%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW538_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:46 AM UTC 2026
% Result : Theorem 9.01s 3.20s
% Output : Refutation 9.01s
% 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_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(huffma675207370phabet_decl,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > ( bool @ ( TA @ fun ) ) ) ).
thf(huffma854194513Weight_decl,type,
huffma854194513Weight:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(huffma1518433673istent_decl,type,
huffma1518433673istent:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > $o ) ).
thf(huffma1134658180e_cost_decl,type,
huffma1134658180e_cost:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(huffma410068972_depth_decl,type,
huffma410068972_depth:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > TA > nat ) ).
thf(huffma1352802255e_freq_decl,type,
huffma1352802255e_freq:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > TA > nat ) ).
thf(huffma945805758height_decl,type,
huffma945805758height:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(huffma1146269203erNode_decl,type,
huffma1146269203erNode:
!>[TA: $tType] : ( nat > ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) ) ).
thf(huffma2021818691e_Leaf_decl,type,
huffma2021818691e_Leaf:
!>[TA: $tType] : ( nat > TA > ( TA @ huffma1450048681e_tree ) ) ).
thf(huffma107959123e_case_decl,type,
huffma107959123e_case:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) @ ( nat @ fun ) ) > ( TA @ ( TB @ huffma1450048681e_tree @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ) ) > ( TB @ huffma1450048681e_tree ) > TA ) ).
thf(huffma1280178957ee_rec_decl,type,
huffma1280178957ee_rec:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) @ ( nat @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ) ) > ( TB @ huffma1450048681e_tree ) > TA ) ).
thf(huffma1926487300e_size_decl,type,
huffma1926487300e_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(huffma921447403eTrees_decl,type,
huffma921447403eTrees:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) ) ).
thf(huffma83463279weight_decl,type,
huffma83463279weight:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(nat_size_decl,type,
nat_size: nat > nat ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(t_1_decl,type,
t_1: a @ huffma1450048681e_tree ).
thf(t_2_decl,type,
t_2: a @ huffma1450048681e_tree ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__left__imp__eq) ).
thf(404,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(124,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Zero__not__Suc) ).
thf(575,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(63,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_int__eq__0__conv) ).
thf(365,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(104,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ( ( A @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ huffma854194513Weight ) )
= ( A @ ( TA @ huffma83463279weight ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_height__0__imp__cachedWeight__eq__weight) ).
thf(518,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ( ( A @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ huffma854194513Weight ) )
= ( A @ ( TA @ huffma83463279weight ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( ( nat @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus ) ) ) )
<=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_one__is__add) ).
thf(468,plain,
! [A: nat,B: nat] :
( ( ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) )
=> ( ( nat @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( nat @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus ) ) ) )
=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(60,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(352,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(26,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma854194513Weight ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_cachedWeight_Osimps_I2_J) ).
thf(217,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma854194513Weight ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(37,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(247,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nat__add__right__cancel) ).
thf(379,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(82,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(440,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(42,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_int__0) ).
thf(269,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__0__right) ).
thf(500,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(538,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_depth_Osimps_I1_J) ).
thf(570,plain,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(58,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat_Oexhaust) ).
thf(344,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(17,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(196,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_double__eq__0__iff) ).
thf(416,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: nat,C: TA @ huffma1450048681e_tree,D: TA @ huffma1450048681e_tree,E: nat] :
( ( C @ ( D @ ( E @ ( TA @ huffma1146269203erNode ) ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_tree_Osimps_I4_J) ).
thf(152,plain,
! [TA: $tType,A: TA,B: nat,C: TA @ huffma1450048681e_tree,D: TA @ huffma1450048681e_tree,E: nat] :
( ( C @ ( D @ ( E @ ( TA @ huffma1146269203erNode ) ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(228,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_add__left__cancel) ).
thf(316,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1450048681e_tree @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_tree_Osize_I3_J) ).
thf(376,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1450048681e_tree @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(23,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(211,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(93,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA] :
( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member ) ) )
=> ( ( B @ ( A @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_notin__alphabet__imp__freq__0) ).
thf(485,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA] :
( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member ) ) )
=> ( ( B @ ( A @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nat__add__left__cancel) ).
thf(353,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(59,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_nat__induct) ).
thf(348,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(123,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(574,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(71,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(397,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(28,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ! [B: nat,C: TA] :
( A
!= ( C @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) )
=> ~ ! [B: nat,C: TA @ huffma1450048681e_tree,D: TA @ huffma1450048681e_tree] :
( A
!= ( D @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_tree_Oexhaust) ).
thf(221,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ! [B: nat,C: TA] :
( A
!= ( C @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) )
=> ~ ! [B: nat,C: TA @ huffma1450048681e_tree,D: TA @ huffma1450048681e_tree] :
( A
!= ( D @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(132,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(133,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(527,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma83463279weight ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_weight_Osimps_I1_J) ).
thf(248,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma83463279weight ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(102,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1450048681e_tree @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( TA @ huffma1450048681e_tree @ size_size ) @ ( B @ ( TA @ huffma1450048681e_tree @ size_size ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_tree_Osize_I4_J) ).
thf(512,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1450048681e_tree @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( TA @ huffma1450048681e_tree @ size_size ) @ ( B @ ( TA @ huffma1450048681e_tree @ size_size ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(19,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA,E: nat] :
( ( D @ ( E @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_tree_Osimps_I3_J) ).
thf(201,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA,E: nat] :
( ( D @ ( E @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
int @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(220,plain,
int @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(51,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Suc__not__Zero) ).
thf(302,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Suc__inject) ).
thf(160,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__right__imp__eq) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_tree_Osimps_I6_J) ).
thf(275,plain,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_nat_Oinject) ).
thf(165,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_tree_Osimps_I5_J) ).
thf(566,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(18,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_n__not__Suc__n) ).
thf(197,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(62,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat_Osimps_I3_J) ).
thf(361,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(90,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__induct) ).
thf(461,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_of__nat__add) ).
thf(551,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero @ suc ) )
<=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_add__is__1) ).
thf(324,plain,
! [A: nat,B: nat] :
( ( ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero @ suc ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero @ suc ) )
=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(29,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(224,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_tree_Orecs_I2_J) ).
thf(488,plain,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(30,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(225,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__Suc) ).
thf(554,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(112,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(547,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_consistent_Osimps_I1_J) ).
thf(212,plain,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(69,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(393,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(103,axiom,
! [A: nat] :
( ( A @ suc @ nat_size )
= ( nat @ zero_zero @ suc @ ( A @ nat_size @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_nat_Osize_I2_J) ).
thf(515,plain,
! [A: nat] :
( ( A @ suc @ nat_size )
= ( nat @ zero_zero @ suc @ ( A @ nat_size @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(89,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Zero__neq__Suc) ).
thf(457,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(129,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(120,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(569,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_tree_Orecs_I1_J) ).
thf(503,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add_Ocomm__neutral) ).
thf(266,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(110,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Nat_Oadd__0__right) ).
thf(541,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zadd__int) ).
thf(398,plain,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(108,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: nat,C: TA @ huffma1450048681e_tree,D: TA] :
( ( ~ ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ) )
& ( ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( A @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ) )
& ( ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( C @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_depth_Osimps_I2_J) ).
thf(530,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: nat,C: TA @ huffma1450048681e_tree,D: TA] :
( ( ~ ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ) )
& ( ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( A @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ) )
& ( ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( C @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(50,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Suc__neq__Zero) ).
thf(298,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(122,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(573,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(84,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ( ( A @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ huffma1134658180e_cost ) )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_height__0__imp__cost__0) ).
thf(444,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ( ( A @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ huffma1134658180e_cost ) )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(118,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_nat_Osimps_I2_J) ).
thf(562,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(79,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( A @ ( TA @ huffma1134658180e_cost ) @ ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma1134658180e_cost ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_cost_Osimps_I2_J) ).
thf(423,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( A @ ( TA @ huffma1134658180e_cost ) @ ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma1134658180e_cost ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add__0__iff) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(77,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA] :
( ( D @ ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( D @ ( A @ ( TA @ huffma1352802255e_freq ) ) @ ( D @ ( B @ ( TA @ huffma1352802255e_freq ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_freq_Osimps_I2_J) ).
thf(413,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA] :
( ( D @ ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( D @ ( A @ ( TA @ huffma1352802255e_freq ) ) @ ( D @ ( B @ ( TA @ huffma1352802255e_freq ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(125,axiom,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_int__if__cong) ).
thf(579,plain,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(47,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree] :
( ( A @ ( B @ ( TA @ huffma921447403eTrees ) ) )
= ( A @ ( B @ ( A @ ( TA @ huffma854194513Weight ) @ ( B @ ( TA @ huffma854194513Weight ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma1146269203erNode ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_uniteTrees__def) ).
thf(291,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree] :
( ( A @ ( B @ ( TA @ huffma921447403eTrees ) ) )
= ( A @ ( B @ ( A @ ( TA @ huffma854194513Weight ) @ ( B @ ( TA @ huffma854194513Weight ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma1146269203erNode ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__is__0) ).
thf(281,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(20,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Suc__n__not__n) ).
thf(204,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zero__reorient) ).
thf(187,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(451,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(101,axiom,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_zadd__int__left) ).
thf(509,plain,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_add__eq__self__zero) ).
thf(271,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(21,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(208,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(387,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(96,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_plus__nat_Oadd__0) ).
thf(494,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(55,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(323,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_transfer__int__nat__relations_I1_J) ).
thf(251,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ( A @ ( TA @ huffma1518433673istent ) )
=> ? [B: TA] :
( ( ( B @ ( A @ ( TA @ huffma410068972_depth ) ) )
= ( A @ ( TA @ huffma945805758height ) ) )
& ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_exists__at__height) ).
thf(155,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
( ( A @ ( TA @ huffma1518433673istent ) )
=> ? [B: TA] :
( ( ( B @ ( A @ ( TA @ huffma410068972_depth ) ) )
= ( A @ ( TA @ huffma945805758height ) ) )
& ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(521,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_nat__add__left__commute) ).
thf(278,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(31,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(226,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__0) ).
thf(394,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: nat,C: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( TA @ huffma1926487300e_size ) ) )
= ( nat @ zero_zero @ suc @ ( A @ ( C @ ( nat @ ( TA @ aa ) ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_tree_Osize_I1_J) ).
thf(306,plain,
! [TA: $tType,A: TA,B: nat,C: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( TA @ huffma1926487300e_size ) ) )
= ( nat @ zero_zero @ suc @ ( A @ ( C @ ( nat @ ( TA @ aa ) ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_double__zero__sym) ).
thf(426,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(548,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(22,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(209,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__0__left) ).
thf(557,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(49,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma83463279weight ) )
= ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_weight_Osimps_I2_J) ).
thf(295,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma83463279weight ) )
= ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(83,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_not0__implies__Suc) ).
thf(441,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add__Suc__shift) ).
thf(544,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_int__int__eq) ).
thf(175,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_tree_Osimps_I1_J) ).
thf(143,plain,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_of__nat__0) ).
thf(497,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(86,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(450,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(524,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(465,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(34,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA @ huffma1450048681e_tree,E: TA @ huffma1450048681e_tree,F: nat] :
( ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_tree_Osimps_I2_J) ).
thf(231,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA @ huffma1450048681e_tree,E: TA @ huffma1450048681e_tree,F: nat] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_height_Osimps_I1_J) ).
thf(390,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(14,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(186,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__imp__eq) ).
thf(401,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(36,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(246,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_add__right__cancel) ).
thf(433,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(214,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nat__add__commute) ).
thf(447,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(410,plain,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma854194513Weight ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_cachedWeight_Osimps_I1_J) ).
thf(183,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma854194513Weight ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(64,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_nat__add__assoc) ).
thf(373,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(35,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(242,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(341,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_cost_Osimps_I1_J) ).
thf(506,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(16,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(195,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(48,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(294,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
! [A: a] :
( ( A @ ( t_2 @ ( t_1 @ ( a @ huffma921447403eTrees ) ) @ ( a @ huffma1352802255e_freq ) ) )
= ( A @ ( t_2 @ ( a @ huffma1352802255e_freq ) ) @ ( A @ ( t_1 @ ( a @ huffma1352802255e_freq ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: a] :
( ( A @ ( t_2 @ ( t_1 @ ( a @ huffma921447403eTrees ) ) @ ( a @ huffma1352802255e_freq ) ) )
= ( A @ ( t_2 @ ( a @ huffma1352802255e_freq ) ) @ ( A @ ( t_1 @ ( a @ huffma1352802255e_freq ) ) @ ( nat @ plus_plus ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(126,plain,
~ ! [A: a] :
( ( A @ ( t_2 @ ( t_1 @ ( a @ huffma921447403eTrees ) ) @ ( a @ huffma1352802255e_freq ) ) )
= ( A @ ( t_2 @ ( a @ huffma1352802255e_freq ) ) @ ( A @ ( t_1 @ ( a @ huffma1352802255e_freq ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__nat__eq__iff) ).
thf(136,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,axiom,
int @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(227,plain,
int @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(53,axiom,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C != B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_freq_Osimps_I1_J) ).
thf(309,plain,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C != B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(117,axiom,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_transfer__int__nat__numerals_I1_J) ).
thf(560,plain,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__Suc__right) ).
thf(491,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(88,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( TA @ huffma1926487300e_size ) ) )
= ( nat @ zero_zero @ suc @ ( A @ ( D @ ( TA @ huffma1926487300e_size ) ) @ ( B @ ( D @ ( TA @ huffma1926487300e_size ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_tree_Osize_I2_J) ).
thf(454,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( TA @ huffma1926487300e_size ) ) )
= ( nat @ zero_zero @ suc @ ( A @ ( D @ ( TA @ huffma1926487300e_size ) ) @ ( B @ ( D @ ( TA @ huffma1926487300e_size ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(589,plain,
$false,
inference(e,[status(thm)],[404,575,365,518,468,352,217,247,379,440,269,500,538,570,344,196,416,152,228,316,376,211,485,353,348,574,397,221,132,133,527,248,512,201,220,302,160,407,275,165,566,197,361,461,551,324,224,488,225,554,547,212,393,515,457,129,569,503,266,541,398,530,298,573,444,562,423,259,413,579,291,281,204,187,451,509,271,208,387,494,323,251,155,521,278,226,394,306,426,548,209,557,295,441,544,175,143,497,450,524,465,231,390,186,401,246,433,214,447,410,183,373,242,341,506,195,294,126,136,227,309,560,491,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW538_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n005.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 16:11:16 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.68/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/0.95 % [INFO] Parsing done (224ms).
% 1.34/0.96 % [INFO] Running in sequential loop mode.
% 2.32/1.36 % [INFO] eprover registered as external prover.
% 2.32/1.37 % [INFO] Scanning for conjecture ...
% 2.75/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 2.95/1.64 % [INFO] Axiom selection finished. Selected 123 axioms (removed 2 axioms).
% 3.52/1.86 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.52/1.89 % [INFO] Type checking passed.
% 3.83/1.90 % [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 ...
% 4.44/2.16 % [INFO] [Domain constraints] Detected constraint on bool
% 4.44/2.17 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 9.01/3.20 % External prover 'e' found a proof!
% 9.01/3.20 % [INFO] Killing All external provers ...
% 9.01/3.20 % Time passed: 2694ms (effective reasoning time: 2233ms)
% 9.01/3.20 % 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)>
% 9.01/3.20 % 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
% 9.01/3.20 % No. of inferences in proof: 250
% 9.01/3.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2694 ms resp. 2233 ms w/o parsing
% 9.01/3.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.01/3.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------