%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW533_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 : n012.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 09:10:45 AM UTC 2026
% Result : Theorem 16.54s 6.91s
% Output : Refutation 17.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 136
% Syntax : Number of formulae : 274 ( 117 unt; 0 typ; 0 def)
% Number of atoms : 1099 ( 219 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 4592 ( 106 ~; 20 |; 56 &;4170 @)
% ( 22 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 9 con; 0-5 aty)
% Number of variables : 725 ( 0 ^; 715 !; 10 ?; 725 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(semilattice_inf_decl,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(bounded_lattice_bot_decl,type,
bounded_lattice_bot:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(huffma675207370phabet_decl,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > ( bool @ ( TA @ fun ) ) ) ).
thf(huffma1516701463abet_F_decl,type,
huffma1516701463abet_F:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree @ list ) > ( bool @ ( TA @ fun ) ) ) ).
thf(huffma1518433673istent_decl,type,
huffma1518433673istent:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > $o ) ).
thf(huffma594769176tent_F_decl,type,
huffma594769176tent_F:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree @ list ) > $o ) ).
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(huffma409467474freq_F_decl,type,
huffma409467474freq_F:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree @ list ) > TA > nat ) ).
thf(huffma945805758height_decl,type,
huffma945805758height:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(huffma632063779ight_F_decl,type,
huffma632063779ight_F:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree @ list ) > 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(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(dropWhile_decl,type,
dropWhile:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(lexn_decl,type,
lexn:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > nat > ( bool @ ( TA @ list @ ( TA @ list @ product_prod ) @ fun ) ) ) ).
thf(linord467138063of_set_decl,type,
linord467138063of_set:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_rec_decl,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_size_decl,type,
list_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ list ) > nat ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(set_decl,type,
set:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( TA @ fun ) ) ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
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(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a1_decl,type,
a1: a ).
thf(118,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_10_tree_Orecs_I1_J) ).
thf(545,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)],[118]) ).
thf(65,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA] :
( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_notin__alphabet__imp__freq__0) ).
thf(352,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA] :
( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(365,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1,conjecture,
a @ huffma1450048681e_tree @ nil @ ( a @ huffma1450048681e_tree @ set ) @ ( a1 @ ( a1 @ ( a @ huffma1450048681e_tree @ nil @ ( a @ huffma409467474freq_F ) ) @ ( a @ huffma2021818691e_Leaf ) ) @ ( a @ huffma1450048681e_tree @ member @ ( bool @ ( bool @ ( a @ huffma1450048681e_tree @ fun ) @ fun ) @ ( a @ huffma1450048681e_tree @ aa ) ) ) @ ( bool @ ( bool @ ( a @ huffma1450048681e_tree @ fun ) @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( a @ huffma1450048681e_tree @ nil @ ( a @ huffma1450048681e_tree @ set ) @ ( a1 @ ( a1 @ ( a @ huffma1450048681e_tree @ nil @ ( a @ huffma409467474freq_F ) ) @ ( a @ huffma2021818691e_Leaf ) ) @ ( a @ huffma1450048681e_tree @ member @ ( bool @ ( bool @ ( a @ huffma1450048681e_tree @ fun ) @ fun ) @ ( a @ huffma1450048681e_tree @ aa ) ) ) @ ( bool @ ( bool @ ( a @ huffma1450048681e_tree @ fun ) @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(138,plain,
~ ( a @ huffma1450048681e_tree @ nil @ ( a @ huffma1450048681e_tree @ set ) @ ( a1 @ ( a1 @ ( a @ huffma1450048681e_tree @ nil @ ( a @ huffma409467474freq_F ) ) @ ( a @ huffma2021818691e_Leaf ) ) @ ( a @ huffma1450048681e_tree @ member @ ( bool @ ( bool @ ( a @ huffma1450048681e_tree @ fun ) @ fun ) @ ( a @ huffma1450048681e_tree @ aa ) ) ) @ ( bool @ ( bool @ ( a @ huffma1450048681e_tree @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(80,axiom,
bool @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(408,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(42,axiom,
a @ huffma1450048681e_tree @ nil @ ( a @ huffma1516701463abet_F ) @ ( a1 @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Nil_I3_J) ).
thf(276,plain,
a @ huffma1450048681e_tree @ nil @ ( a @ huffma1516701463abet_F ) @ ( a1 @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(76,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ! [D: TA] :
( ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C != D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_disjoint__iff__not__equal) ).
thf(384,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ! [C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ! [D: TA] :
( ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C != D ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ! [D: TA] :
( ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma1516701463abet_F ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_alphabet_092_060_094isub_062F_Osimps_I1_J) ).
thf(550,plain,
! [TA: $tType] :
( ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma1516701463abet_F ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_ord__less__eq__trans) ).
thf(142,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(107,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ list_ex1 ) ) )
<=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_list__ex1__iff) ).
thf(500,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ list_ex1 ) ) )
=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(340,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(153,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(84,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_IntD2) ).
thf(417,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(36,axiom,
nat @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(257,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(128,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_empty__def) ).
thf(570,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(72,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_22_tree_Oexhaust) ).
thf(372,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)],[72]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_inf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).
thf(559,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_inf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zero__reorient) ).
thf(228,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)],[27]) ).
thf(46,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__Collect__eq) ).
thf(289,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma632063779ight_F ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_height_092_060_094isub_062F_Osimps_I1_J) ).
thf(316,plain,
! [TA: $tType] :
( ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma632063779ight_F ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Int__assoc) ).
thf(475,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_not__less__iff__gr__or__eq) ).
thf(164,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( ( B = A )
| ( B @ ( A @ ( TA @ ord_less ) ) ) )
=> ~ ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(134,axiom,
a @ huffma1450048681e_tree @ nil @ ( a @ huffma594769176tent_F ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Nil_I1_J) ).
thf(591,plain,
a @ huffma1450048681e_tree @ nil @ ( a @ huffma594769176tent_F ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(55,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_15_tree_Osimps_I4_J) ).
thf(321,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)],[55]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_linorder__cases) ).
thf(238,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(101,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1518433673istent ) )
<=> ( ( ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( A @ ( TA @ huffma1518433673istent ) )
& ( B @ ( TA @ huffma1518433673istent ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_consistent_Osimps_I2_J) ).
thf(480,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( ( ( ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( A @ ( TA @ huffma1518433673istent ) )
& ( B @ ( TA @ huffma1518433673istent ) ) )
=> ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1518433673istent ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1518433673istent ) )
=> ( ( ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( A @ ( TA @ huffma1518433673istent ) )
& ( B @ ( TA @ huffma1518433673istent ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_order__less__imp__not__eq) ).
thf(211,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,axiom,
nat @ lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).
thf(253,plain,
nat @ lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).
thf(397,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).
thf(280,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(88,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Int__commute) ).
thf(428,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(113,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Int__left__absorb) ).
thf(527,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ set ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_set__empty2) ).
thf(307,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ set ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ set ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ linord467138063of_set ) )
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_sorted__list__of__set__empty) ).
thf(452,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ linord467138063of_set ) )
= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_order__less__trans) ).
thf(248,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_list_Osimps_I4_J) ).
thf(439,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(40,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_IntE) ).
thf(270,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
<=> ( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_linorder__neq__iff) ).
thf(201,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(75,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Int__absorb) ).
thf(381,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(48,axiom,
bool @ lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).
thf(302,plain,
bool @ lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(125,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_7_tree_Osimps_I5_J) ).
thf(561,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)],[125]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_order__less__asym) ).
thf(260,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).
thf(349,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(57,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(329,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)],[57]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(522,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(104,axiom,
bool @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(493,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Int__iff) ).
thf(324,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(25,axiom,
nat @ semilattice_inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).
thf(224,plain,
nat @ semilattice_inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_inf__left__idem) ).
thf(156,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(110,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_20_tree_Orecs_I2_J) ).
thf(519,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)],[110]) ).
thf(131,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) )
<=> ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dropWhile__eq__Nil__conv) ).
thf(578,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( A @ ( B @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( B @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) )
=> ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(102,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(488,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(26,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__nat__zero__code) ).
thf(225,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).
thf(537,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
~ ( TA @ bot_bot @ ( A @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_not__less__bot) ).
thf(173,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
~ ( TA @ bot_bot @ ( A @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(71,axiom,
bool @ bounded_lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).
thf(371,plain,
bool @ bounded_lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(31,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_order__less__imp__not__eq2) ).
thf(244,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(68,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 @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_exists__at__height) ).
thf(360,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 @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(114,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_ex__in__conv) ).
thf(530,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(132,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_19_tree_Osimps_I6_J) ).
thf(586,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)],[132]) ).
thf(87,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Int__empty__right) ).
thf(425,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(108,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree @ list,B: TA] :
( ~ ( A @ ( TA @ huffma1516701463abet_F ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ huffma409467474freq_F ) ) )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_notin__alphabet_092_060_094isub_062F__imp__freq_092_060_094isub_062F__0) ).
thf(513,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree @ list,B: TA] :
( ~ ( A @ ( TA @ huffma1516701463abet_F ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ huffma409467474freq_F ) ) )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(129,axiom,
( ( a @ huffma1450048681e_tree @ nil @ ( a @ huffma632063779ight_F ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Nil_I2_J) ).
thf(573,plain,
( ( a @ huffma1450048681e_tree @ nil @ ( a @ huffma632063779ight_F ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(375,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(95,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_all__not__in__conv) ).
thf(445,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_order__less__not__sym) ).
thf(236,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(116,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_list_Osize_I1_J) ).
thf(540,plain,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(11,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(159,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
nat @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(172,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_IntI) ).
thf(274,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(85,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_equals0I) ).
thf(419,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(74,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(377,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(127,axiom,
! [TA: $tType,A: TA,B: TA @ huffma1450048681e_tree,C: TA @ huffma1450048681e_tree] :
( ( ( B @ ( TA @ huffma675207370phabet ) @ ( C @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( C @ ( TA @ huffma675207370phabet ) @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_freq__0__right) ).
thf(567,plain,
! [TA: $tType,A: TA,B: TA @ huffma1450048681e_tree,C: TA @ huffma1450048681e_tree] :
( ( ( B @ ( TA @ huffma675207370phabet ) @ ( C @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( C @ ( TA @ huffma675207370phabet ) @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(91,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma409467474freq_F ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_freq_092_060_094isub_062F_Osimps_I1_J) ).
thf(434,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma409467474freq_F ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(49,axiom,
bool @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(303,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(105,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_11_tree_Osize_I3_J) ).
thf(494,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)],[105]) ).
thf(62,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_equals0D) ).
thf(345,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(136,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(594,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(9,axiom,
nat @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(155,plain,
nat @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(79,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_3_tree_Osimps_I1_J) ).
thf(399,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)],[79]) ).
thf(97,axiom,
! [TA: $tType,A: TA,B: TA @ huffma1450048681e_tree,C: TA @ huffma1450048681e_tree] :
( ( ( B @ ( TA @ huffma675207370phabet ) @ ( C @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( B @ ( TA @ huffma675207370phabet ) @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_freq__0__left) ).
thf(455,plain,
! [TA: $tType,A: TA,B: TA @ huffma1450048681e_tree,C: TA @ huffma1450048681e_tree] :
( ( ( B @ ( TA @ huffma675207370phabet ) @ ( C @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( B @ ( TA @ huffma675207370phabet ) @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(89,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list__ex1__simps_I1_J) ).
thf(431,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(30,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_less__zeroE) ).
thf(241,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(103,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dropWhile_Osimps_I1_J) ).
thf(490,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ dropWhile ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(589,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_order__less__imp__not__less) ).
thf(162,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(119,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(548,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(109,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(516,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(61,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_24_height_Osimps_I1_J) ).
thf(342,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)],[61]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(355,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(122,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Int__def) ).
thf(553,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(98,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( D @ ( TA @ set ) @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( ( D @ ( B @ ( TA @ dropWhile ) ) )
= ( C @ ( A @ ( TA @ dropWhile ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_dropWhile__cong) ).
thf(458,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( D @ ( TA @ set ) @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( ( D @ ( B @ ( TA @ dropWhile ) ) )
= ( C @ ( A @ ( TA @ dropWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(525,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(47,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ set ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_set__empty) ).
thf(295,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ set ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ set ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(45,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_12_freq_Osimps_I1_J) ).
thf(282,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)],[45]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_linorder__neqE) ).
thf(150,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(81,axiom,
bool @ bounded_lattice_bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).
thf(409,plain,
bool @ bounded_lattice_bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(18,axiom,
nat @ bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
thf(182,plain,
nat @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(59,axiom,
! [TA: $tType] : ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma594769176tent_F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_consistent_092_060_094isub_062F_Osimps_I1_J) ).
thf(338,plain,
! [TA: $tType] : ( TA @ huffma1450048681e_tree @ nil @ ( TA @ huffma594769176tent_F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(8,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(154,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ inf_inf ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_inf__bot__right) ).
thf(175,plain,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ inf_inf ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_consistent_Osimps_I1_J) ).
thf(314,plain,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( A @ ( TA @ collect ) @ ( B @ ( TA @ collect ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Collect__conj__eq) ).
thf(497,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) )
= ( A @ ( TA @ collect ) @ ( B @ ( TA @ collect ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(33,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(250,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(123,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_14_tree_Osimps_I3_J) ).
thf(556,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)],[123]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ set ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_List_Oset_Osimps_I1_J) ).
thf(368,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ set ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(54,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
? [B: TA] : ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_exists__in__alphabet) ).
thf(319,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
? [B: TA] : ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(50,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_13_depth_Osimps_I1_J) ).
thf(304,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)],[50]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] :
~ ( A @ ( A @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order__less__irrefl) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] :
~ ( A @ ( A @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(64,axiom,
bool @ semilattice_inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).
thf(351,plain,
bool @ semilattice_inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(3,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree] :
( ( B @ ( TA @ huffma945805758height ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( B @ ( TA @ huffma1518433673istent ) )
=> ( ( ( B @ ( TA @ huffma675207370phabet ) )
= ( A @ ( TA @ huffma675207370phabet ) ) )
=> ( A @ ( TA @ huffma945805758height ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_height__gt__0__alphabet__eq__imp__height__gt__0) ).
thf(139,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree] :
( ( B @ ( TA @ huffma945805758height ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( B @ ( TA @ huffma1518433673istent ) )
=> ( ( ( B @ ( TA @ huffma675207370phabet ) )
= ( A @ ( TA @ huffma675207370phabet ) ) )
=> ( A @ ( TA @ huffma945805758height ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(90,axiom,
bool @ bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(433,plain,
bool @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(100,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(478,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(120,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(549,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( TA @ collect ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Int__Collect) ).
thf(410,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( TA @ collect ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( TA @ collect ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(39,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_neq0__conv) ).
thf(262,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_ord__eq__less__trans) ).
thf(146,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,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_17_tree_Osimps_I2_J) ).
thf(190,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)],[20]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ~ ( B @ ( A @ ( TA @ ord_less ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_linorder__antisym__conv3) ).
thf(183,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) )
& ( ~ ( B @ ( A @ ( TA @ ord_less ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(422,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_list_Orecs_I1_J) ).
thf(564,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(67,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_IntD1) ).
thf(358,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: bool,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_order__less__imp__triv) ).
thf(437,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: bool,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(83,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_emptyE) ).
thf(415,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(77,axiom,
! [TA: $tType,A: nat @ ( TA @ fun ),B: nat,C: TA @ list,D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( nat @ ( TA @ aa ) ) ) @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ list_size ) ) @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_list__size__estimation) ).
thf(395,plain,
! [TA: $tType,A: nat @ ( TA @ fun ),B: nat,C: TA @ list,D: TA] :
( ( C @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( nat @ ( TA @ aa ) ) ) @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ list_size ) ) @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(58,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Collect__empty__eq) ).
thf(332,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_bot__apply) ).
thf(575,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(137,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Int__empty__left) ).
thf(596,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__imp__neq) ).
thf(178,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Int__left__commute) ).
thf(277,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(94,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( nat @ zero_zero @ ( A @ ( TA @ lexn ) ) )
= ( bool @ ( TA @ list @ ( TA @ list @ product_prod ) @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_lexn_Osimps_I1_J) ).
thf(442,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( nat @ zero_zero @ ( A @ ( TA @ lexn ) ) )
= ( bool @ ( TA @ list @ ( TA @ list @ product_prod ) @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_linorder__less__linear) ).
thf(254,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(117,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__iff) ).
thf(543,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( A
!= ( TA @ bot_bot ) )
<=> ( A @ ( TA @ bot_bot @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_bot__less) ).
thf(215,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( ( A @ ( TA @ bot_bot @ ( TA @ ord_less ) ) )
=> ( A
!= ( TA @ bot_bot ) ) )
& ( ( A
!= ( TA @ bot_bot ) )
=> ( A @ ( TA @ bot_bot @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_order__less__asym_H) ).
thf(222,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(135,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(592,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(607,plain,
$false,
inference(e,[status(thm)],[545,352,365,138,408,276,384,550,142,500,340,153,417,257,570,372,559,228,289,316,475,164,591,321,238,480,211,253,397,280,428,527,307,452,248,439,270,201,381,302,561,260,349,329,522,493,324,224,156,519,578,488,225,537,173,371,244,360,530,586,425,513,573,375,445,236,540,159,172,274,419,377,567,434,303,494,345,594,155,399,455,431,241,490,589,162,548,516,342,355,553,458,525,295,282,150,409,182,338,154,175,314,497,250,556,368,319,304,258,351,139,433,478,549,410,262,146,190,183,422,564,358,437,415,395,332,575,596,178,277,442,254,543,215,222,592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW533_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % 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
% 0.05/0.33 % Computer : n012.cluster.edu
% 0.05/0.33 % Model : x86_64 x86_64
% 0.05/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.33 % Memory : 8046.5625MB
% 0.05/0.33 % OS : Linux 6.8.0-71-generic
% 0.05/0.33 % CPULimit : 300
% 0.05/0.33 % WCLimit : 300
% 0.05/0.33 % DateTime : Sat Sep 26 16:10:36 UTC 2026
% 0.05/0.33 % CPUTime :
% 0.05/0.33 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
% 0.49/0.63 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.00/0.81 % [INFO] Parsing done (180ms).
% 1.00/0.82 % [INFO] Running in sequential loop mode.
% 1.67/1.03 % [INFO] eprover registered as external prover.
% 1.67/1.04 % [INFO] Scanning for conjecture ...
% 1.98/1.14 % [INFO] Found a conjecture (or negated_conjecture) and 135 axioms. Running axiom selection ...
% 2.23/1.21 % [INFO] Axiom selection finished. Selected 135 axioms (removed 0 axioms).
% 2.62/1.34 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.62/1.36 % [INFO] Type checking passed.
% 2.62/1.37 % [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 ...
% 3.54/1.65 % [INFO] [Domain constraints] Detected constraint on bool
% 3.54/1.65 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 16.54/6.91 % External prover 'e' found a proof!
% 16.54/6.91 % [INFO] Killing All external provers ...
% 16.54/6.91 % Time passed: 6503ms (effective reasoning time: 6086ms)
% 16.54/6.91 % 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)>
% 16.54/6.91 % Axioms used in derivation (135): fact_58_Int__empty__left, help_fconj_1_1_U, fact_20_tree_Orecs_I2_J, arity_Nat_Onat___Orderings_Obot, fact_98_inf__left__idem, fact_42_bot__fun__def, arity_HOL_Obool___Orderings_Oorder, fact_11_tree_Osize_I3_J, fact_17_tree_Osimps_I2_J, help_COMBS_1_1_U, fact_37_all__not__in__conv, arity_HOL_Obool___Orderings_Oord, fact_26_list__ex1__simps_I1_J, arity_HOL_Obool___Orderings_Opreorder, help_fconj_3_1_U, arity_fun___Orderings_Obot, fact_22_tree_Oexhaust, fact_96_neq0__conv, fact_88_not__less__iff__gr__or__eq, fact_86_Int__def, fact_32_zero__reorient, fact_47_list_Orecs_I1_J, fact_63_IntD1, fact_25_list_Osize_I1_J, arity_fun___Orderings_Oord, fact_15_tree_Osimps_I4_J, fact_7_tree_Osimps_I5_J, fact_12_freq_Osimps_I1_J, fact_67_ord__eq__less__trans, arity_Nat_Onat___Orderings_Opreorder, fact_30_set__empty, fact_89_linorder__neq__iff, fact_65_order__less__trans, fact_61_linorder__cases, fact_38_bot__apply, fact_75_mem__def, fact_71_order__less__imp__not__eq, arity_fun___Lattices_Olattice, fact_43_sorted__list__of__set__empty, fact_53_IntE, fact_9_consistent_Osimps_I1_J, arity_HOL_Obool___Lattices_Obounded__lattice__bot, fact_81_Int__Collect, fact_48_notin__alphabet__imp__freq__0, arity_HOL_Obool___Orderings_Olinorder, fact_41_equals0D, fact_85_Int__commute, fact_72_order__less__imp__not__less, help_fFalse_1_1_T, fact_56_disjoint__iff__not__equal, fact_51_height__gt__0__alphabet__eq__imp__height__gt__0, fact_16_dropWhile__eq__Nil__conv, fact_82_Int__left__commute, fact_74_ext, fact_34_Collect__empty__eq, fact_79_linorder__antisym__conv3, fact_29_set__empty2, fact_2_Nil_I3_J, fact_4_consistent_092_060_094isub_062F_Osimps_I1_J, help_COMBB_1_1_U, fact_40_ex__in__conv, fact_87_Int__absorb, arity_HOL_Obool___Lattices_Osemilattice__inf, arity_fun___Orderings_Oorder, fact_21_dropWhile__cong, arity_Nat_Onat___Orderings_Olinorder, fact_57_Int__empty__right, fact_76_Collect__def, arity_fun___Orderings_Opreorder, fact_64_order__less__asym, fact_54_IntI, help_fconj_2_1_U, fact_18_dropWhile_Osimps_I1_J, fact_33_emptyE, fact_55_Int__iff, fact_6_height_092_060_094isub_062F_Osimps_I1_J, fact_45_lexn_Osimps_I1_J, fact_97_inf__bot__right, fact_44_equals0I, arity_Nat_Onat___Lattices_Olattice, arity_fun___Lattices_Osemilattice__inf, fact_50_exists__in__alphabet, fact_46_exists__at__height, fact_36_empty__Collect__eq, fact_49_consistent_Osimps_I2_J, fact_8_notin__alphabet_092_060_094isub_062F__imp__freq_092_060_094isub_062F__0, fact_39_empty__def, fact_80_Int__assoc, fact_35_empty__iff, arity_Nat_Onat___Groups_Ozero, fact_31_list__ex1__iff, arity_Nat_Onat___Orderings_Oord, fact_93_freq__0__right, fact_91_order__less__irrefl, arity_Nat_Onat___Lattices_Osemilattice__inf, fact_60_not__less__bot, fact_27_alphabet_092_060_094isub_062F_Osimps_I1_J, help_COMBK_1_1_U, fact_73_order__less__not__sym, arity_HOL_Obool___Lattices_Obounded__lattice, fact_69_order__less__imp__triv, fact_94_less__zeroE, fact_77_less__imp__neq, fact_10_tree_Orecs_I1_J, fact_62_IntD2, fact_5_freq_092_060_094isub_062F_Osimps_I1_J, fact_70_order__less__imp__not__eq2, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, fact_68_order__less__asym_H, fact_83_Int__left__absorb, fact_23_list_Osimps_I4_J, fact_13_depth_Osimps_I1_J, help_fFalse_1_1_U, fact_28_List_Oset_Osimps_I1_J, arity_HOL_Obool___Lattices_Olattice, arity_Nat_Onat___Orderings_Oorder, fact_66_ord__less__eq__trans, fact_95_less__nat__zero__code, help_pp_1_1_U, fact_78_linorder__neqE, fact_52_freq__0__left, arity_fun___Lattices_Obounded__lattice__bot, fact_59_bot__less, fact_90_Collect__conj__eq, fact_1_Nil_I2_J, fact_3_tree_Osimps_I1_J, fact_19_tree_Osimps_I6_J, help_pp_2_1_U, arity_fun___Lattices_Obounded__lattice, fact_84_linorder__less__linear, fact_92_list__size__estimation, fact_0_Nil_I1_J, fact_14_tree_Osimps_I3_J, fact_24_height_Osimps_I1_J
% 16.54/6.91 % No. of inferences in proof: 274
% 16.54/6.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6503 ms resp. 6086 ms w/o parsing
% 17.13/7.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.13/7.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------