%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 07:53:02 AM UTC 2026
% Result : Theorem 22.15s 10.49s
% Output : Refutation 23.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 234 ( 151 unt; 0 typ; 0 def)
% Number of atoms : 684 ( 268 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 3798 ( 58 ~; 18 |; 47 &;3578 @)
% ( 17 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 18 con; 0-5 aty)
% Number of variables : 506 ( 0 ^; 486 !; 20 ?; 506 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char1_type,type,
char1: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(nibble_type,type,
nibble: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ fun ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ 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(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bool_size_decl,type,
bool_size: bool > nat ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(abs_decl,type,
abs: dB > dB ).
thf(app_decl,type,
app: dB @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(var_decl,type,
var: nat > dB ).
thf(dB_case_decl,type,
dB_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_size_decl,type,
dB_size: dB > nat ).
thf(lift_decl,type,
lift: dB @ ( nat @ fun ) @ ( dB @ fun ) ).
thf(liftn_decl,type,
liftn: nat > dB > nat > dB ).
thf(subst_decl,type,
subst: dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(substn_decl,type,
substn: dB > dB > nat > dB ).
thf(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(monoid_add_listsum_decl,type,
monoid_add_listsum:
!>[TA: $tType] : ( ( TA @ list ) > TA ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(nat_size_decl,type,
nat_size: nat > nat ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(char_decl,type,
char: nibble > nibble > char1 ).
thf(char_case_decl,type,
char_case:
!>[TA: $tType] : ( ( TA @ ( nibble @ fun ) @ ( nibble @ fun ) ) > char1 > TA ) ).
thf(char_rec_decl,type,
char_rec:
!>[TA: $tType] : ( ( TA @ ( nibble @ fun ) @ ( nibble @ fun ) ) > char1 > TA ) ).
thf(char_size_decl,type,
char_size: char1 > nat ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a_decl,type,
a: dB ).
thf(b_decl,type,
b: dB ).
thf(bs_decl,type,
bs: dB @ list ).
thf(i_decl,type,
i: nat ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(22,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_subst__Var__IT) ).
thf(217,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_dB_Osimps_I8_J) ).
thf(257,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_size__bool) ).
thf(236,plain,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(107,axiom,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_char_Osimps_I2_J) ).
thf(497,plain,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(62,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_nat__induct) ).
thf(347,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_nat__add__right__cancel) ).
thf(333,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(97,axiom,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_nat_Osize_I3_J) ).
thf(468,plain,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(117,axiom,
i @ ( u @ ( b @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096IT_A_Ib_091u_Pi_093_J_096) ).
thf(555,plain,
i @ ( u @ ( b @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(67,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(365,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(7,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(138,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(108,axiom,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Abs__App__neq__Var__apps) ).
thf(500,plain,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(100,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(472,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(74,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(389,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)],[74]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_add__Suc__right) ).
thf(372,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(109,axiom,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_substn__subst__0) ).
thf(504,plain,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(65,axiom,
! [A: nat,B: dB,C: dB @ list,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_subst__map) ).
thf(357,plain,
! [A: nat,B: dB,C: dB @ list,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(115,axiom,
! [A: nat,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_lift__map) ).
thf(542,plain,
! [A: nat,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(421,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)],[84]) ).
thf(34,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_app__Var__IT) ).
thf(261,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ var @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(21,axiom,
bs @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Cons_I3_J) ).
thf(216,plain,
bs @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(90,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_nat_Osimps_I3_J) ).
thf(443,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(53,axiom,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_bool_Osize_I1_J) ).
thf(321,plain,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TC,D: TC @ ( TB @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) @ ( C @ ( D @ ( TB @ ( TC @ foldl ) ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ combc ) ) ) ) @ ( TA @ ( TC @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_foldl__map) ).
thf(514,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TC,D: TC @ ( TB @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) @ ( C @ ( D @ ( TB @ ( TC @ foldl ) ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ combc ) ) ) ) @ ( TA @ ( TC @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_73_ext) ).
thf(480,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)],[103]) ).
thf(18,axiom,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dB_Osimps_I12_J) ).
thf(211,plain,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(31,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_substn_Osimps_I2_J) ).
thf(253,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__is__0) ).
thf(280,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_double__zero__sym) ).
thf(243,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(110,axiom,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_char_Orecs) ).
thf(507,plain,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(49,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_liftn__0) ).
thf(312,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(88,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Var__IT) ).
thf(439,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__reorient) ).
thf(381,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)],[73]) ).
thf(75,axiom,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_char_Osize_I2_J) ).
thf(392,plain,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(85,axiom,
! [A: nat] :
( ( A @ suc @ nat_size )
= ( nat @ zero_zero @ suc @ ( A @ nat_size @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_nat_Osize_I2_J) ).
thf(424,plain,
! [A: nat] :
( ( A @ suc @ nat_size )
= ( nat @ zero_zero @ suc @ ( A @ nat_size @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(79,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Lambda) ).
thf(407,plain,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(87,axiom,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Var__apps__eq__Var__apps__conv) ).
thf(429,plain,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(96,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(467,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(57,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_dB_Osimps_I4_J) ).
thf(329,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(55,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Beta) ).
thf(324,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(51,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(317,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(78,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Zero__not__Suc) ).
thf(403,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(8,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_n__not__Suc__n) ).
thf(141,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(225,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(99,axiom,
i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( u @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
thf(471,plain,
i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( u @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(32,axiom,
t @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(256,plain,
t @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(36,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(266,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)],[36]) ).
thf(66,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
<=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_listsp__conj__eq) ).
thf(360,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) )
=> ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) ) )
& ( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(44,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Suc__not__Zero) ).
thf(296,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(71,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_dB_Osize_I1_J) ).
thf(375,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(13,axiom,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( C @ ( D @ char ) )
= ( A @ ( B @ char ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_char_Oinject) ).
thf(176,plain,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ char ) )
= ( A @ ( B @ char ) ) ) )
& ( ( ( C @ ( D @ char ) )
= ( A @ ( B @ char ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
nat @ zero_zero @ ( i @ ( u @ ( b @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( nat @ zero_zero @ ( i @ ( u @ ( b @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ( nat @ zero_zero @ ( i @ ( u @ ( b @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: char1] :
~ ! [B: nibble,C: nibble] :
( A
!= ( C @ ( B @ char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_char_Oexhaust) ).
thf(204,plain,
! [A: char1] :
~ ! [B: nibble,C: nibble] :
( A
!= ( C @ ( B @ char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(116,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Abs__apps__eq__Abs__apps__conv) ).
thf(545,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(81,axiom,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_nat_Osize_I1_J) ).
thf(413,plain,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(12,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_dB_Osimps_I7_J) ).
thf(172,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_liftn_Osimps_I2_J) ).
thf(219,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(274,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)],[39]) ).
thf(52,axiom,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_liftn__lift) ).
thf(318,plain,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(46,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(303,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(38,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_substn__subst__n) ).
thf(271,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(17,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_map__ident) ).
thf(208,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(102,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( B @ ( dB @ size_size ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_dB_Osize_I5_J) ).
thf(477,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( B @ ( dB @ size_size ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(106,axiom,
! [A: char1] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_char__size) ).
thf(494,plain,
! [A: char1] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(54,axiom,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(323,plain,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(104,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_apps__eq__tail__conv) ).
thf(483,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( C = A )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__right__cancel) ).
thf(155,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(94,axiom,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_nat__size) ).
thf(462,plain,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(61,axiom,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_bool_Osize_I3_J) ).
thf(345,plain,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(68,axiom,
! [A: nat] :
( ( A @ suc @ ( nat @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( nat @ size_size ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_nat_Osize_I4_J) ).
thf(367,plain,
! [A: nat] :
( ( A @ suc @ ( nat @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( nat @ size_size ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(77,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Var__apps__neq__Abs__apps) ).
thf(399,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(92,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_nat_Oexhaust) ).
thf(455,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(47,axiom,
! [A: dB] :
( ( A @ abs @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_dB_Osize_I3_J) ).
thf(306,plain,
! [A: dB] :
( ( A @ abs @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(26,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Osimps_I2_J) ).
thf(226,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_dB_Osimps_I1_J) ).
thf(162,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ var )
= ( A @ var ) ) )
& ( ( ( B @ var )
= ( A @ var ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(342,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)],[60]) ).
thf(64,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_lift__IT) ).
thf(355,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_nat_Oinject) ).
thf(145,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(80,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_dB_Osimps_I5_J) ).
thf(409,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(35,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_dB_Osimps_I11_J) ).
thf(263,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(89,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_True) ).
thf(441,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(69,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(370,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)],[69]) ).
thf(98,axiom,
nat @ zero_zero @ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
thf(470,plain,
nat @ zero_zero @ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(114,axiom,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_char_Osize_I1_J) ).
thf(539,plain,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(30,axiom,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_size__literal__def) ).
thf(250,plain,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(95,axiom,
! [A: dB @ list] :
( ( A @ ( it @ ( dB @ listsp ) ) )
=> ( A @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_lifts__IT) ).
thf(465,plain,
! [A: dB @ list] :
( ( A @ ( it @ ( dB @ listsp ) ) )
=> ( A @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(113,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
<=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_IT_Osimps) ).
thf(517,plain,
! [A: dB] :
( ( ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) )
=> ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
& ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(63,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Zero__neq__Suc) ).
thf(351,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(83,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_subst__App) ).
thf(418,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(111,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zero__induct) ).
thf(510,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(19,axiom,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
thf(214,plain,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(42,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nat_Osimps_I2_J) ).
thf(290,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(119,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__Suc) ).
thf(378,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(45,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 @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(300,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 @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(91,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_nat__add__left__cancel) ).
thf(447,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(50,axiom,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_bool_Osize_I4_J) ).
thf(315,plain,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(14,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dB_Osimps_I3_J) ).
thf(190,plain,
! [A: dB,B: dB] :
( ( ( B = A )
=> ( ( B @ abs )
= ( A @ abs ) ) )
& ( ( ( B @ abs )
= ( A @ abs ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,axiom,
! [A: char1] :
( ( A @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_size__char) ).
thf(326,plain,
! [A: char1] :
( ( A @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(28,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Suc__neq__Zero) ).
thf(239,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(59,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(341,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(37,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_subst__eq) ).
thf(268,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(101,axiom,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_dB_Osize_I4_J) ).
thf(474,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(82,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_not0__implies__Suc) ).
thf(415,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(43,axiom,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_bool_Osize_I2_J) ).
thf(294,plain,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Suc__inject) ).
thf(126,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(76,axiom,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dB_Osimps_I9_J) ).
thf(395,plain,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(86,axiom,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_IT_OVar) ).
thf(427,plain,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_subst__lift) ).
thf(459,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__left__cancel) ).
thf(131,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Suc__n__not__n) ).
thf(200,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_lift_Osimps_I2_J) ).
thf(277,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(4,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_dB_Osimps_I6_J) ).
thf(122,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ monoid_add )
=> ! [A: TB @ list] :
( ( A @ ( TA @ zero_zero @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ map ) ) ) @ ( TA @ monoid_add_listsum ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_listsum__0) ).
thf(309,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ monoid_add )
=> ! [A: TB @ list] :
( ( A @ ( TA @ zero_zero @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ map ) ) ) @ ( TA @ monoid_add_listsum ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(20,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(215,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(105,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( B @ dB_size @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_dB_Osize_I2_J) ).
thf(491,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( B @ dB_size @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(24,axiom,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_dB_Osimps_I10_J) ).
thf(222,plain,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(563,plain,
$false,
inference(e,[status(thm)],[217,257,236,497,347,333,468,555,365,138,500,472,389,372,504,357,542,421,261,216,443,321,514,480,211,253,280,243,507,312,439,381,392,424,407,429,467,329,324,317,403,141,225,471,256,266,360,296,375,176,118,204,545,413,172,219,274,318,303,271,208,477,494,323,483,155,462,345,367,399,455,306,226,162,342,355,145,409,263,441,370,470,539,250,465,517,351,418,510,214,290,119,378,300,447,315,190,326,239,341,268,474,415,294,126,395,427,459,131,200,277,122,309,215,491,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.48 % Computer : n003.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 23:38:38 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.46/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.82/1.82 % [INFO] Parsing done (475ms).
% 2.82/1.84 % [INFO] Running in sequential loop mode.
% 4.07/2.44 % [INFO] eprover registered as external prover.
% 4.07/2.45 % [INFO] Scanning for conjecture ...
% 4.71/2.72 % [INFO] Found a conjecture (or negated_conjecture) and 115 axioms. Running axiom selection ...
% 5.33/2.91 % [INFO] Axiom selection finished. Selected 115 axioms (removed 0 axioms).
% 6.29/3.23 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.29/3.28 % [INFO] Type checking passed.
% 6.29/3.28 % [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 ...
% 7.22/3.64 % [INFO] [Domain constraints] Detected constraint on bool
% 7.22/3.65 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 7.43/3.77 % [INFO] [Domain constraints] Detected constraint on bool
% 7.43/3.77 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 22.15/10.48 % External prover 'e' found a proof!
% 22.15/10.49 % [INFO] Killing All external provers ...
% 22.15/10.49 % Time passed: 9794ms (effective reasoning time: 8634ms)
% 22.15/10.49 % 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)>
% 22.15/10.49 % Axioms used in derivation (115): fact_34_bool_Osize_I3_J, fact_55_apps__eq__tail__conv, help_COMBS_1_1_U, fact_18_dB_Osimps_I1_J, fact_70_n__not__Suc__n, fact_43_char_Osize_I2_J, help_fconj_3_1_U, fact_56_Var__apps__eq__Var__apps__conv, fact_24_app__Var__IT, fact_15_Cons_I3_J, fact_44_char_Oinject, fact_88_add__left__cancel, help_COMBI_1_1_U, fact_8__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096, fact_59_Beta, fact_7__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096, fact_37_liftn__0, fact_61_Lambda, help_fTrue_1_1_T, fact_25_lifts__IT, fact_20_lift_Osimps_I2_J, fact_3__096IT_A_Ib_091u_Pi_093_J_096, fact_2_uIT, fact_81_nat_Oexhaust, fact_50_listsum__0, help_fTrue_1_1_U, fact_64_dB_Osimps_I8_J, fact_0__096IT_At_096, fact_23_dB_Osimps_I5_J, help_fFalse_1_1_T, fact_83_not0__implies__Suc, fact_65_dB_Osimps_I7_J, fact_4_True, fact_47_char_Oexhaust, help_COMBB_1_1_U, fact_17_dB_Osimps_I2_J, fact_78_nat_Osimps_I2_J, fact_93_add__Suc__right, fact_46_nat__size, fact_85_dB_Osize_I3_J, fact_21_substn_Osimps_I2_J, help_fconj_2_1_U, fact_95_nat_Osize_I4_J, fact_84_nat__induct, fact_73_ext, fact_82_zero__induct, fact_67_dB_Osimps_I12_J, fact_87_add__right__cancel, fact_69_Suc__n__not__n, fact_10_subst__Var__IT, fact_13_char__size, fact_52_liftn__lift, fact_26_subst__eq, fact_1_Var_I3_J, fact_60_dB_Osimps_I3_J, fact_38_size__bool, fact_9_zero__reorient, fact_31_dB_Osize_I1_J, fact_12_bool_Osize_I2_J, fact_49_char_Orecs, fact_68_Suc__inject, arity_Nat_Onat___Groups_Ozero, fact_74_Suc__neq__Zero, fact_32_size__char, fact_63_dB_Osimps_I9_J, fact_79_Zero__not__Suc, fact_45_char_Osize_I1_J, help_COMBK_1_1_U, fact_80_IT_Osimps, fact_11_bool_Osize_I1_J, fact_30_substn__subst__n, fact_40_nat_Osize_I3_J, fact_89_nat__add__right__cancel, help_COMBC_1_1_U, fact_39_size__literal__def, fact_16_nat_Osize_I1_J, fact_62_Abs__apps__eq__Abs__apps__conv, fact_76_nat_Osimps_I3_J, fact_35_dB_Osize_I4_J, help_fconj_1_1_U, fact_27_Var__IT, fact_36_liftn_Osimps_I2_J, fact_48_char_Osimps_I2_J, fact_77_Suc__not__Zero, help_fFalse_1_1_U, fact_90_nat__add__left__cancel, fact_57_foldl__map, fact_72_Var__apps__neq__Abs__apps, fact_66_dB_Osimps_I6_J, fact_5_lift__IT, fact_86_dB_Osize_I2_J, fact_97_dB_Osize_I5_J, fact_6_subst__lift, fact_75_Zero__neq__Suc, fact_92_add__is__0, help_pp_1_1_U, fact_91_double__zero__sym, fact_54_subst__map, arity_Nat_Onat___Groups_Omonoid__add, fact_33_bool_Osize_I4_J, fact_14_substn__subst__0, fact_29_map__ident, fact_41_dB_Osimps_I10_J, fact_42_dB_Osimps_I11_J, help_pp_2_1_U, fact_71_Abs__App__neq__Var__apps, fact_51_IT_OVar, fact_19_subst__App, fact_53_lift__map, fact_58_nat_Oinject, fact_96_nat_Osize_I2_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_22_dB_Osimps_I4_J, fact_94_add__Suc, fact_28_listsp__conj__eq
% 22.15/10.49 % No. of inferences in proof: 234
% 22.15/10.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9794 ms resp. 8634 ms w/o parsing
% 23.23/10.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.23/10.62 % [INFO] Killing All external provers ...
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