TSTP Solution File: SWW542_5 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SWW542_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 06:51:13 EDT 2024
% Result : Theorem 11.39s 3.81s
% Output : Refutation 11.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 163
% Syntax : Number of formulae : 290 ( 99 unt; 38 typ; 0 def)
% Number of atoms : 680 ( 216 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 3451 ( 93 ~; 16 |; 74 &;2997 @)
% ( 27 <=>; 244 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 9 con; 0-5 aty)
% Number of variables : 624 ( 0 ^ 576 !; 18 ?; 624 :)
% ( 30 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a1_type,type,
a1: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(huffma675207370phabet_type,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > ( fun @ TA @ bool ) ) ).
thf(huffma1518433673istent_type,type,
huffma1518433673istent:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > $o ) ).
thf(huffma1134658180e_cost_type,type,
huffma1134658180e_cost:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(huffma410068972_depth_type,type,
huffma410068972_depth:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > TA > nat ) ).
thf(huffma1352802255e_freq_type,type,
huffma1352802255e_freq:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > ( fun @ TA @ nat ) ) ).
thf(huffma945805758height_type,type,
huffma945805758height:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(huffma1393970616ptimum_type,type,
huffma1393970616ptimum:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > $o ) ).
thf(huffma1401021291ibling_type,type,
huffma1401021291ibling:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > TA > TA ) ).
thf(huffma1146269203erNode_type,type,
huffma1146269203erNode:
!>[TA: $tType] : ( nat > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) ) ).
thf(huffma2021818691e_Leaf_type,type,
huffma2021818691e_Leaf:
!>[TA: $tType] : ( nat > TA > ( huffma1450048681e_tree @ TA ) ) ).
thf(huffma107959123e_case_type,type,
huffma107959123e_case:
!>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ TA ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).
thf(huffma1280178957ee_rec_type,type,
huffma1280178957ee_rec:
!>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
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(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(a_type,type,
a: a1 ).
thf(t_1_type,type,
t_1: huffma1450048681e_tree @ a1 ).
thf(t_2_type,type,
t_2: huffma1450048681e_tree @ a1 ).
thf(w_type,type,
w: nat ).
thf(90,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_not__less0) ).
thf(436,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(21,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_of__nat__less__iff) ).
thf(184,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(228,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(79,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__0__eq) ).
thf(386,plain,
! [A: nat] :
( ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(13,axiom,
ord @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
thf(158,plain,
ord @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_consistent_Osimps_I1_J) ).
thf(479,plain,
! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_tree_Osimps_I6_J) ).
thf(518,plain,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__imp__le__nat) ).
thf(365,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(138,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(104,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ( member @ TA @ C @ ( huffma675207370phabet @ TA @ D ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ D @ A ) @ C )
= ( huffma1401021291ibling @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_height__gt__0__in__alphabet__imp__sibling__left) ).
thf(481,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ( member @ TA @ C @ ( huffma675207370phabet @ TA @ D ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ D @ A ) @ C )
= ( huffma1401021291ibling @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(72,axiom,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__less__cases) ).
thf(352,plain,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(92,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(449,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(39,axiom,
! [A: fun @ int @ bool] :
( ! [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( pp @ ( aa @ int @ bool @ A @ B ) ) )
<=> ! [B: nat] : ( pp @ ( aa @ int @ bool @ A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_transfer__int__nat__quantifiers_I1_J) ).
thf(247,plain,
! [A: fun @ int @ bool] :
( ( ! [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( pp @ ( aa @ int @ bool @ A @ B ) ) )
=> ! [B: nat] : ( pp @ ( aa @ int @ bool @ A @ ( semiring_1_of_nat @ int @ B ) ) ) )
& ( ! [B: nat] : ( pp @ ( aa @ int @ bool @ A @ ( semiring_1_of_nat @ int @ B ) ) )
=> ! [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( pp @ ( aa @ int @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_tree_Orecs_I1_J) ).
thf(269,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_zless__int) ).
thf(202,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zero__zle__int) ).
thf(217,plain,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(47,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(276,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(78,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(385,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( huffma945805758height @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_height_Osimps_I1_J) ).
thf(472,plain,
! [TA: $tType,A: TA,B: nat] :
( ( huffma945805758height @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(101,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__eq__nat_Osimps_I1_J) ).
thf(475,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zle__int) ).
thf(179,plain,
! [A: nat,B: nat] :
( ( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less_eq @ nat @ B @ A ) )
& ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(63,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order__refl) ).
thf(321,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
<=> ( ( ord_less_eq @ nat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat__less__le) ).
thf(376,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ B @ A )
& ( B != A ) ) )
& ( ( ( ord_less_eq @ nat @ B @ A )
& ( B != A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
<=> ( ( ord_less @ nat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_le__eq__less__or__eq) ).
thf(253,plain,
! [A: nat,B: nat] :
( ( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less @ nat @ B @ A )
| ( B = A ) ) )
& ( ( ( ord_less @ nat @ B @ A )
| ( B = A ) )
=> ( ord_less_eq @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(36,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_of__nat__less__imp__less) ).
thf(238,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(8,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(147,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_int__int__eq) ).
thf(221,plain,
! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(42,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__trans) ).
thf(265,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_linorder__neqE__nat) ).
thf(312,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(34,axiom,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_transfer__int__nat__numerals_I1_J) ).
thf(233,plain,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(118,axiom,
! [TA: $tType,A: nat,B: huffma1450048681e_tree @ TA,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ~ ( member @ TA @ C @ ( huffma675207370phabet @ TA @ B ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ A @ B @ D ) @ C )
= ( huffma1401021291ibling @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_height__gt__0__notin__alphabet__imp__sibling__right) ).
thf(534,plain,
! [TA: $tType,A: nat,B: huffma1450048681e_tree @ TA,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ~ ( member @ TA @ C @ ( huffma675207370phabet @ TA @ B ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ A @ B @ D ) @ C )
= ( huffma1401021291ibling @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(113,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
( ( huffma2021818691e_Leaf @ TA @ E @ D )
!= ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_tree_Osimps_I3_J) ).
thf(512,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
( ( huffma2021818691e_Leaf @ TA @ E @ D )
!= ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_nat__neq__iff) ).
thf(439,plain,
! [A: nat,B: nat] :
( ( ( B != A )
=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) )
& ( ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(68,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_neq0__conv) ).
thf(334,plain,
! [A: nat] :
( ( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
!= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(302,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(71,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( huffma1134658180e_cost @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_cost_Osimps_I1_J) ).
thf(349,plain,
! [TA: $tType,A: TA,B: nat] :
( ( huffma1134658180e_cost @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_tree_Orecs_I2_J) ).
thf(561,plain,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(95,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_le__refl) ).
thf(461,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
( ( huffma1146269203erNode @ TA @ E @ D @ C )
!= ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_tree_Osimps_I4_J) ).
thf(493,plain,
! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
( ( huffma1146269203erNode @ TA @ E @ D @ C )
!= ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_of__nat__less__0__iff) ).
thf(229,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(125,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat,F: TA] :
( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ E @ D @ C ) ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ A ) @ F )
= ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ E @ D @ C ) ) )
=> ( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ A ) @ F )
= ( huffma1401021291ibling @ TA @ A @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ A ) @ F )
= F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sibling_Osimps_I3_J) ).
thf(566,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat,F: TA] :
( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ E @ D @ C ) ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ A ) @ F )
= ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ E @ D @ C ) ) )
=> ( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ A ) @ F )
= ( huffma1401021291ibling @ TA @ A @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ ( huffma1146269203erNode @ TA @ E @ D @ C ) @ A ) @ F )
= F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(105,axiom,
! [TA: $tType,A: nat,B: huffma1450048681e_tree @ TA,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ( member @ TA @ C @ ( huffma675207370phabet @ TA @ B ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ A @ B @ D ) @ C )
= ( huffma1401021291ibling @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_height__gt__0__in__alphabet__imp__sibling__right) ).
thf(484,plain,
! [TA: $tType,A: nat,B: huffma1450048681e_tree @ TA,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ( member @ TA @ C @ ( huffma675207370phabet @ TA @ B ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ A @ B @ D ) @ C )
= ( huffma1401021291ibling @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(17,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_nonneg__eq__int) ).
thf(169,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(141,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(85,axiom,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C = B )
=> ( ( aa @ TA @ nat @ ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) ) @ C )
= A ) )
& ( ( C != B )
=> ( ( aa @ TA @ nat @ ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) ) @ C )
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_freq_Osimps_I1_J) ).
thf(420,plain,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C = B )
=> ( ( aa @ TA @ nat @ ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) ) @ C )
= A ) )
& ( ( C != B )
=> ( ( aa @ TA @ nat @ ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) ) @ C )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(110,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: nat,E: huffma1450048681e_tree @ TA,F: TA] :
( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ E ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ E @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) @ F )
= ( huffma1401021291ibling @ TA @ E @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ E ) )
=> ( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ E @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) @ F )
= ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ E @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) @ F )
= F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_sibling_Osimps_I4_J) ).
thf(499,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: nat,E: huffma1450048681e_tree @ TA,F: TA] :
( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ E ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ E @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) @ F )
= ( huffma1401021291ibling @ TA @ E @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ E ) )
=> ( ( ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ E @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) @ F )
= ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) @ F ) ) )
& ( ~ ( member @ TA @ F @ ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ E @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) @ F )
= F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(66,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_le0) ).
thf(328,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(23,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_int__0) ).
thf(193,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ B )
= ( zero_zero @ nat ) )
=> ( ( huffma1401021291ibling @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_height__0__imp__sibling__id) ).
thf(537,plain,
! [TA: $tType,A: TA,B: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ B )
= ( zero_zero @ nat ) )
=> ( ( huffma1401021291ibling @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ B @ A )
| ( B = A ) )
=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__or__eq__imp__le) ).
thf(393,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ B @ A )
| ( B = A ) )
=> ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(114,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ B ) )
=> ( ( huffma1518433673istent @ TA @ B )
=> ( ( ( huffma675207370phabet @ TA @ B )
= ( huffma675207370phabet @ TA @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_height__gt__0__alphabet__eq__imp__height__gt__0) ).
thf(515,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ B ) )
=> ( ( huffma1518433673istent @ TA @ B )
=> ( ( ( huffma675207370phabet @ TA @ B )
= ( huffma675207370phabet @ TA @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_transfer__int__nat__relations_I2_J) ).
thf(173,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__not__refl) ).
thf(244,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_eq__imp__le) ).
thf(398,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(122,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ! [B: nat,C: TA] :
( A
!= ( huffma2021818691e_Leaf @ TA @ B @ C ) )
=> ~ ! [B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA] :
( A
!= ( huffma1146269203erNode @ TA @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_tree_Oexhaust) ).
thf(558,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ! [B: nat,C: TA] :
( A
!= ( huffma2021818691e_Leaf @ TA @ B @ C ) )
=> ~ ! [B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA] :
( A
!= ( huffma1146269203erNode @ TA @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_tree_Osimps_I1_J) ).
thf(412,plain,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(15,axiom,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(166,plain,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
linorder @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(148,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(279,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(126,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ~ ( member @ TA @ C @ ( huffma675207370phabet @ TA @ D ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ D @ A ) @ C )
= ( huffma1401021291ibling @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_height__gt__0__notin__alphabet__imp__sibling__left) ).
thf(573,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: TA,D: huffma1450048681e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ TA @ D ) )
=> ( ~ ( member @ TA @ C @ ( huffma675207370phabet @ TA @ D ) )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ B @ D @ A ) @ C )
= ( huffma1401021291ibling @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(55,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_less__zeroE) ).
thf(296,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
preorder @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
thf(149,plain,
preorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_depth_Osimps_I1_J) ).
thf(402,plain,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
<=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_less__int__def) ).
thf(286,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ A )
=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) )
& ( ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) )
=> ( ord_less @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(51,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(281,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_of__nat__0__le__iff) ).
thf(144,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_tree_Osimps_I5_J) ).
thf(466,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(120,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( huffma1393970616ptimum @ TA @ A )
<=> ! [B: huffma1450048681e_tree @ TA] :
( ( huffma1518433673istent @ TA @ B )
=> ( ( ( huffma675207370phabet @ TA @ A )
= ( huffma675207370phabet @ TA @ B ) )
=> ( ( ( huffma1352802255e_freq @ TA @ A )
= ( huffma1352802255e_freq @ TA @ B ) )
=> ( ord_less_eq @ nat @ ( huffma1134658180e_cost @ TA @ A ) @ ( huffma1134658180e_cost @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_optimum__def) ).
thf(540,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( ( huffma1393970616ptimum @ TA @ A )
=> ! [B: huffma1450048681e_tree @ TA] :
( ( huffma1518433673istent @ TA @ B )
=> ( ( ( huffma675207370phabet @ TA @ A )
= ( huffma675207370phabet @ TA @ B ) )
=> ( ( ( huffma1352802255e_freq @ TA @ A )
= ( huffma1352802255e_freq @ TA @ B ) )
=> ( ord_less_eq @ nat @ ( huffma1134658180e_cost @ TA @ A ) @ ( huffma1134658180e_cost @ TA @ B ) ) ) ) ) )
& ( ! [B: huffma1450048681e_tree @ TA] :
( ( huffma1518433673istent @ TA @ B )
=> ( ( ( huffma675207370phabet @ TA @ A )
= ( huffma675207370phabet @ TA @ B ) )
=> ( ( ( huffma1352802255e_freq @ TA @ A )
= ( huffma1352802255e_freq @ TA @ B ) )
=> ( ord_less_eq @ nat @ ( huffma1134658180e_cost @ TA @ A ) @ ( huffma1134658180e_cost @ TA @ B ) ) ) ) )
=> ( huffma1393970616ptimum @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(14,axiom,
! [A: nat,B: nat,C: bool] :
( ( ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) )
& ( ~ ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_int__if__cong) ).
thf(159,plain,
! [A: nat,B: nat,C: bool] :
( ( ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) )
& ( ~ ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_of__nat__eq__iff) ).
thf(187,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_zero__le__imp__of__nat) ).
thf(219,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(73,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__irrefl__nat) ).
thf(362,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
<=> ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_le__fun__def) ).
thf(318,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
=> ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) )
& ( ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) )
=> ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(102,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
| ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_linorder__linear) ).
thf(477,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
| ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(75,axiom,
! [A: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_int__le__0__conv) ).
thf(367,plain,
! [A: nat] :
( ( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_le__antisym) ).
thf(323,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(37,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_zero__less__imp__eq__int) ).
thf(240,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(12,axiom,
! [A: nat] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_int__less__0__conv) ).
thf(155,plain,
! [A: nat] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__not__refl2) ).
thf(330,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(116,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(521,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(49,axiom,
ord @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(278,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(135,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_of__nat__0) ).
thf(299,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: huffma1450048681e_tree @ TA] : ( ord_less_eq @ nat @ ( huffma410068972_depth @ TA @ B @ A ) @ ( huffma945805758height @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_depth__le__height) ).
thf(267,plain,
! [TA: $tType,A: TA,B: huffma1450048681e_tree @ TA] : ( ord_less_eq @ nat @ ( huffma410068972_depth @ TA @ B @ A ) @ ( huffma945805758height @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(87,axiom,
linorder @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(431,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(107,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1401021291ibling @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_notin__alphabet__imp__sibling__id) ).
thf(490,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1401021291ibling @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(86,axiom,
! [A: nat] :
( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zero__less__int__conv) ).
thf(426,plain,
! [A: nat] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(76,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(374,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(106,axiom,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma1401021291ibling @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_sibling_Osimps_I1_J) ).
thf(487,plain,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma1401021291ibling @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(54,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(295,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(52,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ~ ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( pp @ ( aa @ nat @ bool @ B @ D ) ) )
& ( pp @ ( aa @ nat @ bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ex__least__nat__le) ).
thf(282,plain,
! [A: nat,B: fun @ nat @ bool] :
( ~ ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( pp @ ( aa @ nat @ bool @ B @ D ) ) )
& ( pp @ ( aa @ nat @ bool @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_transfer__int__nat__relations_I3_J) ).
thf(150,plain,
! [A: nat,B: nat] :
( ( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less_eq @ nat @ B @ A ) )
& ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(96,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_less__nat__zero__code) ).
thf(463,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1,conjecture,
( ( ( member @ a1 @ a @ ( huffma675207370phabet @ a1 @ t_1 ) )
=> ( ( huffma1401021291ibling @ a1 @ ( huffma1146269203erNode @ a1 @ w @ t_1 @ t_2 ) @ a )
= ( huffma1401021291ibling @ a1 @ t_1 @ a ) ) )
& ( ~ ( member @ a1 @ a @ ( huffma675207370phabet @ a1 @ t_1 ) )
=> ( ( huffma1401021291ibling @ a1 @ ( huffma1146269203erNode @ a1 @ w @ t_1 @ t_2 ) @ a )
= ( huffma1401021291ibling @ a1 @ t_2 @ a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( ( ( member @ a1 @ a @ ( huffma675207370phabet @ a1 @ t_1 ) )
=> ( ( huffma1401021291ibling @ a1 @ ( huffma1146269203erNode @ a1 @ w @ t_1 @ t_2 ) @ a )
= ( huffma1401021291ibling @ a1 @ t_1 @ a ) ) )
& ( ~ ( member @ a1 @ a @ ( huffma675207370phabet @ a1 @ t_1 ) )
=> ( ( huffma1401021291ibling @ a1 @ ( huffma1146269203erNode @ a1 @ w @ t_1 @ t_2 ) @ a )
= ( huffma1401021291ibling @ a1 @ t_2 @ a ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(127,plain,
~ ( ( ( member @ a1 @ a @ ( huffma675207370phabet @ a1 @ t_1 ) )
=> ( ( huffma1401021291ibling @ a1 @ ( huffma1146269203erNode @ a1 @ w @ t_1 @ t_2 ) @ a )
= ( huffma1401021291ibling @ a1 @ t_1 @ a ) ) )
& ( ~ ( member @ a1 @ a @ ( huffma675207370phabet @ a1 @ t_1 ) )
=> ( ( huffma1401021291ibling @ a1 @ ( huffma1146269203erNode @ a1 @ w @ t_1 @ t_2 ) @ a )
= ( huffma1401021291ibling @ a1 @ t_2 @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
| ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_nat__le__linear) ).
thf(470,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
| ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(33,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_less__imp__of__nat__less) ).
thf(231,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__not__refl3) ).
thf(450,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(117,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tree_Osimps_I2_J) ).
thf(524,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(35,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( A
= ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zero__le__imp__eq__int) ).
thf(235,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( A
= ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less_eq @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_of__nat__le__iff) ).
thf(207,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less_eq @ nat @ B @ A ) )
& ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(45,axiom,
ord @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(272,plain,
ord @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(70,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma1134658180e_cost @ TA @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_height__0__imp__cost__0) ).
thf(346,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma1134658180e_cost @ TA @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: nat,C: nat,D: nat,E: TA,F: TA] :
( ( ( F = E )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ ( huffma2021818691e_Leaf @ TA @ C @ E ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ) @ F )
= A ) )
& ( ( F != E )
=> ( ( ( F = A )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ ( huffma2021818691e_Leaf @ TA @ C @ E ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ) @ F )
= E ) )
& ( ( F != A )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ ( huffma2021818691e_Leaf @ TA @ C @ E ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ) @ F )
= F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_sibling_Osimps_I2_J) ).
thf(549,plain,
! [TA: $tType,A: TA,B: nat,C: nat,D: nat,E: TA,F: TA] :
( ( ( F = E )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ ( huffma2021818691e_Leaf @ TA @ C @ E ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ) @ F )
= A ) )
& ( ( F != E )
=> ( ( ( F = A )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ ( huffma2021818691e_Leaf @ TA @ C @ E ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ) @ F )
= E ) )
& ( ( F != A )
=> ( ( huffma1401021291ibling @ TA @ ( huffma1146269203erNode @ TA @ D @ ( huffma2021818691e_Leaf @ TA @ C @ E ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ) @ F )
= F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(89,axiom,
! [A: nat,B: nat,C: fun @ nat @ nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ C @ D ) @ ( aa @ nat @ nat @ C @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ ( aa @ nat @ nat @ C @ B ) @ ( aa @ nat @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_less__mono__imp__le__mono) ).
thf(433,plain,
! [A: nat,B: nat,C: fun @ nat @ nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( aa @ nat @ nat @ C @ D ) @ ( aa @ nat @ nat @ C @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ ( aa @ nat @ nat @ C @ B ) @ ( aa @ nat @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(112,axiom,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ a1 @ t_1 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ a1 @ t_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(510,plain,
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ a1 @ t_1 ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma945805758height @ a1 @ t_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( size_size @ ( huffma1450048681e_tree @ TA ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_tree_Osize_I3_J) ).
thf(315,plain,
! [TA: $tType,A: TA,B: nat] :
( ( size_size @ ( huffma1450048681e_tree @ TA ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(88,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(432,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(7,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(146,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(83,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zero__reorient) ).
thf(405,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(46,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_of__nat__0__less__iff) ).
thf(273,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(16,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(168,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( B != A )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_le__neq__implies__less) ).
thf(262,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( B != A )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(124,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
? [B: TA] : ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_exists__in__alphabet) ).
thf(564,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
? [B: TA] : ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(58,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( pp @ ( aa @ nat @ bool @ B @ D ) ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_infinite__descent0) ).
thf(305,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( pp @ ( aa @ nat @ bool @ B @ D ) ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_transfer__int__nat__relations_I1_J) ).
thf(210,plain,
! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(326,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_gr__implies__not0) ).
thf(341,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(111,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( huffma1518433673istent @ TA @ A )
=> ? [B: TA] :
( ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
& ( ( huffma410068972_depth @ TA @ A @ B )
= ( huffma945805758height @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_exists__at__height) ).
thf(506,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( huffma1518433673istent @ TA @ A )
=> ? [B: TA] :
( ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
& ( ( huffma410068972_depth @ TA @ A @ B )
= ( huffma945805758height @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(24,axiom,
! [A: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_int__eq__0__conv) ).
thf(195,plain,
! [A: nat] :
( ( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(178,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(48,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(277,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(98,axiom,
preorder @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(469,plain,
preorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(59,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_gr0I) ).
thf(309,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(109,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( aa @ TA @ nat @ ( huffma1352802255e_freq @ TA @ A ) @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_notin__alphabet__imp__freq__0) ).
thf(496,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( aa @ TA @ nat @ ( huffma1352802255e_freq @ TA @ A ) @ B )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(94,axiom,
! [A: fun @ int @ bool] :
( ? [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( pp @ ( aa @ int @ bool @ A @ B ) ) )
<=> ? [B: nat] : ( pp @ ( aa @ int @ bool @ A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_transfer__int__nat__quantifiers_I2_J) ).
thf(454,plain,
! [A: fun @ int @ bool] :
( ( ? [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( pp @ ( aa @ int @ bool @ A @ B ) ) )
=> ? [B: nat] : ( pp @ ( aa @ int @ bool @ A @ ( semiring_1_of_nat @ int @ B ) ) ) )
& ( ? [B: nat] : ( pp @ ( aa @ int @ bool @ A @ ( semiring_1_of_nat @ int @ B ) ) )
=> ? [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( pp @ ( aa @ int @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(621,plain,
$false,
inference(cvc4,[status(thm)],[436,184,228,386,158,479,518,365,138,481,352,449,247,269,202,217,276,385,472,475,179,321,376,253,238,147,221,265,312,233,534,512,439,334,302,349,561,461,493,229,566,484,169,141,420,499,328,193,537,393,515,173,244,398,558,412,166,148,279,573,296,149,402,286,281,144,466,540,159,187,219,362,318,477,367,323,240,155,330,521,278,135,299,267,431,490,426,374,487,295,282,150,463,127,470,231,450,524,235,207,272,346,549,433,510,315,432,146,405,273,168,262,564,305,210,326,341,506,195,178,277,469,309,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW542_5 : TPTP v8.2.0. Released v6.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n004.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 : Sat May 18 20:54:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.02/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.13 % [INFO] Parsing done (199ms).
% 1.54/1.14 % [INFO] Running in sequential loop mode.
% 2.29/1.33 % [INFO] eprover registered as external prover.
% 2.29/1.34 % [INFO] cvc4 registered as external prover.
% 2.29/1.34 % [INFO] Scanning for conjecture ...
% 2.52/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 124 axioms. Running axiom selection ...
% 2.77/1.51 % [INFO] Axiom selection finished. Selected 124 axioms (removed 0 axioms).
% 3.31/1.62 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.31/1.64 % [INFO] Type checking passed.
% 3.31/1.65 % [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 ...
% 3.80/1.80 % [INFO] [Domain constraints] Detected constraint on bool
% 3.80/1.80 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 11.39/3.81 % External prover 'cvc4' found a proof!
% 11.39/3.81 % [INFO] Killing All external provers ...
% 11.39/3.81 % Time passed: 3277ms (effective reasoning time: 2669ms)
% 11.39/3.81 % 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)>
% 11.39/3.81 % Axioms used in derivation (124): fact_4_height__gt__0__notin__alphabet__imp__sibling__left, fact_46_of__nat__less__0__iff, fact_63_le__neq__implies__less, arity_HOL_Obool___Orderings_Oord, fact_11_less__zeroE, fact_67_eq__imp__le, arity_HOL_Obool___Orderings_Opreorder, arity_Nat_Onat___Rings_Osemiring__1, fact_85_transfer__int__nat__relations_I3_J, fact_39_tree_Oexhaust, fact_56_le0, fact_61_le__eq__less__or__eq, fact_77_zless__int, arity_Int_Oint___Orderings_Oord, fact_5_height__gt__0__notin__alphabet__imp__sibling__right, fact_3_notin__alphabet__imp__sibling__id, arity_fun___Orderings_Oord, fact_9_neq0__conv, arity_Nat_Onat___Orderings_Opreorder, fact_49_notin__alphabet__imp__freq__0, fact_10_less__nat__zero__code, arity_Int_Oint___Orderings_Opreorder, fact_57_of__nat__le__iff, fact_81_transfer__int__nat__numerals_I1_J, fact_75_mem__def, fact_59_int__int__eq, fact_60_nat__less__le, fact_18_sibling_Osimps_I2_J, fact_32_less__irrefl__nat, fact_29_nat__less__cases, fact_80_transfer__int__nat__relations_I2_J, fact_71_zero__le__imp__of__nat, fact_86_less__int__def, fact_53_tree_Orecs_I2_J, fact_42_infinite__descent0, arity_Int_Oint___Rings_Osemiring__1, arity_HOL_Obool___Orderings_Olinorder, fact_97_le__fun__def, fact_30_less__not__refl3, fact_74_ext, fact_88_zero__zle__int, fact_14_gr__implies__not0, fact_15_gr0I, help_If_1_1_T, fact_25_tree_Osimps_I4_J, fact_45_of__nat__less__iff, fact_51_optimum__def, arity_Nat_Onat___Orderings_Olinorder, fact_66_le__trans, fact_37_depth_Osimps_I1_J, arity_fun___Orderings_Opreorder, fact_12_height__gt__0__alphabet__eq__imp__height__gt__0, fact_68_nat__le__linear, fact_69_le__refl, fact_93_nonneg__eq__int, fact_34_nat__neq__iff, fact_83_transfer__int__nat__quantifiers_I2_J, fact_78_zero__less__imp__eq__int, fact_94_zero__le__imp__eq__int, fact_28_zero__reorient, arity_Int_Oint___Orderings_Olinorder, fact_72_depth__le__height, arity_Nat_Onat___Rings_Olinordered__semidom, fact_84_transfer__int__nat__quantifiers_I1_J, fact_87_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_7_height__gt__0__in__alphabet__imp__sibling__right, fact_98_linorder__linear, fact_38_of__nat__0__less__iff, arity_Nat_Onat___Groups_Ozero, fact_26_tree_Osimps_I3_J, fact_31_less__not__refl2, arity_Nat_Onat___Orderings_Oord, help_If_3_1_T, help_If_2_1_T, fact_82_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_35_less__not__refl, fact_8_height__0__imp__sibling__id, fact_91_transfer__int__nat__relations_I1_J, fact_90_int__le__0__conv, fact_50_zero__less__int__conv, fact_36_tree_Osize_I3_J, arity_Nat_Onat___Nat_Osemiring__char__0, fact_23_cost_Osimps_I1_J, fact_20_tree_Osimps_I1_J, fact_44_of__nat__0, fact_58_int__less__0__conv, fact_16_tree_Osimps_I6_J, fact_47_less__imp__of__nat__less, fact_64_less__or__eq__imp__le, fact_13_not__less0, fact_27_sibling_Osimps_I1_J, fact_54_le__0__eq, fact_22_height_Osimps_I1_J, fact_17_exists__in__alphabet, fact_0_tree_Osimps_I2_J, fact_70_of__nat__0__le__iff, fact_33_linorder__neqE__nat, fact_52_tree_Orecs_I1_J, help_pp_1_1_U, fact_76_int__0, fact_62_less__imp__le__nat, fact_65_le__antisym, fact_43_of__nat__eq__iff, fact_21_consistent_Osimps_I1_J, fact_55_less__eq__nat_Osimps_I1_J, fact_2_sibling_Osimps_I3_J, fact_73_int__eq__0__conv, fact_40_freq_Osimps_I1_J, fact_6_height__gt__0__in__alphabet__imp__sibling__left, conj_0, arity_Int_Oint___Nat_Osemiring__char__0, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_89_zle__int, arity_Int_Oint___Groups_Ozero, fact_95_less__mono__imp__le__mono, fact_92_int__if__cong, fact_79_ex__least__nat__le, fact_48_of__nat__less__imp__less, fact_41_exists__at__height, fact_1_sibling_Osimps_I4_J, fact_24_tree_Osimps_I5_J, fact_19_height__0__imp__cost__0, fact_96_order__refl
% 11.39/3.81 % No. of inferences in proof: 252
% 11.39/3.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3277 ms resp. 2669 ms w/o parsing
% 11.39/3.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.39/3.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------