TSTP Solution File: DAT172^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT172^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 07:39:40 EDT 2024
% Result : Theorem 17.09s 5.84s
% Output : Refutation 17.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 237
% Syntax : Number of formulae : 436 ( 145 unt; 40 typ; 0 def)
% Number of atoms : 1079 ( 330 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 5332 ( 134 ~; 11 |; 56 &;4593 @)
% ( 0 <=>; 538 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 102 ( 102 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 12 con; 0-6 aty)
% Number of variables : 1184 ( 46 ^1073 !; 34 ?;1184 :)
% ( 31 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(linordered_field_type,type,
linordered_field:
!>[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(ordere1818651114id_add_type,type,
ordere1818651114id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(strict797366125id_add_type,type,
strict797366125id_add:
!>[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(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(huffma505251170phabet_type,type,
huffma505251170phabet:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > ( set @ TA ) ) ).
thf(huffma1050891809istent_type,type,
huffma1050891809istent:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > $o ) ).
thf(huffma636208924e_cost_type,type,
huffma636208924e_cost:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat ) ).
thf(huffma223349076_depth_type,type,
huffma223349076_depth:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > nat ) ).
thf(huffma854352999e_freq_type,type,
huffma854352999e_freq:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > nat ) ).
thf(huffma1554076246height_type,type,
huffma1554076246height:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat ) ).
thf(huffma1954420889ibling_type,type,
huffma1954420889ibling:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > ( huffma16452318e_tree @ TA ) ) ).
thf(huffma1154738298minima_type,type,
huffma1154738298minima:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > TA > $o ) ).
thf(huffma936049440ptimum_type,type,
huffma936049440ptimum:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > $o ) ).
thf(huffma943100115ibling_type,type,
huffma943100115ibling:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > TA ) ).
thf(huffma454997449itLeaf_type,type,
huffma454997449itLeaf:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat > TA > nat > TA > ( huffma16452318e_tree @ TA ) ) ).
thf(huffma304375860urSyms_type,type,
huffma304375860urSyms:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > TA > TA > TA > ( huffma16452318e_tree @ TA ) ) ).
thf(huffma2094459102Leaves_type,type,
huffma2094459102Leaves:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat > TA > nat > TA > ( huffma16452318e_tree @ TA ) ) ).
thf(huffma469337550apSyms_type,type,
huffma469337550apSyms:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > TA > TA > ( huffma16452318e_tree @ TA ) ) ).
thf(huffma691733767weight_type,type,
huffma691733767weight:
!>[TA: $tType] : ( ( huffma16452318e_tree @ TA ) > nat ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > 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(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_type,type,
a2: a ).
thf(b_type,type,
b: a ).
thf(c_type,type,
c: a ).
thf(t_type,type,
t: huffma16452318e_tree @ a ).
thf(u_type,type,
u: huffma16452318e_tree @ a ).
thf(w_a_type,type,
w_a: nat ).
thf(w_b_type,type,
w_b: nat ).
thf(57,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_nat__add__left__cancel) ).
thf(352,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)],[57]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_91_add__le__same__cancel2) ).
thf(408,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)],[72]) ).
thf(170,axiom,
( ( huffma505251170phabet @ a @ ( huffma454997449itLeaf @ a @ t @ w_a @ a2 @ w_b @ b ) )
= ( huffma505251170phabet @ a @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_a_092_060_094sub_062u) ).
thf(677,plain,
( ( huffma505251170phabet @ a @ ( huffma454997449itLeaf @ a @ t @ w_a @ a2 @ w_b @ b ) )
= ( huffma505251170phabet @ a @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_le__trans) ).
thf(440,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(161,axiom,
~ ( member @ a @ b @ ( huffma505251170phabet @ a @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_assms_I4_J) ).
thf(655,plain,
~ ( member @ a @ b @ ( huffma505251170phabet @ a @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(63,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ nat @ A @ C )
=> ~ ( ord_less_eq @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_add__leE) ).
thf(384,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ nat @ A @ C )
=> ~ ( ord_less_eq @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_add__lessD1) ).
thf(550,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)],[121]) ).
thf(197,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
= C )
=> ( ( huffma943100115ibling @ TA @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_sibling__reciprocal) ).
thf(747,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
= C )
=> ( ( huffma943100115ibling @ TA @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_87_zero__le__double__add__iff__zero__le__single__add) ).
thf(538,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)],[117]) ).
thf(167,axiom,
( ( huffma223349076_depth @ a @ u @ c )
= ( huffma1554076246height @ a @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_d_092_060_094sub_062c) ).
thf(670,plain,
( ( huffma223349076_depth @ a @ u @ c )
= ( huffma1554076246height @ a @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(75,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_less__not__refl) ).
thf(417,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',fact_94_add__less__same__cancel2) ).
thf(565,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)],[126]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_add__leD2) ).
thf(257,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(186,axiom,
huffma1050891809istent @ a @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I1_J) ).
thf(724,plain,
huffma1050891809istent @ a @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(128,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_le__add1) ).
thf(570,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(106,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_not__less0) ).
thf(504,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(198,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: TA,D: TA,E: TA] :
( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ E @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma505251170phabet @ TA @ ( huffma304375860urSyms @ TA @ B @ A @ C @ D @ E ) )
= ( huffma505251170phabet @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_alphabet__swapFourSyms) ).
thf(751,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: TA,D: TA,E: TA] :
( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ E @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma505251170phabet @ TA @ ( huffma304375860urSyms @ TA @ B @ A @ C @ D @ E ) )
= ( huffma505251170phabet @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(134,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_ex__has__least__nat) ).
thf(587,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(147,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: nat,D: TA,E: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ~ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( huffma1050891809istent @ TA @ ( huffma454997449itLeaf @ TA @ A @ C @ D @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_consistent__splitLeaf) ).
thf(619,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: nat,D: TA,E: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ~ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( huffma1050891809istent @ TA @ ( huffma454997449itLeaf @ TA @ A @ C @ D @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(155,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: huffma16452318e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ A ) )
=> ( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma505251170phabet @ TA @ A )
= ( huffma505251170phabet @ TA @ B ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_height__gt__0__alphabet__eq__imp__height__gt__0) ).
thf(638,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: huffma16452318e_tree @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ A ) )
=> ( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma505251170phabet @ TA @ A )
= ( huffma505251170phabet @ TA @ B ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: TA] :
( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma505251170phabet @ TA @ ( huffma469337550apSyms @ TA @ B @ A @ C ) )
= ( huffma505251170phabet @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_alphabet__swapSyms) ).
thf(284,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: TA] :
( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma505251170phabet @ TA @ ( huffma469337550apSyms @ TA @ B @ A @ C ) )
= ( huffma505251170phabet @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_148_add__mono__thms__linordered__field_I5_J) ).
thf(228,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)],[16]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_add__leD1) ).
thf(448,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',fact_140_add__less__mono) ).
thf(316,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)],[44]) ).
thf(96,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ? [F: TA] :
( ( A @ F )
& ~ ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) )
=> ? [E: TA] :
( ( A @ E )
& ~ ( ord_less @ nat @ ( C @ E ) @ ( plus_plus @ nat @ ( C @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ex__has__greatest__nat__lemma) ).
thf(475,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ? [F: TA] :
( ( A @ F )
& ~ ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) )
=> ? [E: TA] :
( ( A @ E )
& ~ ( ord_less @ nat @ ( C @ E ) @ ( plus_plus @ nat @ ( C @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_nat__le__linear) ).
thf(443,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(61,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less @ nat @ ( C @ E ) @ D ) )
=> ? [E: TA] :
( ( A @ E )
& ! [F: TA] :
( ( A @ F )
=> ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ex__has__greatest__nat) ).
thf(376,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less @ nat @ ( C @ E ) @ D ) )
=> ? [E: TA] :
( ( A @ E )
& ! [F: TA] :
( ( A @ F )
=> ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',fact_145_add__mono__thms__linordered__field_I2_J) ).
thf(211,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)],[8]) ).
thf(99,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] : ( ord_less_eq @ nat @ ( huffma223349076_depth @ TA @ A @ B ) @ ( huffma1554076246height @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_depth__le__height) ).
thf(485,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] : ( ord_less_eq @ nat @ ( huffma223349076_depth @ TA @ A @ B ) @ ( huffma1554076246height @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(97,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_less__irrefl__nat) ).
thf(480,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(153,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: nat,D: nat,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma854352999e_freq @ TA @ A @ B )
= ( plus_plus @ nat @ C @ D ) )
=> ( ( huffma691733767weight @ TA @ ( huffma454997449itLeaf @ TA @ A @ C @ B @ D @ E ) )
= ( huffma691733767weight @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_weight__splitLeaf) ).
thf(634,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: nat,D: nat,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma854352999e_freq @ TA @ A @ B )
= ( plus_plus @ nat @ C @ D ) )
=> ( ( huffma691733767weight @ TA @ ( huffma454997449itLeaf @ TA @ A @ C @ B @ D @ E ) )
= ( huffma691733767weight @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__decreasing2) ).
thf(453,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(67,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA] :
? [B: TA] : ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_exists__in__alphabet) ).
thf(396,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA] :
? [B: TA] : ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_137_add__less__mono1) ).
thf(411,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)],[73]) ).
thf(22,axiom,
ordere1818651114id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add) ).
thf(243,plain,
ordere1818651114id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(79,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_le__add2) ).
thf(428,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_le__Suc__ex) ).
thf(265,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(107,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__nat__zero__code) ).
thf(507,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(190,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( huffma854352999e_freq @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) )
= ( huffma854352999e_freq @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_freq__swapSyms) ).
thf(734,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( huffma854352999e_freq @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) )
= ( huffma854352999e_freq @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(12,axiom,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(221,plain,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA] :
( ( ( huffma1554076246height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma636208924e_cost @ TA @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_height__0__imp__cost__0) ).
thf(292,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA] :
( ( ( huffma1554076246height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma636208924e_cost @ TA @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(248,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',fact_224_linordered__field__class_Osign__simps_I26_J) ).
thf(201,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)],[4]) ).
thf(62,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_neq0__conv) ).
thf(381,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(183,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_swapLeaves__id) ).
thf(714,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_203_infinite__descent__measure) ).
thf(334,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)],[50]) ).
thf(196,axiom,
member @ a @ c @ ( huffma505251170phabet @ a @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_a_092_060_094sub_062c) ).
thf(746,plain,
member @ a @ c @ ( huffma505251170phabet @ a @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',fact_130_less__add__eq__less) ).
thf(302,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)],[40]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_add__le__mono) ).
thf(349,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(151,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma223349076_depth @ TA @ A @ B )
= ( huffma1554076246height @ TA @ A ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ A ) )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( huffma943100115ibling @ TA @ A @ B )
!= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_depth__height__imp__sibling__ne) ).
thf(630,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma223349076_depth @ TA @ A @ B )
= ( huffma1554076246height @ TA @ A ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ TA @ A ) )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( huffma943100115ibling @ TA @ A @ B )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(188,axiom,
( ( huffma943100115ibling @ a @ u @ c )
!= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_dc) ).
thf(729,plain,
( ( huffma943100115ibling @ a @ u @ c )
!= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(94,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_add__nonneg__eq__0__iff) ).
thf(467,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_85_nat__add__left__cancel__less) ).
thf(435,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)],[82]) ).
thf(48,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_field__le__epsilon) ).
thf(329,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(165,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma223349076_depth @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
= ( huffma223349076_depth @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_depth__sibling) ).
thf(665,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma223349076_depth @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
= ( huffma223349076_depth @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: nat,D: nat] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma2094459102Leaves @ TA @ B @ C @ A @ D @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_swapLeaves__id__when__notin__alphabet) ).
thf(522,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: nat,D: nat] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma2094459102Leaves @ TA @ B @ C @ A @ D @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_nat__neq__iff) ).
thf(461,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)],[92]) ).
thf(172,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma943100115ibling @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_sibling__sibling__id) ).
thf(682,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma943100115ibling @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(178,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( B != C )
=> ( ( huffma854352999e_freq @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
= ( ^ [F: TA] : ( if @ nat @ ( F = B ) @ ( if @ nat @ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) ) @ D @ ( zero_zero @ nat ) ) @ ( if @ nat @ ( F = C ) @ ( if @ nat @ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ) @ E @ ( zero_zero @ nat ) ) @ ( huffma854352999e_freq @ TA @ A @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_freq__swapLeaves) ).
thf(697,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( B != C )
=> ( ( huffma854352999e_freq @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ B @ E @ C ) )
= ( ^ [F: TA] : ( if @ nat @ ( F = B ) @ ( if @ nat @ ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) ) @ D @ ( zero_zero @ nat ) ) @ ( if @ nat @ ( F = C ) @ ( if @ nat @ ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) ) @ E @ ( zero_zero @ nat ) ) @ ( huffma854352999e_freq @ TA @ A @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(145,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( huffma854352999e_freq @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) )
= ( ^ [C: TA] :
( if @ nat @ ( C = B ) @ ( plus_plus @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) ) )
@ ( if @ nat
@ ( C
= ( huffma943100115ibling @ TA @ A @ B ) )
@ ( zero_zero @ nat )
@ ( huffma854352999e_freq @ TA @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_freq__mergeSibling) ).
thf(615,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( huffma854352999e_freq @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) )
= ( ^ [C: TA] :
( if @ nat @ ( C = B ) @ ( plus_plus @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) ) )
@ ( if @ nat
@ ( C
= ( huffma943100115ibling @ TA @ A @ B ) )
@ ( zero_zero @ nat )
@ ( huffma854352999e_freq @ TA @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(187,axiom,
? [A: a] :
( ( member @ a @ A @ ( huffma505251170phabet @ a @ u ) )
& ( ( huffma223349076_depth @ a @ u @ A )
= ( huffma1554076246height @ a @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__092_060open_062_092_060exists_062a_092_060in_062alphabet_Au_O_Adepth_Au_Aa_A_061_Aheight_Au_092_060close_062) ).
thf(725,plain,
? [A: a] :
( ( member @ a @ A @ ( huffma505251170phabet @ a @ u ) )
& ( ( huffma223349076_depth @ a @ u @ A )
= ( huffma1554076246height @ a @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(70,axiom,
! [TA: $tType] :
( ( huffma469337550apSyms @ TA )
= ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] : ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_swapSyms__def) ).
thf(403,plain,
! [TA: $tType] :
( ( huffma469337550apSyms @ TA )
= ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] : ( huffma2094459102Leaves @ TA @ A @ ( huffma854352999e_freq @ TA @ A @ B ) @ B @ ( huffma854352999e_freq @ TA @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(136,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(593,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(142,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ 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/sandbox/benchmark/theBenchmark.p',fact_118_add__nonneg__pos) ).
thf(610,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ 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)],[142]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_108_add__le__less__mono) ).
thf(420,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)],[76]) ).
thf(104,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add__decreasing) ).
thf(499,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',fact_99_add__gr__0) ).
thf(519,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)],[111]) ).
thf(194,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_consistent__swapLeaves) ).
thf(742,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(15,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(225,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_147_add__mono__thms__linordered__field_I4_J) ).
thf(339,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)],[52]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_146_add__mono__thms__linordered__field_I3_J) ).
thf(554,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)],[123]) ).
thf(174,axiom,
( ( huffma223349076_depth @ a @ u @ ( huffma943100115ibling @ a @ u @ c ) )
= ( huffma1554076246height @ a @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_d_092_060_094sub_062d) ).
thf(686,plain,
( ( huffma223349076_depth @ a @ u @ ( huffma943100115ibling @ a @ u @ c ) )
= ( huffma1554076246height @ a @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(154,axiom,
member @ a @ a2 @ ( huffma505251170phabet @ a @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_a_092_060_094sub_062a) ).
thf(637,plain,
member @ a @ a2 @ ( huffma505251170phabet @ a @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_le__neq__implies__less) ).
thf(590,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(171,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: nat,D: nat,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma854352999e_freq @ TA @ A @ B )
= ( plus_plus @ nat @ C @ D ) )
=> ( ( huffma636208924e_cost @ TA @ ( huffma454997449itLeaf @ TA @ A @ C @ B @ D @ E ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_cost__splitLeaf) ).
thf(679,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: nat,D: nat,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma854352999e_freq @ TA @ A @ B )
= ( plus_plus @ nat @ C @ D ) )
=> ( ( huffma636208924e_cost @ TA @ ( huffma454997449itLeaf @ TA @ A @ C @ B @ D @ E ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_le__antisym) ).
thf(393,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(158,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_consistent__swapFourSyms) ).
thf(647,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(192,axiom,
huffma1050891809istent @ a @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_c_092_060_094sub_062u) ).
thf(738,plain,
huffma1050891809istent @ a @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(23,axiom,
ordere216010020id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(244,plain,
ordere216010020id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(152,axiom,
huffma936049440ptimum @ a @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I2_J) ).
thf(633,plain,
huffma936049440ptimum @ a @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_less__not__refl3) ).
thf(541,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(162,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_consistent__swapSyms) ).
thf(657,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_197_measure__induct) ).
thf(398,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)],[68]) ).
thf(169,axiom,
! [TA: $tType] :
( ( huffma936049440ptimum @ TA )
= ( ^ [A: huffma16452318e_tree @ TA] :
! [B: huffma16452318e_tree @ TA] :
( ( huffma1050891809istent @ TA @ B )
=> ( ( ( huffma505251170phabet @ TA @ A )
= ( huffma505251170phabet @ TA @ B ) )
=> ( ( ( huffma854352999e_freq @ TA @ A )
= ( huffma854352999e_freq @ TA @ B ) )
=> ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( huffma636208924e_cost @ TA @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_optimum__def) ).
thf(674,plain,
! [TA: $tType] :
( ( huffma936049440ptimum @ TA )
= ( ^ [A: huffma16452318e_tree @ TA] :
! [B: huffma16452318e_tree @ TA] :
( ( huffma1050891809istent @ TA @ B )
=> ( ( ( huffma505251170phabet @ TA @ A )
= ( huffma505251170phabet @ TA @ B ) )
=> ( ( ( huffma854352999e_freq @ TA @ A )
= ( huffma854352999e_freq @ TA @ B ) )
=> ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ A ) @ ( huffma636208924e_cost @ TA @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(164,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= C )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( C != B )
=> ( ( huffma943100115ibling @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ B ) @ ( huffma943100115ibling @ TA @ A @ B ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_sibling__swapSyms__other__sibling) ).
thf(662,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= C )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( C != B )
=> ( ( huffma943100115ibling @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ B ) @ ( huffma943100115ibling @ TA @ A @ B ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(54,axiom,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add__strict__increasing) ).
thf(343,plain,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(20,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_linordered__field__no__lb) ).
thf(237,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)],[20]) ).
thf(38,axiom,
ord_less_eq @ nat @ w_a @ w_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_assms_I7_J) ).
thf(298,plain,
ord_less_eq @ nat @ w_a @ w_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(146,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ a @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_h_092_060_094sub_062u) ).
thf(618,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ ( huffma1554076246height @ a @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(78,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_le__0__eq) ).
thf(425,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',fact_89_le__add__same__cancel2) ).
thf(601,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)],[139]) ).
thf(109,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
( ( huffma1554076246height @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) )
= ( huffma1554076246height @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_height__swapLeaves) ).
thf(513,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: nat,C: TA,D: nat,E: TA] :
( ( huffma1554076246height @ TA @ ( huffma2094459102Leaves @ TA @ A @ B @ C @ D @ E ) )
= ( huffma1554076246height @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_less__imp__le__nat) ).
thf(430,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(133,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma1954420889ibling @ TA @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_notin__alphabet__imp__mergeSibling__id) ).
thf(584,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma1954420889ibling @ TA @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(177,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( B != C )
=> ( ( B != D )
=> ( ( huffma223349076_depth @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ D ) @ B )
= ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_depth__swapSyms__neither) ).
thf(694,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( B != C )
=> ( ( B != D )
=> ( ( huffma223349076_depth @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ D ) @ B )
= ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(189,axiom,
( ( huffma854352999e_freq @ a @ t @ a2 )
= ( plus_plus @ nat @ w_a @ w_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_assms_I5_J) ).
thf(732,plain,
( ( huffma854352999e_freq @ a @ t @ a2 )
= ( plus_plus @ nat @ w_a @ w_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_226_linordered__field__class_Osign__simps_I28_J) ).
thf(204,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)],[5]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_96_less__add__same__cancel2) ).
thf(545,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)],[119]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_nat__add__right__cancel) ).
thf(259,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)],[29]) ).
thf(131,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_less__mono__imp__le__mono) ).
thf(577,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(182,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma469337550apSyms @ TA @ A @ B @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_swapSyms__id) ).
thf(711,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma469337550apSyms @ TA @ A @ B @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(156,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( ( huffma1554076246height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma943100115ibling @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_height__0__imp__sibling__id) ).
thf(641,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( ( huffma1554076246height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma943100115ibling @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_93_add__less__same__cancel1) ).
thf(445,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)],[86]) ).
thf(129,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_add__eq__self__zero) ).
thf(572,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_trans__less__add2) ).
thf(313,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)],[43]) ).
thf(168,axiom,
( ( huffma854352999e_freq @ a @ ( huffma454997449itLeaf @ a @ t @ w_a @ a2 @ w_b @ b ) )
= ( huffma854352999e_freq @ a @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_f_092_060_094sub_062u) ).
thf(672,plain,
( ( huffma854352999e_freq @ a @ ( huffma454997449itLeaf @ a @ t @ w_a @ a2 @ w_b @ b ) )
= ( huffma854352999e_freq @ a @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_gr__implies__not0) ).
thf(604,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(71,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_nat__less__le) ).
thf(406,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',fact_103_add__strict__right__mono) ).
thf(219,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)],[11]) ).
thf(17,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_linordered__field__no__ub) ).
thf(230,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)],[17]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(245,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(191,axiom,
member @ a @ ( huffma943100115ibling @ a @ u @ c ) @ ( huffma505251170phabet @ a @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_a_092_060_094sub_062d) ).
thf(737,plain,
member @ a @ ( huffma943100115ibling @ a @ u @ c ) @ ( huffma505251170phabet @ a @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(159,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma943100115ibling @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_notin__alphabet__imp__sibling__id) ).
thf(649,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma943100115ibling @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(7,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_linordered__field__class_Osign__simps_I27_J) ).
thf(208,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)],[7]) ).
thf(138,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_add__increasing2) ).
thf(599,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma854352999e_freq @ TA @ B @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_notin__alphabet__imp__freq__0) ).
thf(387,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma854352999e_freq @ TA @ B @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(102,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_nat__le__iff__add) ).
thf(494,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(46,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma691733767weight @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) )
= ( huffma691733767weight @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_weight__mergeSibling) ).
thf(323,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma691733767weight @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) )
= ( huffma691733767weight @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(148,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma1154738298minima @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ E @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma223349076_depth @ TA @ A @ D )
= ( huffma1554076246height @ TA @ A ) )
=> ( ( ( huffma223349076_depth @ TA @ A @ E )
= ( huffma1554076246height @ TA @ A ) )
=> ( ( D != E )
=> ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ E ) ) @ ( huffma636208924e_cost @ TA @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_cost__swapFourSyms__le) ).
thf(621,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( huffma1154738298minima @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ E @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ( huffma223349076_depth @ TA @ A @ D )
= ( huffma1554076246height @ TA @ A ) )
=> ( ( ( huffma223349076_depth @ TA @ A @ E )
= ( huffma1554076246height @ TA @ A ) )
=> ( ( D != E )
=> ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ E ) ) @ ( huffma636208924e_cost @ TA @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_188_pos__add__strict) ).
thf(483,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)],[98]) ).
thf(179,axiom,
! [A: a] :
( ( member @ a @ A @ ( huffma505251170phabet @ a @ t ) )
=> ( ( ord_less_eq @ nat @ w_a @ ( huffma854352999e_freq @ a @ t @ A ) )
& ( ord_less_eq @ nat @ w_b @ ( huffma854352999e_freq @ a @ t @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_assms_I6_J) ).
thf(700,plain,
! [A: a] :
( ( member @ a @ A @ ( huffma505251170phabet @ a @ t ) )
=> ( ( ord_less_eq @ nat @ w_a @ ( huffma854352999e_freq @ a @ t @ A ) )
& ( ord_less_eq @ nat @ w_b @ ( huffma854352999e_freq @ a @ t @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_88_double__add__le__zero__iff__single__add__le__zero) ).
thf(251,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)],[26]) ).
thf(166,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
=> ( ( ord_less_eq @ nat @ ( huffma223349076_depth @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ C ) )
=> ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) @ ( huffma636208924e_cost @ TA @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_cost__swapSyms__le) ).
thf(668,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
=> ( ( ord_less_eq @ nat @ ( huffma223349076_depth @ TA @ A @ B ) @ ( huffma223349076_depth @ TA @ A @ C ) )
=> ( ord_less_eq @ nat @ ( huffma636208924e_cost @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ C ) ) @ ( huffma636208924e_cost @ TA @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(55,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( A @ B ) @ C ) @ ( A @ ( plus_plus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_mono__nat__linear__lb) ).
thf(345,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( A @ B ) @ C ) @ ( A @ ( plus_plus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(122,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__pos__nonneg) ).
thf(552,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(173,axiom,
member @ a @ a2 @ ( huffma505251170phabet @ a @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_assms_I3_J) ).
thf(685,plain,
member @ a @ a2 @ ( huffma505251170phabet @ a @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_97_double__add__less__zero__iff__single__add__less__zero) ).
thf(455,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)],[90]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_202_measure__induct__rule) ).
thf(306,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)],[41]) ).
thf(125,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add__nonneg__nonneg) ).
thf(563,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_linorder__neqE__nat) ).
thf(299,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)],[39]) ).
thf(83,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_le__eq__less__or__eq) ).
thf(438,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_106_add__strict__left__mono) ).
thf(223,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)],[14]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_107_add__less__le__mono) ).
thf(608,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)],[141]) ).
thf(115,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_infinite__descent) ).
thf(531,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)],[115]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_187_add__pos__pos) ).
thf(548,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)],[120]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',fact_186_add__neg__neg) ).
thf(374,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)],[60]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_less__not__refl2) ).
thf(487,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_add__le__mono1) ).
thf(516,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(58,axiom,
! [A: nat > $o,B: nat] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ( A @ B )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_ex__least__nat__le) ).
thf(355,plain,
! [A: nat > $o,B: nat] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ( A @ B )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_92_add__le__same__cancel1) ).
thf(458,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)],[91]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nat__add__left__cancel__le) ).
thf(525,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(37,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_plus__nat_Oadd__0) ).
thf(295,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(74,axiom,
! [TA: $tType] :
( ( huffma1154738298minima @ TA )
= ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
& ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
& ( B != C )
& ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
& ! [D: TA] :
( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( D != B )
=> ( ( D != C )
=> ( ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ D ) )
& ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma854352999e_freq @ TA @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_minima__def) ).
thf(414,plain,
! [TA: $tType] :
( ( huffma1154738298minima @ TA )
= ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
& ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
& ( B != C )
& ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ C ) )
& ! [D: TA] :
( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( D != B )
=> ( ( D != C )
=> ( ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ B ) @ ( huffma854352999e_freq @ TA @ A @ D ) )
& ( ord_less_eq @ nat @ ( huffma854352999e_freq @ TA @ A @ C ) @ ( huffma854352999e_freq @ TA @ A @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(193,axiom,
a2 != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_ab) ).
thf(739,plain,
a2 != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1,conjecture,
huffma1050891809istent @ a @ ( huffma304375860urSyms @ a @ u @ a2 @ b @ c @ ( huffma943100115ibling @ a @ u @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( huffma1050891809istent @ a @ ( huffma304375860urSyms @ a @ u @ a2 @ b @ c @ ( huffma943100115ibling @ a @ u @ c ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(199,plain,
~ ( huffma1050891809istent @ a @ ( huffma304375860urSyms @ a @ u @ a2 @ b @ c @ ( huffma943100115ibling @ a @ u @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(184,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( C != B )
=> ( ( huffma943100115ibling @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ C @ E @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_sibling__swapLeaves__sibling) ).
thf(717,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: nat,E: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( C != B )
=> ( ( huffma943100115ibling @ TA @ ( huffma2094459102Leaves @ TA @ A @ D @ C @ E @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_less__or__eq__imp__le) ).
thf(470,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(195,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( member @ TA @ ( huffma943100115ibling @ TA @ B @ A ) @ ( huffma505251170phabet @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_in__alphabet__imp__sibling__in__alphabet) ).
thf(744,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA] :
( ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( member @ TA @ ( huffma943100115ibling @ TA @ B @ A ) @ ( huffma505251170phabet @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(180,axiom,
~ ! [A: a] :
( ( member @ a @ A @ ( huffma505251170phabet @ a @ u ) )
=> ( ( huffma223349076_depth @ a @ u @ A )
!= ( huffma1554076246height @ a @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_A_092_060lbrakk_062c_A_092_060in_062_Aalphabet_Au_059_Adepth_Au_Ac_A_061_Aheight_Au_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(703,plain,
~ ! [A: a] :
( ( member @ a @ A @ ( huffma505251170phabet @ a @ u ) )
=> ( ( huffma223349076_depth @ a @ u @ A )
!= ( huffma1554076246height @ a @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(144,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_consistent__mergeSibling) ).
thf(613,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( huffma1050891809istent @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(143,axiom,
member @ a @ b @ ( huffma505251170phabet @ a @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_a_092_060_094sub_062b) ).
thf(612,plain,
member @ a @ b @ ( huffma505251170phabet @ a @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(150,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) ) @ ( huffma854352999e_freq @ TA @ A @ B ) ) @ ( huffma854352999e_freq @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) ) )
= ( huffma636208924e_cost @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_cost__mergeSibling) ).
thf(627,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma636208924e_cost @ TA @ ( huffma1954420889ibling @ TA @ A @ B ) ) @ ( huffma854352999e_freq @ TA @ A @ B ) ) @ ( huffma854352999e_freq @ TA @ A @ ( huffma943100115ibling @ TA @ A @ B ) ) )
= ( huffma636208924e_cost @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(88,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(450,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_62_infinite__descent0__measure) ).
thf(556,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)],[124]) ).
thf(175,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( B != C )
=> ( ( ( huffma943100115ibling @ TA @ A @ D )
!= D )
=> ( ( huffma943100115ibling @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ ( huffma943100115ibling @ TA @ A @ D ) ) @ B )
= C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_sibling__swapFourSyms__when__4th__is__sibling) ).
thf(688,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( B != C )
=> ( ( ( huffma943100115ibling @ TA @ A @ D )
!= D )
=> ( ( huffma943100115ibling @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ ( huffma943100115ibling @ TA @ A @ D ) ) @ B )
= C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_add__nonpos__eq__0__iff) ).
thf(581,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ 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)],[132]) ).
thf(10,axiom,
ordere223160158up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(218,plain,
ordere223160158up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_eq__imp__le) ).
thf(319,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(160,axiom,
! [TA: $tType] :
( ( huffma304375860urSyms @ TA )
= ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] : ( if @ ( huffma16452318e_tree @ TA ) @ ( B = E ) @ ( huffma469337550apSyms @ TA @ A @ C @ D ) @ ( if @ ( huffma16452318e_tree @ TA ) @ ( C = D ) @ ( huffma469337550apSyms @ TA @ A @ B @ E ) @ ( huffma469337550apSyms @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ D ) @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_swapFourSyms__def) ).
thf(652,plain,
! [TA: $tType] :
( ( huffma304375860urSyms @ TA )
= ( ^ [A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] : ( if @ ( huffma16452318e_tree @ TA ) @ ( B = E ) @ ( huffma469337550apSyms @ TA @ A @ C @ D ) @ ( if @ ( huffma16452318e_tree @ TA ) @ ( C = D ) @ ( huffma469337550apSyms @ TA @ A @ B @ E ) @ ( huffma469337550apSyms @ TA @ ( huffma469337550apSyms @ TA @ A @ B @ D ) @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',fact_98_zero__less__double__add__iff__zero__less__single__add) ).
thf(390,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)],[65]) ).
thf(69,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add__increasing) ).
thf(401,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(127,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_le0) ).
thf(568,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_add__nonpos__nonpos) ).
thf(290,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_109_add__strict__mono) ).
thf(235,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)],[19]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_add__is__0) ).
thf(510,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)],[108]) ).
thf(6,axiom,
strict797366125id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add) ).
thf(207,plain,
strict797366125id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(116,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ 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/sandbox/benchmark/theBenchmark.p',fact_117_add__nonpos__neg) ).
thf(536,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ 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)],[116]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_trans__less__add1) ).
thf(287,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)],[34]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_95_less__add__same__cancel1) ).
thf(432,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)],[81]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: nat,D: nat,E: TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma454997449itLeaf @ TA @ B @ C @ A @ D @ E )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_notin__alphabet__imp__splitLeaf__id) ).
thf(262,plain,
! [TA: $tType,A: TA,B: huffma16452318e_tree @ TA,C: nat,D: nat,E: TA] :
( ~ ( member @ TA @ A @ ( huffma505251170phabet @ TA @ B ) )
=> ( ( huffma454997449itLeaf @ TA @ B @ C @ A @ D @ E )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_90_le__add__same__cancel1) ).
thf(422,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)],[77]) ).
thf(47,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Nat_Oadd__0__right) ).
thf(326,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',fact_144_add__mono__thms__linordered__field_I1_J) ).
thf(239,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)],[21]) ).
thf(53,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_add__neg__nonpos) ).
thf(341,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_64_infinite__descent0) ).
thf(268,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)],[32]) ).
thf(185,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA] :
( ( huffma1050891809istent @ TA @ A )
=> ? [B: TA] :
( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
& ( ( huffma223349076_depth @ TA @ A @ B )
= ( huffma1554076246height @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_exists__at__height) ).
thf(720,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA] :
( ( huffma1050891809istent @ TA @ A )
=> ? [B: TA] :
( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
& ( ( huffma223349076_depth @ TA @ A @ B )
= ( huffma1554076246height @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(149,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ E @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( huffma854352999e_freq @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ E ) )
= ( huffma854352999e_freq @ TA @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_freq__swapFourSyms) ).
thf(624,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( member @ TA @ B @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ C @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ D @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( member @ TA @ E @ ( huffma505251170phabet @ TA @ A ) )
=> ( ( huffma854352999e_freq @ TA @ ( huffma304375860urSyms @ TA @ A @ B @ C @ D @ E ) )
= ( huffma854352999e_freq @ TA @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(93,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_trans__le__add2) ).
thf(464,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(49,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_le__refl) ).
thf(332,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(130,axiom,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add__strict__increasing2) ).
thf(575,plain,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ 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)],[130]) ).
thf(137,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_not__add__less1) ).
thf(596,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_trans__le__add1) ).
thf(528,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(157,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: nat,F: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( B != C )
=> ( ( B != D )
=> ( ( huffma223349076_depth @ TA @ ( huffma2094459102Leaves @ TA @ A @ E @ C @ F @ D ) @ B )
= ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_depth__swapLeaves__neither) ).
thf(644,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA,D: TA,E: nat,F: nat] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( B != C )
=> ( ( B != D )
=> ( ( huffma223349076_depth @ TA @ ( huffma2094459102Leaves @ TA @ A @ E @ C @ F @ D ) @ B )
= ( huffma223349076_depth @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(3,axiom,
strict2144017051up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(200,plain,
strict2144017051up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(176,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( C != B )
=> ( ( huffma943100115ibling @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_sibling__swapSyms__sibling) ).
thf(691,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA,C: TA] :
( ( huffma1050891809istent @ TA @ A )
=> ( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( ( C != B )
=> ( ( huffma943100115ibling @ TA @ ( huffma469337550apSyms @ TA @ A @ C @ ( huffma943100115ibling @ TA @ A @ B ) ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(105,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_not__gr0) ).
thf(501,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(59,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_nat__less__induct) ).
thf(369,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)],[59]) ).
thf(27,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_not__add__less2) ).
thf(254,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(51,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_less__eq__nat_Osimps_I1_J) ).
thf(337,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',fact_76_double__zero__sym) ).
thf(215,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)],[9]) ).
thf(101,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_gr0I) ).
thf(491,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(13,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(222,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(103,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__zeroE) ).
thf(496,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',fact_189_less__imp__add__positive) ).
thf(309,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)],[42]) ).
thf(163,axiom,
( ( huffma1554076246height @ a @ ( huffma454997449itLeaf @ a @ t @ w_a @ a2 @ w_b @ b ) )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_False) ).
thf(659,plain,
( ( huffma1554076246height @ a @ ( huffma454997449itLeaf @ a @ t @ w_a @ a2 @ w_b @ b ) )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(181,axiom,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( member @ TA @ ( huffma943100115ibling @ TA @ A @ B ) @ ( huffma505251170phabet @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_sibling__ne__imp__sibling__in__alphabet) ).
thf(708,plain,
! [TA: $tType,A: huffma16452318e_tree @ TA,B: TA] :
( ( ( huffma943100115ibling @ TA @ A @ B )
!= B )
=> ( member @ TA @ ( huffma943100115ibling @ TA @ A @ B ) @ ( huffma505251170phabet @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fact_77_double__zero) ).
thf(232,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)],[18]) ).
thf(754,plain,
$false,
inference(e,[status(thm)],[352,408,677,440,655,384,550,747,538,670,417,565,257,724,570,504,751,587,619,638,284,228,448,316,475,443,376,211,485,480,634,453,396,411,243,428,265,507,734,221,292,248,201,381,714,334,746,302,349,630,729,467,435,329,665,522,461,682,697,615,725,403,593,610,420,499,519,742,225,339,554,686,637,590,679,393,647,738,244,633,541,657,398,674,662,343,237,298,618,425,601,513,430,584,694,732,204,545,259,577,711,641,445,572,313,672,604,406,219,230,245,737,649,208,599,387,494,323,621,483,700,251,668,345,552,685,455,306,563,299,438,223,608,531,548,374,487,516,355,458,525,295,414,739,199,717,470,744,703,613,612,627,450,556,688,581,218,319,652,390,401,568,290,235,510,207,536,287,432,262,422,326,239,341,268,720,624,464,332,575,596,528,644,200,691,501,369,254,337,215,491,222,496,309,659,708,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : DAT172^1 : TPTP v8.1.2. Released v7.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 11:33:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.00/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.84/1.11 % [INFO] Parsing done (251ms).
% 1.84/1.12 % [INFO] Running in sequential loop mode.
% 2.65/1.35 % [INFO] eprover registered as external prover.
% 2.65/1.35 % [INFO] cvc4 registered as external prover.
% 2.65/1.36 % [INFO] Scanning for conjecture ...
% 3.01/1.46 % [INFO] Found a conjecture and 287 axioms. Running axiom selection ...
% 3.32/1.55 % [INFO] Axiom selection finished. Selected 196 axioms (removed 91 axioms).
% 3.83/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 3.83/1.72 % [INFO] Type checking passed.
% 3.83/1.72 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 17.09/5.84 % External prover 'e' found a proof!
% 17.09/5.84 % [INFO] Killing All external provers ...
% 17.09/5.84 % Time passed: 5324ms (effective reasoning time: 4716ms)
% 17.09/5.84 % 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)>
% 17.09/5.84 % Axioms used in derivation (196): fact_219_height__0__imp__cost__0, fact_63_less__nat__zero__code, fact_106_add__strict__left__mono, fact_135_less__imp__le__nat, fact_76_double__zero__sym, fact_20_assms_I3_J, fact_6_a_092_060_094sub_062c, fact_142_add__lessD1, fact_203_infinite__descent__measure, fact_57_assms_I5_J, fact_119_add__neg__nonpos, fact_225_linordered__field__class_Osign__simps_I27_J, fact_96_less__add__same__cancel2, fact_144_add__mono__thms__linordered__field_I1_J, fact_19_assms_I4_J, fact_117_add__nonpos__neg, fact_8_consistent__swapFourSyms, fact_0_c_092_060_094sub_062u, fact_197_measure__induct, fact_128_mono__nat__linear__lb, fact_215_cost__swapSyms__le, fact_110_add__nonpos__eq__0__iff, fact_77_double__zero, fact_129_less__or__eq__imp__le, fact_196_less__not__refl3, fact_44_height__0__imp__sibling__id, fact_105_add__strict__increasing, fact_193_nat__neq__iff, fact_141_nat__less__le, fact_24_swapLeaves__id__when__notin__alphabet, fact_187_add__pos__pos, fact_171_nat__add__left__cancel, fact_86_nat__add__left__cancel__le, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_137_add__less__mono1, fact_202_measure__induct__rule, fact_190_ex__least__nat__le, fact_112_add__nonpos__nonpos, fact_111_add__nonneg__eq__0__iff, fact_161_le__trans, fact_145_add__mono__thms__linordered__field_I2_J, fact_131_le__eq__less__or__eq, fact_120_add__increasing, fact_87_zero__le__double__add__iff__zero__le__single__add, fact_7_sibling__reciprocal, fact_102_add__strict__increasing2, fact_36_consistent__swapSyms, fact_28_alphabet__swapFourSyms, fact_40_False, fact_58_height__gt__0__alphabet__eq__imp__height__gt__0, fact_217_optimum__def, fact_147_add__mono__thms__linordered__field_I4_J, fact_49_notin__alphabet__imp__splitLeaf__id, fact_164_le__antisym, fact_90_le__add__same__cancel1, fact_39_freq__swapFourSyms, fact_198_less__irrefl__nat, fact_127_le__neq__implies__less, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add, fact_194_less__not__refl, fact_3_assms_I2_J, fact_37_swapFourSyms__def, fact_46_Collect__mem__eq, fact_186_add__neg__neg, fact_136_plus__nat_Oadd__0, fact_200_infinite__descent, fact_91_add__le__same__cancel2, fact_189_less__imp__add__positive, fact_64_infinite__descent0, fact_157_le__add2, fact_158_le__refl, fact_227_ex__has__least__nat, fact_229_ex__has__greatest__nat, fact_16_sibling__swapLeaves__sibling, fact_170_nat__le__iff__add, fact_140_add__less__mono, fact_21__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_A_092_060lbrakk_062c_A_092_060in_062_Aalphabet_Au_059_Adepth_Au_Ac_A_061_Aheight_Au_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_82_Nat_Oadd__0__right, fact_22__092_060open_062_092_060exists_062a_092_060in_062alphabet_Au_O_Adepth_Au_Aa_A_061_Aheight_Au_092_060close_062, fact_226_linordered__field__class_Osign__simps_I28_J, fact_228_cost__swapFourSyms__le, fact_23_notin__alphabet__imp__sibling__id, help_If_1_1_T, fact_195_less__not__refl2, fact_167_nat__le__linear, fact_188_pos__add__strict, fact_26_height__swapLeaves, fact_53_notin__alphabet__imp__freq__0, fact_11_a_092_060_094sub_062a, fact_88_double__add__le__zero__iff__single__add__le__zero, fact_160_add__leD2, fact_103_add__strict__right__mono, fact_30_depth__swapSyms__neither, fact_42_freq__swapSyms, fact_162_eq__imp__le, fact_214_cost__splitLeaf, fact_34_sibling__ne__imp__sibling__in__alphabet, fact_130_less__add__eq__less, fact_126_less__mono__imp__le__mono, fact_54_assms_I7_J, fact_168_trans__le__add1, fact_146_add__mono__thms__linordered__field_I3_J, fact_65_gr__implies__not0, fact_29_depth__swapLeaves__neither, fact_211_field__le__epsilon, fact_13_sibling__swapSyms__sibling, fact_165_add__le__mono, fact_51_depth__height__imp__sibling__ne, fact_108_add__le__less__mono, fact_31_exists__at__height, fact_199_nat__less__induct, fact_155_add__leE, fact_143_le__0__eq, fact_97_double__add__less__zero__iff__single__add__less__zero, fact_113_add__nonneg__nonneg, fact_15_d_092_060_094sub_062d, fact_121_add__decreasing, fact_148_add__mono__thms__linordered__field_I5_J, fact_45_mem__Collect__eq, fact_35_consistent__swapLeaves, fact_115_add__decreasing2, fact_56_assms_I6_J, fact_118_add__nonneg__pos, fact_14_sibling__swapSyms__other__sibling, fact_224_linordered__field__class_Osign__simps_I26_J, fact_218_notin__alphabet__imp__mergeSibling__id, fact_201_linorder__neqE__nat, fact_85_nat__add__left__cancel__less, fact_114_add__increasing2, fact_94_add__less__same__cancel2, fact_169_trans__le__add2, fact_60_neq0__conv, fact_9_a_092_060_094sub_062d, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add, fact_209_not__gr0, fact_47_Collect__cong, fact_132_add__eq__self__zero, fact_84_le0, help_If_3_1_T, fact_17_depth__sibling, fact_149_less__eq__nat_Osimps_I1_J, fact_109_add__strict__mono, help_If_2_1_T, fact_25_alphabet__swapSyms, fact_18_sibling__swapFourSyms__when__4th__is__sibling, fact_107_add__less__le__mono, fact_66_less__zeroE, fact_212_ex__has__greatest__nat__lemma, fact_213_minima__def, fact_12_d_092_060_094sub_062c, fact_4_dc, fact_163_le__Suc__ex, fact_52_h_092_060_094sub_062u, fact_222_linordered__field__no__ub, fact_208_gr0I, fact_99_add__gr__0, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_10_a_092_060_094sub_062b, fact_223_linordered__field__no__lb, fact_133_trans__less__add2, fact_89_le__add__same__cancel2, fact_27_swapSyms__id, fact_43_consistent__splitLeaf, fact_98_zero__less__double__add__iff__zero__less__single__add, fact_221_cost__mergeSibling, fact_55_freq__swapLeaves, fact_33_in__alphabet__imp__sibling__in__alphabet, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, fact_38_a_092_060_094sub_062u, fact_232_weight__mergeSibling, fact_156_le__add1, fact_41_f_092_060_094sub_062u, fact_159_add__leD1, fact_216_freq__mergeSibling, fact_50_swapLeaves__id, fact_166_add__le__mono1, fact_191_depth__le__height, fact_95_less__add__same__cancel1, fact_2_assms_I1_J, fact_62_infinite__descent0__measure, fact_83_add__is__0, fact_220_consistent__mergeSibling, fact_116_add__pos__nonneg, fact_1_ab, fact_172_nat__add__right__cancel, fact_138_not__add__less2, fact_93_add__less__same__cancel1, fact_210_not__less0, fact_32_exists__in__alphabet, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_139_not__add__less1, fact_134_trans__less__add1, fact_5_sibling__sibling__id, fact_59_swapSyms__def, fact_92_add__le__same__cancel1, fact_230_weight__splitLeaf
% 17.09/5.84 % No. of inferences in proof: 396
% 17.09/5.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5324 ms resp. 4716 ms w/o parsing
% 17.83/6.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.83/6.00 % [INFO] Killing All external provers ...
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