TSTP Solution File: SWW538_5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW538_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:23:37 EDT 2024
% Result : Theorem 6.14s 2.45s
% Output : Refutation 6.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 124
% Syntax : Number of formulae : 250 ( 144 unt; 0 typ; 0 def)
% Number of atoms : 530 ( 329 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2529 ( 48 ~; 8 |; 53 &;2259 @)
% ( 19 <=>; 142 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 7 con; 0-5 aty)
% Number of variables : 583 ( 0 ^ 579 !; 4 ?; 583 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(huffma675207370phabet_type,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > ( fun @ TA @ bool ) ) ).
thf(huffma854194513Weight_type,type,
huffma854194513Weight:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(huffma1518433673istent_type,type,
huffma1518433673istent:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > $o ) ).
thf(huffma1134658180e_cost_type,type,
huffma1134658180e_cost:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(huffma410068972_depth_type,type,
huffma410068972_depth:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > TA > nat ) ).
thf(huffma1352802255e_freq_type,type,
huffma1352802255e_freq:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > TA > nat ) ).
thf(huffma945805758height_type,type,
huffma945805758height:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(huffma1146269203erNode_type,type,
huffma1146269203erNode:
!>[TA: $tType] : ( nat > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) ) ).
thf(huffma2021818691e_Leaf_type,type,
huffma2021818691e_Leaf:
!>[TA: $tType] : ( nat > TA > ( huffma1450048681e_tree @ TA ) ) ).
thf(huffma107959123e_case_type,type,
huffma107959123e_case:
!>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ TA ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).
thf(huffma1280178957ee_rec_type,type,
huffma1280178957ee_rec:
!>[TA: $tType,TB: $tType] : ( ( fun @ nat @ ( fun @ TB @ TA ) ) > ( fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ ( huffma1450048681e_tree @ TB ) @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) ) > ( huffma1450048681e_tree @ TB ) > TA ) ).
thf(huffma1926487300e_size_type,type,
huffma1926487300e_size:
!>[TA: $tType] : ( ( fun @ TA @ nat ) > ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(huffma921447403eTrees_type,type,
huffma921447403eTrees:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) ) ).
thf(huffma83463279weight_type,type,
huffma83463279weight:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(nat_size_type,type,
nat_size: nat > nat ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(t_1_type,type,
t_1: huffma1450048681e_tree @ a ).
thf(t_2_type,type,
t_2: huffma1450048681e_tree @ a ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_nat__add__left__cancel) ).
thf(336,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(63,axiom,
! [A: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_int__eq__0__conv) ).
thf(347,plain,
! [A: nat] :
( ( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__Suc__shift) ).
thf(518,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( huffma1134658180e_cost @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_cost_Osimps_I1_J) ).
thf(481,plain,
! [TA: $tType,A: TA,B: nat] :
( ( huffma1134658180e_cost @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(30,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(217,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(55,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(308,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__is__0) ).
thf(269,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(74,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__left__imp__eq) ).
thf(384,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_tree_Osimps_I1_J) ).
thf(142,plain,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(97,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_of__nat__0) ).
thf(472,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(9,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( huffma1518433673istent @ TA @ A )
=> ? [B: TA] :
( ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
& ( ( huffma410068972_depth @ TA @ A @ B )
= ( huffma945805758height @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_exists__at__height) ).
thf(153,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( huffma1518433673istent @ TA @ A )
=> ? [B: TA] :
( ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
& ( ( huffma410068972_depth @ TA @ A @ B )
= ( huffma945805758height @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(417,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(42,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_int__0) ).
thf(257,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( size_size @ ( huffma1450048681e_tree @ TA ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_tree_Osize_I3_J) ).
thf(357,plain,
! [TA: $tType,A: TA,B: nat] :
( ( size_size @ ( huffma1450048681e_tree @ TA ) @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Suc__n__not__n) ).
thf(196,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(93,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1352802255e_freq @ TA @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_notin__alphabet__imp__freq__0) ).
thf(460,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma1352802255e_freq @ TA @ A @ B )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Suc__inject) ).
thf(157,plain,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_n__not__Suc__n) ).
thf(189,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(84,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma1134658180e_cost @ TA @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_height__0__imp__cost__0) ).
thf(421,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma1134658180e_cost @ TA @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(57,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(325,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(51,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Suc__not__Zero) ).
thf(289,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(29,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(216,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(98,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__0__right) ).
thf(475,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(14,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(179,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( huffma83463279weight @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_weight_Osimps_I1_J) ).
thf(238,plain,
! [TA: $tType,A: TA,B: nat] :
( ( huffma83463279weight @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: nat,C: fun @ TA @ nat] :
( ( huffma1926487300e_size @ TA @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( plus_plus @ nat @ ( aa @ TA @ nat @ C @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_tree_Osize_I1_J) ).
thf(293,plain,
! [TA: $tType,A: TA,B: nat,C: fun @ TA @ nat] :
( ( huffma1926487300e_size @ TA @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( plus_plus @ nat @ ( aa @ TA @ nat @ C @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(132,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_double__eq__0__iff) ).
thf(396,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(133,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(81,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_add__right__cancel) ).
thf(411,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(87,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(428,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(206,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(233,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(40,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( plus_plus @ TA @ B @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_add__0__iff) ).
thf(248,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( plus_plus @ TA @ B @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( B
= ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(109,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(512,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(22,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(201,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(73,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_add__imp__eq) ).
thf(381,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(220,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(117,axiom,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_transfer__int__nat__numerals_I1_J) ).
thf(534,plain,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(54,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_add__left__cancel) ).
thf(302,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_nat__add__commute) ).
thf(424,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(101,axiom,
! [A: int,B: nat,C: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ C ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ A ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ C @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_zadd__int__left) ).
thf(484,plain,
! [A: int,B: nat,C: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ C ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ A ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ C @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(113,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(522,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(104,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma854194513Weight @ TA @ A )
= ( huffma83463279weight @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_height__0__imp__cachedWeight__eq__weight) ).
thf(493,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ( ( huffma945805758height @ TA @ A )
= ( zero_zero @ nat ) )
=> ( ( huffma854194513Weight @ TA @ A )
= ( huffma83463279weight @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(50,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Suc__neq__Zero) ).
thf(285,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(17,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(188,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_int__int__eq) ).
thf(169,plain,
! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(106,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(499,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(58,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_nat_Oexhaust) ).
thf(328,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(19,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
( ( huffma2021818691e_Leaf @ TA @ E @ D )
!= ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_tree_Osimps_I3_J) ).
thf(193,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
( ( huffma2021818691e_Leaf @ TA @ E @ D )
!= ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(122,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(547,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(27,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(212,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(77,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA] :
( ( huffma1352802255e_freq @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) @ D )
= ( plus_plus @ nat @ ( huffma1352802255e_freq @ TA @ B @ D ) @ ( huffma1352802255e_freq @ TA @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_freq_Osimps_I2_J) ).
thf(393,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA] :
( ( huffma1352802255e_freq @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) @ D )
= ( plus_plus @ nat @ ( huffma1352802255e_freq @ TA @ B @ D ) @ ( huffma1352802255e_freq @ TA @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(110,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Nat_Oadd__0__right) ).
thf(515,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(129,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_nat__add__left__commute) ).
thf(266,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_nat__add__right__cancel) ).
thf(360,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(62,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_nat_Osimps_I3_J) ).
thf(343,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(37,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(237,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_nat_Oinject) ).
thf(161,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( suc @ B )
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) )
<=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_one__is__add) ).
thf(444,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) )
=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) )
& ( ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) )
=> ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(15,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__reorient) ).
thf(180,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(53,axiom,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C = B )
=> ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
= A ) )
& ( ( C != B )
=> ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_freq_Osimps_I1_J) ).
thf(296,plain,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C = B )
=> ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
= A ) )
& ( ( C != B )
=> ( ( huffma1352802255e_freq @ TA @ ( huffma2021818691e_Leaf @ TA @ A @ B ) @ C )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( huffma854194513Weight @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_cachedWeight_Osimps_I1_J) ).
thf(176,plain,
! [TA: $tType,A: TA,B: nat] :
( ( huffma854194513Weight @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(79,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma1134658180e_cost @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma1134658180e_cost @ TA @ B ) ) @ ( huffma83463279weight @ TA @ A ) ) @ ( huffma1134658180e_cost @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_cost_Osimps_I2_J) ).
thf(402,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma1134658180e_cost @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma1134658180e_cost @ TA @ B ) ) @ ( huffma83463279weight @ TA @ A ) ) @ ( huffma1134658180e_cost @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_add__eq__self__zero) ).
thf(259,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(281,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_consistent_Osimps_I1_J) ).
thf(204,plain,
! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_add__Suc__right) ).
thf(466,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(60,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(335,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(36,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(236,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_tree_Osimps_I5_J) ).
thf(540,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(16,axiom,
one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(187,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
monoid_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(219,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(71,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(377,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(89,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Zero__neq__Suc) ).
thf(434,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(75,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__right__imp__eq) ).
thf(387,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(367,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(28,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ! [B: nat,C: TA] :
( A
!= ( huffma2021818691e_Leaf @ TA @ B @ C ) )
=> ~ ! [B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA] :
( A
!= ( huffma1146269203erNode @ TA @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_tree_Oexhaust) ).
thf(213,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
( ! [B: nat,C: TA] :
( A
!= ( huffma2021818691e_Leaf @ TA @ B @ C ) )
=> ~ ! [B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA] :
( A
!= ( huffma1146269203erNode @ TA @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(112,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(521,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(47,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA] :
( ( huffma921447403eTrees @ TA @ B @ A )
= ( huffma1146269203erNode @ TA @ ( plus_plus @ nat @ ( huffma854194513Weight @ TA @ B ) @ ( huffma854194513Weight @ TA @ A ) ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_uniteTrees__def) ).
thf(278,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA] :
( ( huffma921447403eTrees @ TA @ B @ A )
= ( huffma1146269203erNode @ TA @ ( plus_plus @ nat @ ( huffma854194513Weight @ TA @ B ) @ ( huffma854194513Weight @ TA @ A ) ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(34,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_tree_Osimps_I2_J) ).
thf(223,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(88,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ TA @ nat] :
( ( huffma1926487300e_size @ TA @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma1926487300e_size @ TA @ D @ B ) @ ( huffma1926487300e_size @ TA @ D @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_tree_Osize_I2_J) ).
thf(431,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ TA @ nat] :
( ( huffma1926487300e_size @ TA @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( huffma1926487300e_size @ TA @ D @ B ) @ ( huffma1926487300e_size @ TA @ D @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_transfer__int__nat__relations_I1_J) ).
thf(241,plain,
! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(108,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: TA] :
( ( ( member @ TA @ D @ ( huffma675207370phabet @ TA @ C ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ C @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( member @ TA @ D @ ( huffma675207370phabet @ TA @ C ) )
=> ( ( ( member @ TA @ D @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ A @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( member @ TA @ D @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_depth_Osimps_I2_J) ).
thf(505,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: TA] :
( ( ( member @ TA @ D @ ( huffma675207370phabet @ TA @ C ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ C @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( member @ TA @ D @ ( huffma675207370phabet @ TA @ C ) )
=> ( ( ( member @ TA @ D @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ A @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( member @ TA @ D @ ( huffma675207370phabet @ TA @ A ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( zero_zero @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(90,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zero__induct) ).
thf(438,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(103,axiom,
! [A: nat] :
( ( nat_size @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_size @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_nat_Osize_I2_J) ).
thf(490,plain,
! [A: nat] :
( ( nat_size @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_size @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(116,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_add__0__left) ).
thf(531,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(123,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(548,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(70,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__0) ).
thf(374,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(125,axiom,
! [A: nat,B: nat,C: bool] :
( ( ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) )
& ( ~ ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_int__if__cong) ).
thf(553,plain,
! [A: nat,B: nat,C: bool] :
( ( ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) )
& ( ~ ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(26,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma854194513Weight @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_cachedWeight_Osimps_I2_J) ).
thf(209,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma854194513Weight @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(102,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( size_size @ ( huffma1450048681e_tree @ TA ) @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( huffma1450048681e_tree @ TA ) @ B ) @ ( size_size @ ( huffma1450048681e_tree @ TA ) @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_tree_Osize_I4_J) ).
thf(487,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( size_size @ ( huffma1450048681e_tree @ TA ) @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( huffma1450048681e_tree @ TA ) @ B ) @ ( size_size @ ( huffma1450048681e_tree @ TA ) @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(114,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_of__nat__add) ).
thf(525,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(49,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma83463279weight @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma83463279weight @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_weight_Osimps_I2_J) ).
thf(282,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma83463279weight @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( plus_plus @ nat @ ( huffma83463279weight @ TA @ B ) @ ( huffma83463279weight @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
( ( huffma1146269203erNode @ TA @ E @ D @ C )
!= ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_tree_Osimps_I4_J) ).
thf(150,plain,
! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
( ( huffma1146269203erNode @ TA @ E @ D @ C )
!= ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_tree_Osimps_I6_J) ).
thf(263,plain,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma107959123e_case @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ ( huffma1450048681e_tree @ TA ) @ TB @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(91,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(441,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( huffma945805758height @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_height_Osimps_I1_J) ).
thf(370,plain,
! [TA: $tType,A: TA,B: nat] :
( ( huffma945805758height @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(107,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(502,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_tree_Orecs_I2_J) ).
thf(463,plain,
! [TA: $tType,TB: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),E: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) @ ( aa @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) @ ( aa @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ) @ D @ C ) @ B ) @ A ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ B ) ) @ ( huffma1280178957ee_rec @ TA @ TB @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_depth_Osimps_I1_J) ).
thf(544,plain,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(23,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(203,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(31,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(218,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(390,plain,
! [A: nat,B: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(83,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_not0__implies__Suc) ).
thf(418,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zadd__int) ).
thf(378,plain,
! [A: nat,B: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_tree_Orecs_I1_J) ).
thf(478,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: fun @ nat @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ ( huffma1450048681e_tree @ TA ) @ ( fun @ TB @ ( fun @ TB @ TB ) ) ) ),D: fun @ nat @ ( fun @ TA @ TB )] :
( ( huffma1280178957ee_rec @ TA @ TB @ D @ C @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ nat @ ( fun @ TA @ TB ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(124,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Zero__not__Suc) ).
thf(549,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(118,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_nat_Osimps_I2_J) ).
thf(536,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(80,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_double__zero__sym) ).
thf(405,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(69,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(373,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1,conjecture,
! [A: a] :
( ( huffma1352802255e_freq @ a @ ( huffma921447403eTrees @ a @ t_1 @ t_2 ) @ A )
= ( plus_plus @ nat @ ( huffma1352802255e_freq @ a @ t_1 @ A ) @ ( huffma1352802255e_freq @ a @ t_2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: a] :
( ( huffma1352802255e_freq @ a @ ( huffma921447403eTrees @ a @ t_1 @ t_2 ) @ A )
= ( plus_plus @ nat @ ( huffma1352802255e_freq @ a @ t_1 @ A ) @ ( huffma1352802255e_freq @ a @ t_2 @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(126,plain,
~ ! [A: a] :
( ( huffma1352802255e_freq @ a @ ( huffma921447403eTrees @ a @ t_1 @ t_2 ) @ A )
= ( plus_plus @ nat @ ( huffma1352802255e_freq @ a @ t_1 @ A ) @ ( huffma1352802255e_freq @ a @ t_2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_of__nat__eq__iff) ).
thf(136,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(59,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_nat__induct) ).
thf(332,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(86,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(427,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__Suc) ).
thf(528,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(21,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(200,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(41,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_add_Ocomm__neutral) ).
thf(254,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(96,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_plus__nat_Oadd__0) ).
thf(469,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(64,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_nat__add__assoc) ).
thf(354,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
<=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__is__1) ).
thf(309,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) )
& ( ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(120,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(543,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(105,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(496,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(562,plain,
$false,
inference(e,[status(thm)],[336,347,518,481,217,308,269,384,142,472,153,417,257,357,196,460,157,189,421,325,289,216,475,179,238,293,132,396,133,411,428,206,233,248,512,201,381,220,534,302,424,484,522,493,285,188,169,499,328,193,547,212,393,515,129,266,360,343,237,161,444,180,296,176,402,259,281,204,466,335,236,540,187,219,377,434,387,367,213,521,278,223,431,241,505,438,490,531,548,374,553,209,487,525,282,150,263,441,370,502,463,544,203,218,390,418,378,478,549,536,405,373,126,136,332,427,528,200,254,469,354,309,543,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW538_5 : TPTP v8.2.0. Released v6.0.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jun 19 07:41:25 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.04 % [INFO] Parsing done (178ms).
% 1.43/1.05 % [INFO] Running in sequential loop mode.
% 2.14/1.25 % [INFO] eprover registered as external prover.
% 2.14/1.25 % [INFO] Scanning for conjecture ...
% 2.44/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 2.61/1.41 % [INFO] Axiom selection finished. Selected 123 axioms (removed 2 axioms).
% 3.03/1.53 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.11/1.54 % [INFO] Type checking passed.
% 3.11/1.55 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.31/1.68 % [INFO] [Domain constraints] Detected constraint on bool
% 3.31/1.68 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 6.14/2.45 % External prover 'e' found a proof!
% 6.14/2.45 % [INFO] Killing All external provers ...
% 6.14/2.45 % Time passed: 1926ms (effective reasoning time: 1396ms)
% 6.14/2.45 % 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)>
% 6.14/2.45 % Axioms used in derivation (123): fact_76_Zero__neq__Suc, fact_23_cachedWeight_Osimps_I2_J, fact_91_not0__implies__Suc, arity_Int_Oint___Groups_Oone, fact_41_double__zero__sym, fact_68_exists__at__height, fact_56_Nat_Oadd__0__right, arity_Nat_Onat___Rings_Osemiring__1, fact_7_nat__add__assoc, fact_1_nat__add__right__cancel, fact_21_tree_Osimps_I6_J, fact_5_nat__add__commute, fact_27_tree_Osimps_I4_J, arity_Int_Oint___Groups_Ocomm__monoid__add, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_42_add__is__0, fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_12_tree_Osimps_I2_J, fact_75_mem__def, fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_19_uniteTrees__def, fact_83_n__not__Suc__n, fact_67_tree_Osize_I4_J, fact_2_add__left__cancel, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_66_int__eq__0__conv, arity_Int_Oint___Rings_Osemiring__1, fact_13_add__right__imp__eq, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_38_zadd__int, fact_51_add__0__right, fact_47_zero__reorient, fact_52_add__0, fact_74_ext, fact_35_cost_Osimps_I1_J, fact_61_height__0__imp__cachedWeight__eq__weight, fact_62_height_Osimps_I1_J, help_If_1_1_T, fact_32_cachedWeight_Osimps_I1_J, fact_60_depth_Osimps_I1_J, fact_4_freq_Osimps_I2_J, fact_40_double__eq__0__iff, fact_84_add__Suc__shift, fact_58_zadd__int__left, fact_30_tree_Osimps_I5_J, fact_15_add__left__imp__eq, fact_87_one__is__add, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_55_add__eq__self__zero, fact_37_consistent_Osimps_I1_J, fact_28_of__nat__eq__iff, fact_10_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_14_add__imp__eq, fact_34_tree_Oexhaust, fact_71_add__Suc__right, fact_82_Suc__n__not__n, fact_22_tree_Orecs_I2_J, fact_3_add__right__cancel, fact_8_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_25_of__nat__add, fact_88_notin__alphabet__imp__freq__0, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_54_add__0__left, arity_Int_Oint___Groups_Omonoid__add, arity_Nat_Onat___Groups_Ozero, fact_26_tree_Osimps_I3_J, fact_44_int__if__cong, fact_63_height__0__imp__cost__0, help_If_3_1_T, fact_95_depth_Osimps_I2_J, help_If_2_1_T, fact_6_nat__add__left__commute, fact_46_int__int__eq, fact_92_nat__induct, fact_18_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_0_nat__add__left__cancel, fact_24_cost_Osimps_I2_J, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_36_freq_Osimps_I1_J, fact_90_tree_Osize_I1_J, arity_Nat_Onat___Nat_Osemiring__char__0, fact_39_Nat__Transfer_Otransfer__int__nat__functions_I1_J, fact_64_transfer__int__nat__numerals_I1_J, arity_Nat_Onat___Groups_Oone, fact_11_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_59_tree_Osize_I3_J, fact_94_zero__induct, fact_48_add__0__iff, arity_Int_Oint___Groups_Oab__semigroup__add, fact_33_weight_Osimps_I1_J, fact_93_nat_Oexhaust, fact_78_Suc__not__Zero, fact_43_of__nat__0, fact_73_Suc__neq__Zero, fact_45_transfer__int__nat__relations_I1_J, fact_65_int__0, help_pp_1_1_U, fact_86_add__is__1, fact_77_nat_Osimps_I3_J, fact_29_tree_Osimps_I1_J, fact_49_add_Ocomm__neutral, arity_Nat_Onat___Groups_Omonoid__add, fact_20_weight_Osimps_I2_J, fact_81_Suc__inject, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_79_nat_Osimps_I2_J, arity_Int_Oint___Groups_Ozero, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_80_Zero__not__Suc, arity_Int_Oint___Nat_Osemiring__char__0, help_pp_2_1_U, fact_89_tree_Osize_I2_J, fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_31_tree_Orecs_I1_J, fact_57_plus__nat_Oadd__0, fact_96_nat_Osize_I2_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_72_add__Suc, fact_70_nat_Oinject
% 6.14/2.45 % No. of inferences in proof: 250
% 6.14/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1926 ms resp. 1396 ms w/o parsing
% 6.59/2.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.59/2.53 % [INFO] Killing All external provers ...
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