ TA @ ( leaf @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_bst_Osimps_I1_J) ).
thf(625,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( linorder_bst @ TA @ ( leaf @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(42,axiom,
size @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Nat_Osize_2) ).
thf(435,plain,
size @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_add__eq__self__zero) ).
thf(830,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(285,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_linordered__field__class_Osign__simps_I27_J) ).
thf(1159,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(61,axiom,
comm_monoid_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocomm__monoid__add_16) ).
thf(493,plain,
comm_monoid_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(259,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_add_Oleft__cancel) ).
thf(1079,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(321,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_add__less__le__mono) ).
thf(1281,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(224,axiom,
( rr
!= ( leaf @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062rr_A_092_060noteq_062_A_092_060langle_062_092_060rangle_062_092_060close_062) ).
thf(974,plain,
( rr
!= ( leaf @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(268,axiom,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_natural_Osize_I1_J) ).
thf(1106,plain,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_nat__neq__iff) ).
thf(847,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(95,axiom,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
= ( ? [B: tree @ TA,C: TA,D: tree @ TA] :
( A
= ( node @ TA @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_neq__Leaf__iff) ).
thf(566,plain,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
= ( ? [B: tree @ TA,C: TA,D: tree @ TA] :
( A
= ( node @ TA @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(252,axiom,
linorder @ a @ ( type2 @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(1064,plain,
linorder @ a @ ( type2 @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(308,axiom,
! [TA: $tType,A: tree @ TA] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size1 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_size1__ge0) ).
thf(1227,plain,
! [TA: $tType,A: tree @ TA] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(28,axiom,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_zero__reorient) ).
thf(403,plain,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(264,axiom,
! [TA: $tType,A: tree @ TA] :
( ( ( size_size @ ( tree @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( leaf @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_size__0__iff__Leaf) ).
thf(1096,plain,
! [TA: $tType,A: tree @ TA] :
( ( ( size_size @ ( tree @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( leaf @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(36,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_linordered__field__no__ub) ).
thf(420,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(260,axiom,
( ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) )
!= ( leaf @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30__C3_Oprems_C_I2_J) ).
thf(1082,plain,
( ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) )
!= ( leaf @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(3,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq @ real @ A @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_powr__mono2_H) ).
thf(339,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq @ real @ A @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(324,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_not__add__less1) ).
thf(1292,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(293,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( leaf @ TA ) @ B @ C ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_t__splay__simps_I2_J) ).
thf(1182,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( leaf @ TA ) @ B @ C ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(82,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( powr @ real @ B @ A ) @ ( powr @ real @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_powr__mono2) ).
thf(537,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( powr @ real @ B @ A ) @ ( powr @ real @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(136,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_less__zeroE) ).
thf(669,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ C @ A @ D ) @ B @ E ) )
= ( node @ TA @ C @ A @ ( node @ TA @ D @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_splay_Osimps_I3_J) ).
thf(526,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ C @ A @ D ) @ B @ E ) )
= ( node @ TA @ C @ A @ ( node @ TA @ D @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(124,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_linordered__field__class_Osign__simps_I28_J) ).
thf(637,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(59,axiom,
ordere223160158up_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__ab__semigroup__add_30) ).
thf(489,plain,
ordere223160158up_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(107,axiom,
strict797366125id_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__comm__monoid__add_32) ).
thf(590,plain,
strict797366125id_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(89,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ C @ A @ ( leaf @ TA ) ) )
= ( node @ TA @ C @ A @ ( leaf @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_splay_Osimps_I10_J) ).
thf(554,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ C @ A @ ( leaf @ TA ) ) )
= ( node @ TA @ C @ A @ ( leaf @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(154,axiom,
strict797366125id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add) ).
thf(753,plain,
strict797366125id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(206,axiom,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_natural_Osize_I3_J) ).
thf(901,plain,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(257,axiom,
ordere223160158up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1075,plain,
ordere223160158up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(53,axiom,
ordere779506340up_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_33) ).
thf(476,plain,
ordere779506340up_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(336,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) )
= ( ord_less @ real @ ( one_one @ real ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_ln__gt__zero__iff) ).
thf(1324,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) )
= ( ord_less @ real @ ( one_one @ real ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(282,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_plus__nat_Oadd__0) ).
thf(1150,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(326,axiom,
( ( one_one @ nat )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_one__natural_Orsp) ).
thf(1297,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(250,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__cancel__left__right) ).
thf(1060,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(234,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__one) ).
thf(1002,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(96,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_zero__less__iff__neq__zero) ).
thf(569,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(315,axiom,
( ( size_bool @ $false )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_bool_Osize_I2_J) ).
thf(1246,plain,
( ( size_bool @ $false )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(13,axiom,
group_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add) ).
thf(371,plain,
group_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(118,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(622,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(184,axiom,
size @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(837,plain,
size @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(265,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( ln_ln @ real @ A ) @ ( zero_zero @ real ) )
= ( ord_less @ real @ A @ ( one_one @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ln__less__zero__iff) ).
thf(1099,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( ln_ln @ real @ A ) @ ( zero_zero @ real ) )
= ( ord_less @ real @ A @ ( one_one @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(228,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_nat__add__left__cancel) ).
thf(985,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(5,axiom,
( ( ord_less_eq @ real )
= ( ^ [A: real,B: real] :
( ( ord_less @ real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_less__eq__real__def) ).
thf(343,plain,
( ( ord_less_eq @ real )
= ( ^ [A: real,B: real] :
( ( ord_less @ real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(313,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_not__add__less2) ).
thf(1241,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(172,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ A @ ( one_one @ real ) )
=> ( ord_less @ real @ ( ln_ln @ real @ A ) @ ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_ln__less__zero) ).
thf(805,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ A @ ( one_one @ real ) )
=> ( ord_less @ real @ ( ln_ln @ real @ A ) @ ( zero_zero @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(71,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ C @ A @ ( node @ TA @ D @ B @ E ) ) )
= ( node @ TA @ ( node @ TA @ C @ A @ D ) @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_splay_Osimps_I9_J) ).
thf(508,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ C @ A @ ( node @ TA @ D @ B @ E ) ) )
= ( node @ TA @ ( node @ TA @ C @ A @ D ) @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(215,axiom,
! [TA: $tType] :
( ( size @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_size__ne__size__imp__ne) ).
thf(921,plain,
! [TA: $tType] :
( ( size @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(84,axiom,
comm_semiring_1 @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_39) ).
thf(541,plain,
comm_semiring_1 @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(249,axiom,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_powr__zero__eq__one) ).
thf(1054,plain,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( powr @ TA @ A @ ( zero_zero @ TA ) )
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(289,axiom,
! [TA: $tType,A: splay_2011811431op_s_t @ TA] :
( ( size_size @ ( splay_2011811431op_s_t @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_op_092_060_094sub_062s_092_060_094sub_062t_Osize__neq) ).
thf(1170,plain,
! [TA: $tType,A: splay_2011811431op_s_t @ TA] :
( ( size_size @ ( splay_2011811431op_s_t @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(295,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ C @ A @ D ) @ B @ E ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_t__splay__simps_I3_J) ).
thf(1187,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ C @ A @ D ) @ B @ E ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(288,axiom,
! [TA: $tType] :
( ( size_size @ ( tree @ TA ) @ ( leaf @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_tree_Osize_I3_J) ).
thf(1167,plain,
! [TA: $tType] :
( ( size_size @ ( tree @ TA ) @ ( leaf @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(294,axiom,
( ( size_size @ $o )
= ( ^ [A: $o] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_size__bool) ).
thf(1185,plain,
( ( size_size @ $o )
= ( ^ [A: $o] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(300,axiom,
monoid_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add) ).
thf(1202,plain,
monoid_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(167,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_less__numeral__extra_I1_J) ).
thf(792,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(323,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ E @ C @ D ) @ B @ F ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ E @ C @ D ) @ B @ F ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ A @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_t__splay__simps_I5_J) ).
thf(1286,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ E @ C @ D ) @ B @ F ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ E @ C @ D ) @ B @ F ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ A @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(24,axiom,
zero_less_one @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ozero__less__one_19) ).
thf(398,plain,
zero_less_one @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(242,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_add__left__imp__eq) ).
thf(1035,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(168,axiom,
comm_semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(794,plain,
comm_semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(105,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_linorder__neqE__linordered__idom) ).
thf(586,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(38,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( linorder_bst @ TA @ A )
=> ? [B: TA] :
( ( splay_splay_max @ TA @ A )
= ( splay_splay @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_splay__max__eq__splay__ex) ).
thf(425,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( linorder_bst @ TA @ A )
=> ? [B: TA] :
( ( splay_splay_max @ TA @ A )
= ( splay_splay @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(267,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_double__add__less__zero__iff__single__add__less__zero) ).
thf(1103,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(318,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_not__gr0) ).
thf(1273,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(191,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_less__add__eq__less) ).
thf(856,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(48,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( linorder_bst @ TA @ A )
=> ( linorder_bst @ TA @ ( splay_splay @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bst__splay) ).
thf(444,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: TA] :
( ( linorder_bst @ TA @ A )
=> ( linorder_bst @ TA @ ( splay_splay @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zero__less__double__add__iff__zero__less__single__add) ).
thf(733,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(113,axiom,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43__092_060Phi_062_Oinduct) ).
thf(601,plain,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(317,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: nat] :
( ( ( splay_878424299ay_max @ TA @ A )
= B )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( B
!= ( one_one @ nat ) ) )
=> ( ( ? [C: tree @ TA,D: TA] :
( A
= ( node @ TA @ C @ D @ ( leaf @ TA ) ) )
=> ( B
!= ( one_one @ nat ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA,F: TA,G: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) )
=> ~ ( ( ( G
= ( leaf @ TA ) )
=> ( B
= ( one_one @ nat ) ) )
& ( ( G
!= ( leaf @ TA ) )
=> ( B
= ( plus_plus @ nat @ ( splay_878424299ay_max @ TA @ G ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_t__splay__max_Oelims) ).
thf(1251,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: nat] :
( ( ( splay_878424299ay_max @ TA @ A )
= B )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( B
!= ( one_one @ nat ) ) )
=> ( ( ? [C: tree @ TA,D: TA] :
( A
= ( node @ TA @ C @ D @ ( leaf @ TA ) ) )
=> ( B
!= ( one_one @ nat ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA,F: TA,G: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) )
=> ~ ( ( ( G
= ( leaf @ TA ) )
=> ( B
= ( one_one @ nat ) ) )
& ( ( G
!= ( leaf @ TA ) )
=> ( B
= ( plus_plus @ nat @ ( splay_878424299ay_max @ TA @ G ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(116,axiom,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( powr @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_powr__0) ).
thf(618,plain,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( powr @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(177,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_add_Oleft__commute) ).
thf(819,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(27,axiom,
ordere236663937imp_le @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_7) ).
thf(402,plain,
ordere236663937imp_le @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(161,axiom,
! [A: real] :
( ( ( powr @ real @ A @ ( one_one @ real ) )
= A )
= ( ord_less_eq @ real @ ( zero_zero @ real ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_powr__one__gt__zero__iff) ).
thf(772,plain,
! [A: real] :
( ( ( powr @ real @ A @ ( one_one @ real ) )
= A )
= ( ord_less_eq @ real @ ( zero_zero @ real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(151,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dbl__dec__simps_I3_J) ).
thf(743,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(101,axiom,
ordere216010020id_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__comm__monoid__add_34) ).
thf(579,plain,
ordere216010020id_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(32,axiom,
comm_monoid_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_38) ).
thf(413,plain,
comm_monoid_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(92,axiom,
strict2144017051up_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__ab__semigroup__add_29) ).
thf(562,plain,
strict2144017051up_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(208,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__add__same__cancel1) ).
thf(904,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( linorder_bst @ TA @ A )
=> ( linorder_bst @ TA @ ( splay_splay_max @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_bst__splay__max) ).
thf(572,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( linorder_bst @ TA @ A )
=> ( linorder_bst @ TA @ ( splay_splay_max @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( ( splay_splay_max @ TA @ A )
= ( leaf @ TA ) )
= ( A
= ( leaf @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_splay__max__Leaf__iff) ).
thf(498,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( ( splay_splay_max @ TA @ A )
= ( leaf @ TA ) )
= ( A
= ( leaf @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(263,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: tree @ TA,C: TA,D: tree @ TA,E: TA] :
( ( ( A
= ( leaf @ TA ) )
=> ( ( splay_878424299ay_max @ TA @ ( node @ TA @ B @ C @ ( node @ TA @ D @ E @ A ) ) )
= ( one_one @ nat ) ) )
& ( ( A
!= ( leaf @ TA ) )
=> ( ( splay_878424299ay_max @ TA @ ( node @ TA @ B @ C @ ( node @ TA @ D @ E @ A ) ) )
= ( plus_plus @ nat @ ( splay_878424299ay_max @ TA @ A ) @ ( one_one @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_t__splay__max_Osimps_I3_J) ).
thf(1090,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: tree @ TA,C: TA,D: tree @ TA,E: TA] :
( ( ( A
= ( leaf @ TA ) )
=> ( ( splay_878424299ay_max @ TA @ ( node @ TA @ B @ C @ ( node @ TA @ D @ E @ A ) ) )
= ( one_one @ nat ) ) )
& ( ( A
!= ( leaf @ TA ) )
=> ( ( splay_878424299ay_max @ TA @ ( node @ TA @ B @ C @ ( node @ TA @ D @ E @ A ) ) )
= ( plus_plus @ nat @ ( splay_878424299ay_max @ TA @ A ) @ ( one_one @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(214,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_zero__less__two) ).
thf(919,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(307,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( size_size @ ( tree @ TA ) @ ( splay_splay_max @ TA @ A ) )
= ( size_size @ ( tree @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_size__splay__max) ).
thf(1224,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( size_size @ ( tree @ TA ) @ ( splay_splay_max @ TA @ A ) )
= ( size_size @ ( tree @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(83,axiom,
ordere223160158up_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_6) ).
thf(540,plain,
ordere223160158up_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(137,axiom,
canoni770627133id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(672,plain,
canoni770627133id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(22,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( leaf @ TA ) @ B @ C ) )
= ( node @ TA @ ( leaf @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_splay_Osimps_I4_J) ).
thf(391,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( leaf @ TA ) @ B @ C ) )
= ( node @ TA @ ( leaf @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(277,axiom,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ( ( ln_ln @ TA @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_ln__one) ).
thf(1139,plain,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ( ( ln_ln @ TA @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(297,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_add_Oright__cancel) ).
thf(1194,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(29,axiom,
linordered_idom @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom) ).
thf(406,plain,
linordered_idom @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_not__one__less__zero) ).
thf(1011,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(150,axiom,
! [TA: $tType,A: nat > TA > TA,B: nat,C: nat,D: TA,E: TA] :
( ( ( set_fo292404081st_nat @ TA @ A @ B @ C @ D )
= E )
=> ( ( ( ord_less @ nat @ C @ B )
=> ( E = D ) )
& ( ~ ( ord_less @ nat @ C @ B )
=> ( E
= ( set_fo292404081st_nat @ TA @ A @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) @ C @ ( A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_fold__atLeastAtMost__nat_Oelims) ).
thf(736,plain,
! [TA: $tType,A: nat > TA > TA,B: nat,C: nat,D: TA,E: TA] :
( ( ( set_fo292404081st_nat @ TA @ A @ B @ C @ D )
= E )
=> ( ( ( ord_less @ nat @ C @ B )
=> ( E = D ) )
& ( ~ ( ord_less @ nat @ C @ B )
=> ( E
= ( set_fo292404081st_nat @ TA @ A @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) @ C @ ( A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(111,axiom,
ordere779506340up_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_10) ).
thf(599,plain,
ordere779506340up_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_less__not__refl3) ).
thf(764,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(226,axiom,
! [TA: $tType,A: TA > nat] :
( ( size_tree @ TA @ A @ ( leaf @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_tree_Osize__gen_I1_J) ).
thf(979,plain,
! [TA: $tType,A: TA > nat] :
( ( size_tree @ TA @ A @ ( leaf @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(16,axiom,
zero_neq_one @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ozero__neq__one_20) ).
thf(377,plain,
zero_neq_one @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(230,axiom,
! [A: real] :
( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( powr @ real @ A @ ( one_one @ real ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_powr__one) ).
thf(990,plain,
! [A: real] :
( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( powr @ real @ A @ ( one_one @ real ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(198,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_less__irrefl__nat) ).
thf(880,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(245,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__less__same__cancel2) ).
thf(1043,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(41,axiom,
zero @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ozero_44) ).
thf(434,plain,
zero @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(202,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_less__add__one) ).
thf(890,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(54,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( splay_splay @ TA @ A @ ( leaf @ TA ) )
= ( leaf @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_splay_Osimps_I1_J) ).
thf(477,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( splay_splay @ TA @ A @ ( leaf @ TA ) )
= ( leaf @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(20,axiom,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ A @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ B @ C )
=> ( ord_less @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_powr__less__mono2__neg) ).
thf(387,plain,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ A @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ B @ C )
=> ( ord_less @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(62,axiom,
zero @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_23) ).
thf(494,plain,
zero @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(6,axiom,
linordered_semidom @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semidom_14) ).
thf(345,plain,
linordered_semidom @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(80,axiom,
linord219039673up_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add) ).
thf(535,plain,
linord219039673up_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Nat_Osize_27) ).
thf(594,plain,
! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(117,axiom,
linord1659791738miring @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_9) ).
thf(621,plain,
linord1659791738miring @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(56,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ B )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ D @ A @ ( node @ TA @ E @ C @ ( leaf @ TA ) ) ) )
= ( node @ TA @ ( node @ TA @ D @ A @ E ) @ C @ ( leaf @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_splay_Osimps_I13_J) ).
thf(483,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ B )
=> ( ( splay_splay @ TA @ B @ ( node @ TA @ D @ A @ ( node @ TA @ E @ C @ ( leaf @ TA ) ) ) )
= ( node @ TA @ ( node @ TA @ D @ A @ E ) @ C @ ( leaf @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(281,axiom,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1149,plain,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(213,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_add__mono__thms__linordered__field_I1_J) ).
thf(915,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(271,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_semiring__normalization__rules_I5_J) ).
thf(1112,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(171,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ C )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ D @ C @ E ) @ B @ F ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ D @ C @ E ) @ B @ F ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ A @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_t__splay__simps_I4_J) ).
thf(799,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ C )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ D @ C @ E ) @ B @ F ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ D @ C @ E ) @ B @ F ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ A @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(286,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_add__neg__neg) ).
thf(1162,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(240,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_double__add__le__zero__iff__single__add__le__zero) ).
thf(1029,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ( size_size @ ( sum_sum @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_sum_Osize__neq) ).
thf(895,plain,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ( size_size @ ( sum_sum @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(51,axiom,
semigroup_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_40) ).
thf(462,plain,
semigroup_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(219,axiom,
! [TA: $tType,A: tree @ TA,B: nat] :
( ( ( path_len @ TA @ A )
= B )
=> ( ( accp @ ( tree @ TA ) @ ( path_len_rel @ TA ) @ A )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( ( B
= ( zero_zero @ nat ) )
=> ~ ( accp @ ( tree @ TA ) @ ( path_len_rel @ TA ) @ ( leaf @ TA ) ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ E ) )
=> ( ( B
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ TA @ C ) @ ( size_size @ ( tree @ TA ) @ C ) ) @ ( path_len @ TA @ E ) ) @ ( size_size @ ( tree @ TA ) @ E ) ) )
=> ~ ( accp @ ( tree @ TA ) @ ( path_len_rel @ TA ) @ ( node @ TA @ C @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_path__len_Opelims) ).
thf(932,plain,
! [TA: $tType,A: tree @ TA,B: nat] :
( ( ( path_len @ TA @ A )
= B )
=> ( ( accp @ ( tree @ TA ) @ ( path_len_rel @ TA ) @ A )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( ( B
= ( zero_zero @ nat ) )
=> ~ ( accp @ ( tree @ TA ) @ ( path_len_rel @ TA ) @ ( leaf @ TA ) ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ E ) )
=> ( ( B
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ TA @ C ) @ ( size_size @ ( tree @ TA ) @ C ) ) @ ( path_len @ TA @ E ) ) @ ( size_size @ ( tree @ TA ) @ E ) ) )
=> ~ ( accp @ ( tree @ TA ) @ ( path_len_rel @ TA ) @ ( node @ TA @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(211,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(912,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(25,axiom,
! [TA: $tType] : ( size @ ( splay_2011811431op_s_t @ TA ) @ ( type2 @ ( splay_2011811431op_s_t @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t___Nat_Osize_47) ).
thf(399,plain,
! [TA: $tType] : ( size @ ( splay_2011811431op_s_t @ TA ) @ ( type2 @ ( splay_2011811431op_s_t @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(160,axiom,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( A
!= ( one_one @ real ) )
=> ( ( ( powr @ real @ A @ B )
= ( powr @ real @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_powr__inj) ).
thf(768,plain,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( A
!= ( one_one @ real ) )
=> ( ( ( powr @ real @ A @ B )
= ( powr @ real @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(195,axiom,
! [TA: $tType] :
( ( size1 @ TA )
= ( ^ [A: tree @ TA] : ( plus_plus @ nat @ ( size_size @ ( tree @ TA ) @ A ) @ ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_size1__def) ).
thf(868,plain,
! [TA: $tType] :
( ( size1 @ TA )
= ( ^ [A: tree @ TA] : ( plus_plus @ nat @ ( size_size @ ( tree @ TA ) @ A ) @ ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(199,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_le__add__same__cancel1) ).
thf(883,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(291,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add_Ocomm__neutral) ).
thf(1176,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(23,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_gr__implies__not__zero) ).
thf(394,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(93,axiom,
cancel_semigroup_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_36) ).
thf(563,plain,
cancel_semigroup_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(266,axiom,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(1102,plain,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(68,axiom,
cancel_semigroup_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__semigroup__add_13) ).
thf(505,plain,
cancel_semigroup_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(40,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_le__zero__eq) ).
thf(431,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(129,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_add__le__cancel__right) ).
thf(653,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(258,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_linordered__field__class_Osign__simps_I26_J) ).
thf(1076,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(60,axiom,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA] :
( ( ( node @ TA @ A @ B @ C )
= ( node @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_tree_Oinject) ).
thf(490,plain,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA] :
( ( ( node @ TA @ A @ B @ C )
= ( node @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(133,axiom,
linord1659791738miring @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).
thf(663,plain,
linord1659791738miring @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(58,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ord_less @ real @ ( ln_ln @ real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_ln__less__self) ).
thf(487,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ord_less @ real @ ( ln_ln @ real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(175,axiom,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(812,plain,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(115,axiom,
cancel1352612707id_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_12) ).
thf(617,plain,
cancel1352612707id_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(4,axiom,
ordere516151231imp_le @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__monoid__add__imp__le_28) ).
thf(342,plain,
ordere516151231imp_le @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(279,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add__le__same__cancel1) ).
thf(1145,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_add__less__imp__less__right) ).
thf(754,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(183,axiom,
zero_neq_one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one) ).
thf(836,plain,
zero_neq_one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(247,axiom,
( ( size_size @ $o @ $false )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_bool_Osize_I4_J) ).
thf(1049,plain,
( ( size_size @ $o @ $false )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(301,axiom,
! [A: real] :
( ( ord_less_eq @ real @ ( one_one @ real ) @ A )
=> ( ord_less_eq @ real @ ( ln_ln @ real @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_ln__bound) ).
thf(1203,plain,
! [A: real] :
( ( ord_less_eq @ real @ ( one_one @ real ) @ A )
=> ( ord_less_eq @ real @ ( ln_ln @ real @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(303,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_gr__implies__not0) ).
thf(1208,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(106,axiom,
semiri456707255roduct @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_3) ).
thf(589,plain,
semiri456707255roduct @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(169,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_add__strict__left__mono) ).
thf(795,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(141,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add__mono__thms__linordered__semiring_I4_J) ).
thf(680,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Nat_Osize_26) ).
thf(557,plain,
! [TA: $tType,TB: $tType] : ( size @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(102,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__numeral__extra_I3_J) ).
thf(580,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(144,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add__less__cancel__left) ).
thf(690,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(125,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_comm__monoid__add__class_Oadd__0) ).
thf(640,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(284,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_semiring__normalization__rules_I25_J) ).
thf(1156,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(201,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( splay_914434265_splay @ TA @ A @ ( leaf @ TA ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_t__splay_Osimps_I1_J) ).
thf(887,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( splay_914434265_splay @ TA @ A @ ( leaf @ TA ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(231,axiom,
( ( size_size @ ( tree @ a ) @ rr )
= ( size_size @ ( tree @ a ) @ ( splay_splay_max @ a @ rr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062size_Arr_A_061_Asize_A_Isplay__max_Arr_J_092_060close_062) ).
thf(993,plain,
( ( size_size @ ( tree @ a ) @ rr )
= ( size_size @ ( tree @ a ) @ ( splay_splay_max @ a @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(33,axiom,
ln @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Transcendental_Oln) ).
thf(414,plain,
ln @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(223,axiom,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add_Oleft__neutral) ).
thf(971,plain,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(138,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__is__0) ).
thf(673,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA] :
( ( ( splay_splay @ TA @ A @ B )
= ( leaf @ TA ) )
= ( B
= ( leaf @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_splay__Leaf__iff) ).
thf(502,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA] :
( ( ( splay_splay @ TA @ A @ B )
= ( leaf @ TA ) )
= ( B
= ( leaf @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(311,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_semiring__normalization__rules_I22_J) ).
thf(1235,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(52,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_bst__eq_Oinduct) ).
thf(463,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( leaf @ TA ) )
=> ( ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A @ C )
=> ( ( A @ E )
=> ( A @ ( node @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(334,axiom,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA] :
( ( size1 @ TA @ ( node @ TA @ A @ B @ C ) )
= ( plus_plus @ nat @ ( size1 @ TA @ A ) @ ( size1 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_size1__simps_I2_J) ).
thf(1317,plain,
! [TA: $tType,A: tree @ TA,B: TA,C: tree @ TA] :
( ( size1 @ TA @ ( node @ TA @ A @ B @ C ) )
= ( plus_plus @ nat @ ( size1 @ TA @ A ) @ ( size1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(306,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ D @ C @ F ) ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ D @ C @ F ) ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ B @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_t__splay__simps_I8_J) ).
thf(1218,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ( ( D
= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ D @ C @ F ) ) )
= ( one_one @ nat ) ) )
& ( ( D
!= ( leaf @ TA ) )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ E @ A @ ( node @ TA @ D @ C @ F ) ) )
= ( plus_plus @ nat @ ( splay_914434265_splay @ TA @ B @ D ) @ ( one_one @ nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(126,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_double__zero__sym) ).
thf(643,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(209,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ ( plus_plus @ TA @ A @ A ) @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_dbl__inc__def) ).
thf(907,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ ( plus_plus @ TA @ A @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(243,axiom,
( ( splay_splay_max @ a @ rr )
= ( node @ a @ l @ u @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_sp) ).
thf(1038,plain,
( ( splay_splay_max @ a @ rr )
= ( node @ a @ l @ u @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(104,axiom,
neg_numeral @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Oneg__numeral) ).
thf(585,plain,
neg_numeral @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(261,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__numeral__extra_I2_J) ).
thf(1085,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_natural_Osimps_I4_J) ).
thf(576,plain,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(130,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( ( splay_splay_max @ TA @ A )
= ( node @ TA @ B @ C @ D ) )
=> ( ( size_size @ ( tree @ TA ) @ A )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ TA ) @ B ) @ ( size_size @ ( tree @ TA ) @ D ) ) @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_size__if__splay__max) ).
thf(656,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( ( splay_splay_max @ TA @ A )
= ( node @ TA @ B @ C @ D ) )
=> ( ( size_size @ ( tree @ TA ) @ A )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ TA ) @ B ) @ ( size_size @ ( tree @ TA ) @ D ) ) @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(112,axiom,
strict797366125id_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add_8) ).
thf(600,plain,
strict797366125id_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(147,axiom,
! [TA: $tType] :
( ( path_len @ TA @ ( leaf @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_path__len_Osimps_I1_J) ).
thf(727,plain,
! [TA: $tType] :
( ( path_len @ TA @ ( leaf @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(236,axiom,
semiri456707255roduct @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1008,plain,
semiri456707255roduct @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(49,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( ( splay_splay_max @ TA @ A )
= ( node @ TA @ B @ C @ D ) )
=> ( D
= ( leaf @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_splay__max__Leaf) ).
thf(446,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( ( splay_splay_max @ TA @ A )
= ( node @ TA @ B @ C @ D ) )
=> ( D
= ( leaf @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(120,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_semiring__normalization__rules_I23_J) ).
thf(627,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(207,axiom,
zero @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(903,plain,
zero @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(74,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_linordered__field__no__lb) ).
thf(524,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(63,axiom,
monoid_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_22) ).
thf(495,plain,
monoid_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(157,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_add__lessD1) ).
thf(759,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(269,axiom,
( ( zero_zero @ nat )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_zero__natural_Orsp) ).
thf(1108,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(12,axiom,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_tree_Oexhaust) ).
thf(368,plain,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(187,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_not__less0) ).
thf(844,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(319,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_less__not__refl2) ).
thf(1276,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(176,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ind__euclid) ).
thf(813,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(221,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_add__0__iff) ).
thf(963,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(128,axiom,
one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(652,plain,
one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(21,axiom,
zero_neq_one @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_41) ).
thf(390,plain,
zero_neq_one @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(122,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__le__same__cancel2) ).
thf(632,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(26,axiom,
ordere516151231imp_le @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_4) ).
thf(401,plain,
ordere516151231imp_le @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(314,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__le__less__mono) ).
thf(1244,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(164,axiom,
~ ! [A: tree @ a,B: a,C: tree @ a] :
( ( splay_splay_max @ a @ rr )
!= ( node @ a @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062l_H_Au_Ar_H_O_Asplay__max_Arr_A_061_A_092_060langle_062l_H_M_Au_M_Ar_H_092_060rangle_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(781,plain,
~ ! [A: tree @ a,B: a,C: tree @ a] :
( ( splay_splay_max @ a @ rr )
!= ( node @ a @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(232,axiom,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( powr @ real @ A @ B ) @ ( powr @ real @ A @ C ) )
= ( ord_less_eq @ real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_powr__le__cancel__iff) ).
thf(995,plain,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( powr @ real @ A @ B ) @ ( powr @ real @ A @ C ) )
= ( ord_less_eq @ real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(35,axiom,
! [A: real,B: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( powr @ real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_powr__ge__pzero) ).
thf(418,plain,
! [A: real,B: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( powr @ real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(165,axiom,
! [TA: $tType,A: ( nat > TA > TA ) > nat > nat > TA > $o,B: nat > TA > TA,C: nat,D: nat,E: TA] :
( ! [F: nat > TA > TA,G: nat,H: nat,I: TA] :
( ( ~ ( ord_less @ nat @ H @ G )
=> ( A @ F @ ( plus_plus @ nat @ G @ ( one_one @ nat ) ) @ H @ ( F @ G @ I ) ) )
=> ( A @ F @ G @ H @ I ) )
=> ( A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_fold__atLeastAtMost__nat_Oinduct) ).
thf(786,plain,
! [TA: $tType,A: ( nat > TA > TA ) > nat > nat > TA > $o,B: nat > TA > TA,C: nat,D: nat,E: TA] :
( ! [F: nat > TA > TA,G: nat,H: nat,I: TA] :
( ( ~ ( ord_less @ nat @ H @ G )
=> ( A @ F @ ( plus_plus @ nat @ G @ ( one_one @ nat ) ) @ H @ ( F @ G @ I ) ) )
=> ( A @ F @ G @ H @ I ) )
=> ( A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(17,axiom,
cancel1352612707id_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_35) ).
thf(378,plain,
cancel1352612707id_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(135,axiom,
( ( size_size @ $o @ $true )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_bool_Osize_I3_J) ).
thf(667,plain,
( ( size_size @ $o @ $true )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(218,axiom,
! [A: real,B: real] :
( ( ord_less_eq @ real @ ( one_one @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B )
=> ( ord_less_eq @ real @ ( one_one @ real ) @ ( powr @ real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_ge__one__powr__ge__zero) ).
thf(929,plain,
! [A: real,B: real] :
( ( ord_less_eq @ real @ ( one_one @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B )
=> ( ord_less_eq @ real @ ( one_one @ real ) @ ( powr @ real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(331,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA] :
( ( size_size @ ( tree @ TA ) @ ( splay_splay @ TA @ A @ B ) )
= ( size_size @ ( tree @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_size__splay) ).
thf(1308,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: tree @ TA] :
( ( size_size @ ( tree @ TA ) @ ( splay_splay @ TA @ A @ B ) )
= ( size_size @ ( tree @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(304,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Nat_Oadd__0__right) ).
thf(1212,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(19,axiom,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ( ln_ln @ real @ A )
= ( ln_ln @ real @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_ln__inj__iff) ).
thf(383,plain,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ( ln_ln @ real @ A )
= ( ln_ln @ real @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(142,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add__eq__0__iff__both__eq__0) ).
thf(684,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(7,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( type @ TA @ ( type2 @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype) ).
thf(346,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( type @ TA @ ( type2 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(88,axiom,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ord_less @ real @ C @ A )
& ( ord_less @ real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_real__lbound__gt__zero) ).
thf(549,plain,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ord_less @ real @ C @ A )
& ( ord_less @ real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(81,axiom,
strict2144017051up_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_5) ).
thf(536,plain,
strict2144017051up_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(275,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) )
= ( ord_less_eq @ real @ ( one_one @ real ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_ln__ge__zero__iff) ).
thf(1133,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ A ) )
= ( ord_less_eq @ real @ ( one_one @ real ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(233,axiom,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( one_one @ real ) @ C )
=> ( ord_less @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_powr__less__mono) ).
thf(999,plain,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( one_one @ real ) @ C )
=> ( ord_less @ real @ ( powr @ real @ C @ A ) @ ( powr @ real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(320,axiom,
ordere216010020id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(1280,plain,
ordere216010020id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(309,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_add__left__cancel) ).
thf(1229,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(280,axiom,
linorder_bst @ a @ ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40__C3_Oprems_C_I1_J) ).
thf(1148,plain,
linorder_bst @ a @ ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(194,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_trans__less__add2) ).
thf(865,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(182,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ C @ A @ ( node @ TA @ D @ B @ E ) ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_t__splay__simps_I7_J) ).
thf(833,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( splay_914434265_splay @ TA @ B @ ( node @ TA @ C @ A @ ( node @ TA @ D @ B @ E ) ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(31,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ C )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ ( leaf @ TA ) @ B @ D ) @ C @ E ) )
= ( node @ TA @ ( leaf @ TA ) @ B @ ( node @ TA @ D @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_splay_Osimps_I5_J) ).
thf(410,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ C )
=> ( ( splay_splay @ TA @ A @ ( node @ TA @ ( node @ TA @ ( leaf @ TA ) @ B @ D ) @ C @ E ) )
= ( node @ TA @ ( leaf @ TA ) @ B @ ( node @ TA @ D @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ( splay_splay_max @ TA @ ( leaf @ TA ) )
= ( leaf @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_splay__max_Osimps_I1_J) ).
thf(422,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ( splay_splay_max @ TA @ ( leaf @ TA ) )
= ( leaf @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(316,axiom,
! [TA: $tType] :
( ( size1 @ TA @ ( leaf @ TA ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_size1__simps_I1_J) ).
thf(1248,plain,
! [TA: $tType] :
( ( size1 @ TA @ ( leaf @ TA ) )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(94,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_not__less__zero) ).
thf(564,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(333,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_semiring__normalization__rules_I20_J) ).
thf(1314,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(69,axiom,
monoid_add @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Omonoid__add_43) ).
thf(506,plain,
monoid_add @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(173,axiom,
( size_bool
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_size__bool__def) ).
thf(807,plain,
( size_bool
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(44,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_less__numeral__extra_I3_J) ).
thf(437,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(134,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__less__cancel__right) ).
thf(664,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(298,axiom,
! [TA: $tType] :
( ( zero_less_one @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_zero__less__one) ).
thf(1197,plain,
! [TA: $tType] :
( ( zero_less_one @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(180,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_add__pos__pos) ).
thf(828,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(146,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: nat] :
( ( ( splay_878424299ay_max @ TA @ A )
= B )
=> ( ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ A )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( ( B
= ( one_one @ nat ) )
=> ~ ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ ( leaf @ TA ) ) ) )
=> ( ! [C: tree @ TA,D: TA] :
( ( A
= ( node @ TA @ C @ D @ ( leaf @ TA ) ) )
=> ( ( B
= ( one_one @ nat ) )
=> ~ ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ ( node @ TA @ C @ D @ ( leaf @ TA ) ) ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA,F: TA,G: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) )
=> ( ( ( ( G
= ( leaf @ TA ) )
=> ( B
= ( one_one @ nat ) ) )
& ( ( G
!= ( leaf @ TA ) )
=> ( B
= ( plus_plus @ nat @ ( splay_878424299ay_max @ TA @ G ) @ ( one_one @ nat ) ) ) ) )
=> ~ ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_t__splay__max_Opelims) ).
thf(696,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA,B: nat] :
( ( ( splay_878424299ay_max @ TA @ A )
= B )
=> ( ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ A )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( ( B
= ( one_one @ nat ) )
=> ~ ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ ( leaf @ TA ) ) ) )
=> ( ! [C: tree @ TA,D: TA] :
( ( A
= ( node @ TA @ C @ D @ ( leaf @ TA ) ) )
=> ( ( B
= ( one_one @ nat ) )
=> ~ ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ ( node @ TA @ C @ D @ ( leaf @ TA ) ) ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA,F: TA,G: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) )
=> ( ( ( ( G
= ( leaf @ TA ) )
=> ( B
= ( one_one @ nat ) ) )
& ( ( G
!= ( leaf @ TA ) )
=> ( B
= ( plus_plus @ nat @ ( splay_878424299ay_max @ TA @ G ) @ ( one_one @ nat ) ) ) ) )
=> ~ ( accp @ ( tree @ TA ) @ ( splay_1816415694ax_rel @ TA ) @ ( node @ TA @ C @ D @ ( node @ TA @ E @ F @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(220,axiom,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( powr @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_powr__one__eq__one) ).
thf(960,plain,
! [TA: $tType] :
( ( ln @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( powr @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_less__numeral__extra_I4_J) ).
thf(635,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(77,axiom,
comm_semiring_1 @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__semiring__1_17) ).
thf(532,plain,
comm_semiring_1 @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(253,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_less__nat__zero__code) ).
thf(1065,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(200,axiom,
cancel1352612707id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(886,plain,
cancel1352612707id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(217,axiom,
strict2144017051up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(928,plain,
strict2144017051up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(34,axiom,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( powr @ real @ A @ B ) )
= ( A
!= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_powr__gt__zero) ).
thf(415,plain,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( powr @ real @ A @ B ) )
= ( A
!= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(99,axiom,
linordered_field @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(575,plain,
linordered_field @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(192,axiom,
! [TA: $tType] :
( ( strict797366125id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_pos__add__strict) ).
thf(860,plain,
! [TA: $tType] :
( ( strict797366125id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_bst__eq_Ocases) ).
thf(596,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(178,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(822,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(189,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_is__num__normalize_I1_J) ).
thf(850,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(227,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__cancel__right__right) ).
thf(982,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(328,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ( splay_878424299ay_max @ TA @ ( leaf @ TA ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_t__splay__max_Osimps_I1_J) ).
thf(1299,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ( ( splay_878424299ay_max @ TA @ ( leaf @ TA ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(46,axiom,
size @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Nat_Osize_46) ).
thf(442,plain,
size @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(196,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_infinite__descent0__measure) ).
thf(871,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(274,axiom,
! [TA: $tType,A: tree @ TA,B: nat] :
( ( ( path_len @ TA @ A )
= B )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( B
!= ( zero_zero @ nat ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ E ) )
=> ( B
!= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ TA @ C ) @ ( size_size @ ( tree @ TA ) @ C ) ) @ ( path_len @ TA @ E ) ) @ ( size_size @ ( tree @ TA ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_path__len_Oelims) ).
thf(1120,plain,
! [TA: $tType,A: tree @ TA,B: nat] :
( ( ( path_len @ TA @ A )
= B )
=> ( ( ( A
= ( leaf @ TA ) )
=> ( B
!= ( zero_zero @ nat ) ) )
=> ~ ! [C: tree @ TA,D: TA,E: tree @ TA] :
( ( A
= ( node @ TA @ C @ D @ E ) )
=> ( B
!= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ TA @ C ) @ ( size_size @ ( tree @ TA ) @ C ) ) @ ( path_len @ TA @ E ) ) @ ( size_size @ ( tree @ TA ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(66,axiom,
ab_semigroup_add @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__semigroup__add_15) ).
thf(501,plain,
ab_semigroup_add @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(57,axiom,
one @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Oone_45) ).
thf(486,plain,
one @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(335,axiom,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ( ord_less @ real @ ( powr @ real @ A @ B ) @ ( powr @ real @ A @ C ) )
= ( ord_less @ real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_powr__less__cancel__iff) ).
thf(1320,plain,
! [A: real,B: real,C: real] :
( ( ord_less @ real @ ( one_one @ real ) @ A )
=> ( ( ord_less @ real @ ( powr @ real @ A @ B ) @ ( powr @ real @ A @ C ) )
= ( ord_less @ real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1,conjecture,
( ( size_size @ ( tree @ a ) @ rr )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ a ) @ l ) @ ( size_size @ ( tree @ a ) @ r ) ) @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( size_size @ ( tree @ a ) @ rr )
!= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ a ) @ l ) @ ( size_size @ ( tree @ a ) @ r ) ) @ ( one_one @ nat ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(337,plain,
( ( size_size @ ( tree @ a ) @ rr )
!= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ a ) @ l ) @ ( size_size @ ( tree @ a ) @ r ) ) @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(237,axiom,
( ( size_size @ $o )
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_size__bool__overloaded__def) ).
thf(1009,plain,
( ( size_size @ $o )
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(131,axiom,
ordere779506340up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(659,plain,
ordere779506340up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(86,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ( ! [B: tree @ TA,C: TA] :
( A
!= ( node @ TA @ B @ C @ ( leaf @ TA ) ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA,E: TA,F: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ ( node @ TA @ D @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_t__splay__max_Ocases) ).
thf(543,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: tree @ TA] :
( ( A
!= ( leaf @ TA ) )
=> ( ! [B: tree @ TA,C: TA] :
( A
!= ( node @ TA @ B @ C @ ( leaf @ TA ) ) )
=> ~ ! [B: tree @ TA,C: TA,D: tree @ TA,E: TA,F: tree @ TA] :
( A
!= ( node @ TA @ B @ C @ ( node @ TA @ D @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(162,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA @ ( zero_zero @ TA ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_dbl__inc__simps_I2_J) ).
thf(775,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA @ ( zero_zero @ TA ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(139,axiom,
ab_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(676,plain,
ab_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(64,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_zero__le) ).
thf(496,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(255,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_gr0I) ).
thf(1069,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1350,plain,
$false,
inference(cvc4,[status(thm)],[892,809,1179,1295,352,365,1190,977,582,1005,730,1068,1305,1173,1205,449,1142,379,878,511,614,677,533,913,1063,1164,797,898,841,1046,436,1298,372,838,751,542,559,853,1087,1013,1115,1232,789,591,443,376,646,1136,514,966,1283,1051,480,1302,756,1040,1109,348,574,687,1215,1072,1119,660,988,428,507,439,529,546,925,1199,1153,761,1311,534,910,746,825,778,1238,862,349,407,693,630,1032,625,435,830,1159,493,1079,1281,974,1106,847,566,1064,1227,403,1096,420,1082,339,1292,1182,537,669,526,637,489,590,554,753,901,1075,476,1324,1150,1297,1060,1002,569,1246,371,622,837,1099,985,343,1241,805,508,921,541,1054,1170,1187,1167,1185,1202,792,1286,398,1035,794,586,425,1103,1273,856,444,733,601,1251,618,819,402,772,743,579,413,562,904,572,498,1090,919,1224,540,672,391,1139,1194,406,1011,736,599,764,979,377,990,880,1043,434,890,477,387,494,345,535,594,621,483,1149,915,1112,799,1162,1029,895,462,932,912,399,768,868,883,1176,394,563,1102,505,431,653,1076,490,663,487,812,617,342,1145,754,836,1049,1203,1208,589,795,680,557,580,690,640,1156,887,993,414,971,673,502,1235,463,1317,1218,643,907,1038,585,1085,576,656,600,727,1008,446,627,903,524,495,759,1108,368,844,1276,813,963,652,390,632,401,1244,781,995,418,786,378,667,929,1308,1212,383,684,346,549,536,1133,999,1280,1229,1148,865,833,410,422,1248,564,1314,506,807,437,664,1197,828,696,960,635,532,1065,886,928,415,575,860,596,822,850,982,1299,442,871,1120,501,486,1320,337,1009,659,543,775,676,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT214^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n005.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 11:30:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.90/1.13 % [INFO] Parsing done (256ms).
% 1.90/1.14 % [INFO] Running in sequential loop mode.
% 2.73/1.37 % [INFO] eprover registered as external prover.
% 2.73/1.37 % [INFO] cvc4 registered as external prover.
% 2.73/1.37 % [INFO] Scanning for conjecture ...
% 2.98/1.48 % [INFO] Found a conjecture and 335 axioms. Running axiom selection ...
% 3.42/1.58 % [INFO] Axiom selection finished. Selected 334 axioms (removed 1 axioms).
% 4.07/1.76 % [INFO] Problem is higher-order (TPTP THF).
% 4.16/1.77 % [INFO] Type checking passed.
% 4.16/1.78 % [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 ...
% 19.62/5.79 % External prover 'cvc4' found a proof!
% 19.62/5.79 % [INFO] Killing All external provers ...
% 19.62/5.79 % Time passed: 5252ms (effective reasoning time: 4645ms)
% 19.62/5.79 % 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)>
% 19.62/5.79 % Axioms used in derivation (334): fact_68_dbl__inc__simps_I2_J, fact_63_splay__not__Leaf, fact_42_t__splay__max_Ocases, tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__comm__monoid__add_32, fact_29_linordered__field__class_Osign__simps_I27_J, fact_248_less__eq__real__def, fact_207_ln__less__zero__iff, tcon_Real_Oreal___Rings_Ocomm__semiring__1_17, fact_100_t__splay__simps_I8_J, tfree_0, fact_95_t__splay__simps_I3_J, fact_210_ln__gt__zero__imp__gt__one, tcon_HOL_Obool___Orderings_Olinorder_1, fact_8_size__ne__size__imp__ne, fact_249_zero__le, fact_65_A__simps_I1_J, tcon_Code__Numeral_Onatural___Groups_Omonoid__add_43, fact_4_add__left__cancel, fact_156_path__len_Osimps_I1_J, tcon_Nat_Onat___Orderings_Olinorder, fact_243_powr__mono2, fact_215_powr__gt__zero, fact_174_less__irrefl__nat, tcon_Nat_Onat___Nat_Osize, fact_198_semiring__normalization__rules_I23_J, fact_228_le__zero__eq, fact_124_add__neg__neg, fact_179_infinite__descent__measure, tcon_Real_Oreal___Groups_Omonoid__add_22, fact_214_powr__one__eq__one, fact_72_neq0__conv, fact_189_bool_Osize_I2_J, fact_238_powr__one__gt__zero__iff, tcon_Code__Numeral_Onatural___Groups_Ozero_44, fact_203_fold__atLeastAtMost__nat_Osimps, fact_77_double__zero, fact_152_splay_Osimps_I3_J, fact_108_less__zeroE, fact_64_path__len_Oelims, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_11, fact_51_dbl__inc__def, fact_70_splay_Osimps_I13_J, fact_92_less__add__same__cancel2, fact_247_ge__one__powr__ge__zero, tcon_Real_Oreal___Groups_Ocancel__semigroup__add_13, tcon_Nat_Onat___Rings_Ozero__neq__one, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062l_H_Au_Ar_H_O_Asplay__max_Arr_A_061_A_092_060langle_062l_H_M_Au_M_Ar_H_092_060rangle_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_35_tree_Oexhaust, fact_22_add_Oleft__commute, fact_114_infinite__descent0__measure, fact_23_add_Ocommute, fact_199_semiring__normalization__rules_I24_J, fact_233_le__add__same__cancel2, fact_175_nat__less__induct, tcon_Nat_Onat___Rings_Ozero__less__one, fact_26_add_Oassoc, fact_204_fold__atLeastAtMost__nat_Oelims, fact_222_powr__less__mono2__neg, fact_231_zero__le__double__add__iff__zero__le__single__add, fact_178_measure__induct__rule, fact_193_add__0__iff, fact_232_double__add__le__zero__iff__single__add__le__zero, fact_165_zero__less__one, fact_59_splay_Osimps_I2_J, fact_38_bst__eq_Oinduct, fact_251_add__less__le__mono, fact_197_semiring__normalization__rules_I22_J, fact_212_ln__gt__zero, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_37_bst__eq_Ocases, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_158_splay_Osimps_I5_J, fact_39__092_060Phi_062_Ocases, tcon_Code__Numeral_Onatural___Groups_Oone_45, fact_62_bst__splay__max, fact_111_infinite__descent0, fact_138_add__less__mono, fact_57_bst__splay, fact_230_add__le__cancel__right, fact_69_t__splay__simps_I1_J, tcon_Nat_Onat___Groups_Ocomm__monoid__add, fact_185_natural_Osize_I1_J, fact_133_add__strict__right__mono, tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_39, tcon_Code__Numeral_Onatural___Nat_Osize_46, fact_1_sp, fact_190_size__bool__def, fact_192_size__bool__overloaded__def, fact_20_add__right__imp__eq, tcon_Nat_Onat___Groups_Oone, fact_194_semiring__normalization__rules_I5_J, fact_250_le__numeral__extra_I3_J, tcon_Real_Oreal___Groups_Oone_24, fact_177_linorder__neqE__nat, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, tcon_Nat_Onat___Rings_Olinordered__semidom, fact_245_powr__ge__pzero, fact_3__092_060open_062rr_A_092_060noteq_062_A_092_060langle_062_092_060rangle_062_092_060close_062, fact_17_splay__max_Osimps_I1_J, fact_16_splay__max_Osimps_I2_J, tcon_Real_Oreal___Rings_Ozero__neq__one_20, fact_119_gr__implies__not__zero, tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_35, fact_40__C3_Oprems_C_I1_J, fact_103_size1__ge0, fact_56_size1__simps_I1_J, fact_123_less__numeral__extra_I1_J, tcon_Nat_Onat___Groups_Omonoid__add, fact_181_prod_Osize__neq, fact_9_nat__add__left__cancel, fact_79_add__cancel__left__left, fact_0__092_060open_062size_Arr_A_061_Asize_A_Isplay__max_Arr_J_092_060close_062, tcon_Product__Type_Oprod___Nat_Osize_27, tcon_Tree_Otree___Nat_Osize_25, fact_159_splay_Osimps_I7_J, fact_78_double__zero__sym, fact_202_natural_Osimps_I6_J, fact_13_is__num__normalize_I1_J, tcon_Real_Oreal___Groups_Ozero_23, fact_246_powr__less__mono2, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_10, fact_241_ln__bound, fact_211_ln__less__zero, fact_46_t__splay__max_Oelims, fact_162_path__len_Opelims, tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_37, fact_88_less__one, help_If_1_1_T, fact_45_t__splay__max_Osimps_I3_J, tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__ab__semigroup__add_29, fact_121_less__imp__add__positive, fact_21_add__left__imp__eq, fact_116_linordered__field__no__ub, fact_160_splay_Osimps_I10_J, tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_36, fact_191_ind__euclid, fact_187_natural_Osimps_I4_J, fact_28_linordered__field__class_Osign__simps_I26_J, fact_55_size1__simps_I2_J, fact_150_add__eq__self__zero, fact_15_splay__max__Leaf__iff, fact_147_add_Ogroup__left__neutral, fact_94_zero__less__double__add__iff__zero__less__single__add, fact_6_size__if__splay__max, fact_14_linordered__field__class_Osign__simps_I28_J, fact_216_powr__less__cancel__iff, fact_226_real__lbound__gt__zero, fact_200_semiring__normalization__rules_I25_J, fact_87_Nat_Oadd__0__right, fact_98_t__splay__simps_I6_J, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_80_add__cancel__left__right, fact_155_t__splay_Osimps_I1_J, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_9, tcon_Nat_Onat___Groups_Ozero, fact_173_measure__induct, fact_27_add__mono__thms__linordered__semiring_I4_J, fact_186_fold__atLeastAtMost__nat_Oinduct, fact_67_dbl__dec__simps_I3_J, fact_76_add_Oright__neutral, fact_153_size__0__iff__Leaf, fact_176_infinite__descent, fact_131_add__strict__mono, fact_140_not__add__less2, fact_122_less__numeral__extra_I2_J, fact_137_add__lessD1, fact_183_size__bool, fact_168_bool_Osize_I3_J, fact_209_ln__eq__zero__iff, fact_148_add__eq__0__iff__both__eq__0, fact_163_zero__less__two, fact_236_add__le__same__cancel1, fact_48_t__splay__max_Osimps_I2_J, fact_11_one__reorient, fact_25_add_Oleft__cancel, tcon_Code__Numeral_Onatural___Orderings_Olinorder_42, fact_169_nat__neq__iff, fact_110_zero__reorient, fact_145_comm__monoid__add__class_Oadd__0, tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_12, tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__monoid__add__imp__le_28, fact_195_semiring__normalization__rules_I20_J, fact_89_add__less__same__cancel1, fact_107_not__less0, fact_18_splay__max__Leaf, fact_157_splay_Osimps_I4_J, fact_161_splay_Osimps_I12_J, fact_229_add__le__cancel__left, fact_120_zero__less__iff__neq__zero, fact_85_add__gr__0, tcon_Real_Oreal___Rings_Ozero__less__one_19, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add, fact_86_add__is__0, fact_240_powr__le__cancel__iff, fact_141_add__less__mono1, tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add_8, tcon_Sum__Type_Osum___Nat_Osize_26, fact_50_size1__def, help_If_3_1_T, fact_118_not__less__zero, help_If_2_1_T, tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_33, fact_151_splay_Osimps_I9_J, fact_170_less__not__refl, fact_208_ln__gt__zero__iff, fact_224_powr__less__mono, fact_154_tree_Osize_I3_J, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_7, fact_10_nat__add__right__cancel, fact_188_bool_Osize_I1_J, fact_134_add__less__imp__less__left, fact_60_splay_Osimps_I1_J, fact_81_add__cancel__right__left, fact_167_bool_Osize_I4_J, tcon_Real_Oreal___Groups_Ogroup__add, fact_143_trans__less__add2, fact_33_tree_Oinduct, tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_5, fact_83_add__less__cancel__left, fact_182_sum_Osize__neq, tcon_Real_Oreal___Transcendental_Oln, fact_75_add_Oleft__neutral, fact_53_splay__Leaf__iff, tcon_Real_Oreal___Orderings_Olinorder_21, fact_84_add__less__cancel__right, fact_132_add__strict__left__mono, tcon_Real_Oreal___Groups_Oab__semigroup__add_15, fact_54_size__splay, fact_129_add__mono__thms__linordered__field_I2_J, fact_252_add__le__less__mono, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_30__C3_Oprems_C_I2_J, fact_201_semiring__normalization__rules_I6_J, fact_102_t__splay__simps_I4_J, fact_206_tree_Osize__gen_I1_J, fact_239_powr__one, fact_71_natural_Osize_I3_J, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_126_pos__add__strict, fact_47_path__len_Osimps_I2_J, fact_5_add__right__cancel, fact_242_powr__mono, tcon_Real_Oreal___Fields_Olinordered__field, tcon_Real_Oreal___Rings_Olinordered__semidom_14, fact_43__092_060Phi_062_Oinduct, fact_73_nat__add__left__cancel__less, fact_32_tree_Odistinct_I1_J, fact_180_linorder__neqE__linordered__idom, tcon_Real_Oreal___Rings_Olinordered__idom, fact_196_semiring__normalization__rules_I21_J, fact_66_t__splay__max_Opelims, fact_74_not__gr__zero, fact_52_t__splay__max_Osimps_I1_J, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_219_ln__inj__iff, fact_136_less__numeral__extra_I4_J, fact_12_ab__semigroup__add__class_Oadd__ac_I1_J, fact_82_add__cancel__right__right, fact_144_less__add__eq__less, tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_40, tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_41, fact_109_gr__implies__not0, fact_237_ln__le__cancel__iff, tcon_Real_Oreal___Num_Oneg__numeral, fact_184_zero__neq__one, fact_142_trans__less__add1, fact_227_ln__ge__zero__iff, tcon_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t___Nat_Osize_47, fact_106_not__gr0, tcon_Real_Oreal___Groups_Ocomm__monoid__add_16, fact_58_splay__max__eq__splay__ex, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, fact_130_add__mono__thms__linordered__field_I1_J, fact_49_size__if__splay, fact_223_powr__less__cancel, tcon_Real_Oreal___Groups_Olinordered__ab__group__add, fact_125_add__pos__pos, tcon_Nat_Onat___Groups_Osemigroup__add, fact_101_t__splay__simps_I5_J, tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add__imp__le_31, fact_19_size__splay__max, fact_171_less__not__refl2, fact_104_less__numeral__extra_I3_J, fact_128_add__mono__thms__linordered__field_I5_J, fact_164_less__add__one, tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_6, fact_7_one__natural_Orsp, fact_41_t__splay__max_Oinduct, fact_93_double__add__less__zero__iff__single__add__less__zero, fact_24_add_Oright__cancel, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__ab__semigroup__add_30, tcon_Real_Oreal___Groups_Osemigroup__add_18, fact_135_add__less__imp__less__right, fact_146_add_Ocomm__neutral, fact_117_gr__zeroI, fact_113_zero__natural_Orsp, fact_235_add__le__same__cancel2, fact_234_le__add__same__cancel1, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_112_less__nat__zero__code, fact_172_less__not__refl3, fact_61_bst_Osimps_I1_J, fact_225_powr__inj, fact_166_not__one__less__zero, fact_97_t__splay__simps_I2_J, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_4, fact_91_less__add__same__cancel1, subcl_Orderings_Olinorder___HOL_Otype, fact_115_linordered__field__no__lb, fact_218_powr__eq__0__iff, fact_213_powr__zero__eq__one, fact_244_powr__mono2_H, fact_99_t__splay__simps_I9_J, tcon_HOL_Obool___Nat_Osize_2, tcon_Code__Numeral_Onatural___Groups_Oordered__comm__monoid__add_34, fact_127_op_092_060_094sub_062s_092_060_094sub_062t_Osize__neq, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add, tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_38, fact_139_not__add__less1, fact_34_neq__Leaf__iff, fact_90_add__less__same__cancel2, fact_105_gr0I, fact_205_ln__one, fact_217_powr__0, fact_36_mirror_Oinduct, fact_31_tree_Oinject, tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_3, fact_221_ln__less__self, fact_220_ln__less__cancel__iff, fact_149_plus__nat_Oadd__0, fact_96_t__splay__simps_I7_J
% 19.62/5.79 % No. of inferences in proof: 672
% 19.62/5.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5252 ms resp. 4645 ms w/o parsing
% 20.21/5.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.21/5.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------