%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL840_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 : n007.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 07:53:11 AM UTC 2026
% Result : Theorem 37.66s 18.45s
% Output : Refutation 38.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 109
% Syntax : Number of formulae : 220 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 852 ( 181 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 5125 ( 86 ~; 14 |; 40 &;4800 @)
% ( 11 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 26 con; 0-5 aty)
% Number of variables : 600 ( 0 ^; 578 !; 22 ?; 600 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(type_type,type,
type: $tType ).
thf(zero_decl,type,
zero:
!>[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(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(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(beta_decl,type,
beta: dB > dB > $o ).
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_size_decl,type,
dB_size: dB > nat ).
thf(lift_decl,type,
lift: dB @ ( nat @ fun ) @ ( dB @ fun ) ).
thf(subst_decl,type,
subst: dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(foldr_decl,type,
foldr:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TA @ fun ) @ ( TB @ fun ) ) > ( TB @ list ) > TA > TA ) ).
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(suc_decl,type,
suc: nat > nat ).
thf(shift_decl,type,
shift:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > nat > TA > ( TA @ ( nat @ fun ) ) ) ).
thf(fun1_decl,type,
fun1: type @ ( type @ fun ) @ ( type @ fun ) ).
thf(typing_decl,type,
typing: ( type @ ( nat @ fun ) ) > dB > type > $o ).
thf(typings_decl,type,
typings: ( type @ ( nat @ fun ) ) > ( dB @ list ) > ( type @ list ) > $o ).
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(t2_decl,type,
t2: type ).
thf(t_decl,type,
t: type ).
thf(t_a_decl,type,
t_a: type ).
thf(t1_decl,type,
t1: type ).
thf(ua1_decl,type,
ua1: type ).
thf(a_decl,type,
a: dB ).
thf(as_decl,type,
as: dB @ list ).
thf(e_decl,type,
e: type @ ( nat @ fun ) ).
thf(ea_decl,type,
ea: type @ ( nat @ fun ) ).
thf(i_decl,type,
i: nat ).
thf(ia_decl,type,
ia: nat ).
thf(r_decl,type,
r: dB ).
thf(t3_decl,type,
t3: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(107,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Suc__neq__Zero) ).
thf(481,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(261,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)],[43]) ).
thf(90,axiom,
! [A: type,B: dB,C: type,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( nat @ zero_zero @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( A @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( B @ abs @ ( D @ typing ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Abs) ).
thf(393,plain,
! [A: type,B: dB,C: type,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( nat @ zero_zero @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( A @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( B @ abs @ ( D @ typing ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(30,axiom,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) ) )
=> ( ( C @ ( A @ ( E @ typing ) ) )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_App) ).
thf(217,plain,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) ) )
=> ( ( C @ ( A @ ( E @ typing ) ) )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_dB_Osimps_I6_J) ).
thf(120,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(47,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( F @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( E @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_MI2) ).
thf(269,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( F @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( F @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( E @ ( 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)],[47]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_61_Var__apps__neq__Abs__apps) ).
thf(202,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)],[25]) ).
thf(87,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat_Osimps_I2_J) ).
thf(385,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Suc__inject) ).
thf(153,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(60,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_appL) ).
thf(301,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(69,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_dB_Osimps_I8_J) ).
thf(320,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)],[69]) ).
thf(88,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(389,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(85,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( G @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( E @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MI1) ).
thf(372,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t1
= ( F @ ( G @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( E @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( E @ ( G @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( G @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( E @ ( 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)],[85]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_map__ident) ).
thf(164,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zero__reorient) ).
thf(179,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)],[17]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',fact_95_IT_Osimps) ).
thf(443,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)],[101]) ).
thf(108,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Zero__not__Suc) ).
thf(485,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(37,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_dB_Osize_I1_J) ).
thf(238,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(77,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( a @ ( t1 @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t1 @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_SI2) ).
thf(353,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( a @ ( t1 @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t1 @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( a @ ( 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)],[77]) ).
thf(28,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_appR) ).
thf(211,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(40,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( 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 ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_subst__preserves__beta) ).
thf(253,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( 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 ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
t @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__096e_060i_058T_062_A_092_060turnstile_062_Ar_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
thf(280,plain,
t @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(32,axiom,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) ) )
=> ~ ! [D: type,E: type] :
( ( A
= ( E @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_typing__elims_I3_J) ).
thf(221,plain,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) ) )
=> ~ ! [D: type,E: type] :
( ( A
= ( E @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_32_IT_OBeta) ).
thf(293,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)],[57]) ).
thf(93,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__induct) ).
thf(411,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)],[93]) ).
thf(45,axiom,
t2 @ ( a @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096e_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_096) ).
thf(265,plain,
t2 @ ( a @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',fact_57_subst__eq) ).
thf(312,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)],[66]) ).
thf(26,axiom,
as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35__096Abs_Ar_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_092_060rightarrow_062_092_060_094sub_062_092_060beta_062r_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_096) ).
thf(206,plain,
as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(63,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(307,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)],[63]) ).
thf(4,axiom,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_beta__cases_I1_J) ).
thf(117,plain,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(100,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dB_Osimps_I4_J) ).
thf(439,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)],[100]) ).
thf(24,axiom,
as @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( i @ suc @ ( nat @ zero_zero @ ( u @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( 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,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66__096IT_A_Ir_091lift_Au_A0_PSuc_Ai_093_091a_091u_Pi_093_P0_093_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_096) ).
thf(201,plain,
as @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( i @ suc @ ( nat @ zero_zero @ ( u @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( 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,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(76,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__induct) ).
thf(349,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)],[76]) ).
thf(13,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Suc__n__not__n) ).
thf(160,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(59,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Suc__not__Zero) ).
thf(297,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(72,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t1 @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_SI1) ).
thf(329,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t1 @ ( A @ ( D @ typing ) ) )
=> ( C @ ( A @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( 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)],[72]) ).
thf(70,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(324,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)],[70]) ).
thf(68,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing ) ) )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_typing__elims_I1_J) ).
thf(317,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( A @ ( B @ var @ ( C @ typing ) ) )
=> ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_dB_Osimps_I1_J) ).
thf(169,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)],[16]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_nat_Oinject) ).
thf(124,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)],[6]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_37_Abs__apps__eq__Abs__apps__conv) ).
thf(339,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)],[75]) ).
thf(20,axiom,
t1 @ ( u @ ( e @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uT) ).
thf(193,plain,
t1 @ ( u @ ( e @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(109,axiom,
! [A: type @ list,B: dB @ list,C: nat,D: type,E: dB,F: type @ ( nat @ fun )] :
( ( D @ ( E @ ( F @ typing ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( F @ ( type @ shift ) ) ) @ typings ) ) )
=> ( A @ ( B @ ( C @ ( E @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( F @ typings ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_substs__lemma) ).
thf(489,plain,
! [A: type @ list,B: dB @ list,C: nat,D: type,E: dB,F: type @ ( nat @ fun )] :
( ( D @ ( E @ ( F @ typing ) ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( F @ ( type @ shift ) ) ) @ typings ) ) )
=> ( A @ ( B @ ( C @ ( E @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( F @ typings ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(7,axiom,
t1 @ ( ua @ ( ea @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Beta_I7_J) ).
thf(134,plain,
t1 @ ( ua @ ( ea @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(266,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(65,axiom,
as @ ( nat @ zero_zero @ ( a @ ( r @ ( 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,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Beta_I1_J) ).
thf(311,plain,
as @ ( nat @ zero_zero @ ( a @ ( r @ ( 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,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(92,axiom,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ beta ) ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ beta ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_beta__cases_I3_J) ).
thf(398,plain,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ beta ) ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ beta ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(95,axiom,
! [A: type,B: nat,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typing ) ) )
=> ( C @ ( B @ ( D @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( E @ ( type @ shift ) ) ) @ typing ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_lift__type) ).
thf(425,plain,
! [A: type,B: nat,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typing ) ) )
=> ( C @ ( B @ ( D @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( E @ ( type @ shift ) ) ) @ typing ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(97,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Var__IT) ).
thf(430,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(44,axiom,
t3 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(264,plain,
t3 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_dB_Osimps_I7_J) ).
thf(149,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_36_Var__apps__eq__Var__apps__conv) ).
thf(375,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)],[86]) ).
thf(54,axiom,
~ ! [A: type] :
~ ( A @ ( a @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096_B_Bthesis_O_A_I_B_BT_H_H_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(286,plain,
~ ! [A: type] :
~ ( A @ ( a @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(56,axiom,
! [A: type,B: nat,C: type @ list,D: dB @ list,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typings ) ) )
=> ( C @ ( D @ ( B @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( B @ ( E @ ( type @ shift ) ) ) @ typings ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_lift__types) ).
thf(291,plain,
! [A: type,B: nat,C: type @ list,D: dB @ list,E: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ typings ) ) )
=> ( C @ ( D @ ( B @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( B @ ( E @ ( type @ shift ) ) ) @ typings ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(52,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_lift__preserves__beta) ).
thf(281,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: TA @ ( nat @ fun ),C: nat,D: nat] :
( ( D = C )
=> ( ( C @ ( A @ ( D @ ( B @ ( TA @ shift ) ) ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_shift__eq) ).
thf(335,plain,
! [TA: $tType,A: TA,B: TA @ ( nat @ fun ),C: nat,D: nat] :
( ( D = C )
=> ( ( C @ ( A @ ( D @ ( B @ ( TA @ shift ) ) ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
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/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(236,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(18,axiom,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_var__app__type__eq) ).
thf(187,plain,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_10_lift__IT) ).
thf(219,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)],[31]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',fact_9_subst__Var__IT) ).
thf(230,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)],[34]) ).
thf(80,axiom,
! [A: dB @ list,B: type,C: type @ list,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( D @ ( E @ typing ) ) )
=> ( ( C @ ( A @ ( E @ typings ) ) )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_list__app__typeI) ).
thf(362,plain,
! [A: dB @ list,B: type,C: type @ list,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( D @ ( E @ typing ) ) )
=> ( ( C @ ( A @ ( E @ typings ) ) )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(61,axiom,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(303,plain,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(106,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Zero__neq__Suc) ).
thf(477,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(82,axiom,
a @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Beta_I3_J) ).
thf(367,plain,
a @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(29,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_nat_Osimps_I3_J) ).
thf(213,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(39,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_apps__preserves__beta) ).
thf(251,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(50,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Lambda) ).
thf(278,plain,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(8,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_n__not__Suc__n) ).
thf(135,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,axiom,
! [A: nat,B: type,C: dB,D: type @ ( nat @ fun ),E: type,F: dB,G: type @ ( nat @ fun )] :
( ( E @ ( F @ ( G @ typing ) ) )
=> ( ( B @ ( C @ ( D @ typing ) ) )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( D @ typing ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__lemma) ).
thf(226,plain,
! [A: nat,B: type,C: dB,D: type @ ( nat @ fun ),E: type,F: dB,G: type @ ( nat @ fun )] :
( ( E @ ( F @ ( G @ typing ) ) )
=> ( ( B @ ( C @ ( D @ typing ) ) )
=> ( ( G
= ( B @ ( A @ ( D @ ( type @ shift ) ) ) ) )
=> ( E @ ( A @ ( C @ ( F @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( D @ typing ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_40_dB_Osimps_I2_J) ).
thf(241,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)],[38]) ).
thf(15,axiom,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing ) ) )
=> ( ( A @ ( C @ beta ) )
=> ( B @ ( A @ ( D @ typing ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subject__reduction) ).
thf(167,plain,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing ) ) )
=> ( ( A @ ( C @ beta ) )
=> ( B @ ( A @ ( D @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(104,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(473,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(41,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(255,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)],[41]) ).
thf(3,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ beta ) )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ beta ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_beta__cases_I2_J) ).
thf(112,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ beta ) )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ beta ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(78,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_dB_Osimps_I5_J) ).
thf(355,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)],[78]) ).
thf(21,axiom,
t @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_T) ).
thf(194,plain,
t @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fact_94_lifts__IT) ).
thf(295,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)],[58]) ).
thf(64,axiom,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Beta_I5_J) ).
thf(310,plain,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t1 @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(73,axiom,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typing ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_typing__elims_I2_J) ).
thf(331,plain,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact_31_app__Var__IT) ).
thf(370,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)],[84]) ).
thf(79,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(359,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)],[79]) ).
thf(102,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nat_Oexhaust) ).
thf(465,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',fact_90_IT_OVar) ).
thf(368,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)],[83]) ).
thf(62,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_not0__implies__Suc) ).
thf(304,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA,C: nat,D: TA @ ( nat @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ ( D @ ( TA @ shift ) ) ) @ ( TA @ shift ) ) ) )
= ( B @ ( C @ suc @ ( A @ ( nat @ zero_zero @ ( D @ ( TA @ shift ) ) ) @ ( TA @ shift ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_shift__commute) ).
thf(258,plain,
! [TA: $tType,A: TA,B: TA,C: nat,D: TA @ ( nat @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ ( D @ ( TA @ shift ) ) ) @ ( TA @ shift ) ) ) )
= ( B @ ( C @ suc @ ( A @ ( nat @ zero_zero @ ( D @ ( TA @ shift ) ) ) @ ( TA @ shift ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(12,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_abs) ).
thf(158,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_83_foldl__map) ).
thf(390,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)],[89]) ).
thf(9,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_dB_Osimps_I3_J) ).
thf(139,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)],[9]) ).
thf(55,axiom,
i @ ( u @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096) ).
thf(290,plain,
i @ ( u @ ( as @ ( nat @ zero_zero @ ( a @ ( r @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( 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)],[55]) ).
thf(27,axiom,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_typing_OVar) ).
thf(207,plain,
! [A: type,B: nat,C: type @ ( nat @ fun )] :
( ( ( B @ ( C @ ( type @ ( nat @ aa ) ) ) )
= A )
=> ( A @ ( B @ var @ ( C @ typing ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(67,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(315,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_92_listsp__conj__eq) ).
thf(432,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)],[98]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_69_subst__map) ).
thf(190,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)],[19]) ).
thf(48,axiom,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dB_Osimps_I9_J) ).
thf(273,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)],[48]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_46_subst__App) ).
thf(326,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)],[71]) ).
thf(22,axiom,
! [A: type,B: type @ list,C: type,D: dB @ list,E: dB @ list,F: nat,G: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) ) )
=> ( ( B @ ( E @ ( G @ typings ) ) )
=> ( ( A @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) ) )
=> ? [H: type @ list] :
( ( H @ ( D @ ( G @ typings ) ) )
& ( A
= ( C @ ( H @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_var__app__types) ).
thf(195,plain,
! [A: type,B: type @ list,C: type,D: dB @ list,E: dB @ list,F: nat,G: type @ ( nat @ fun )] :
( ( C @ ( D @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) ) )
=> ( ( B @ ( E @ ( G @ typings ) ) )
=> ( ( A @ ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( G @ typing ) ) )
=> ? [H: type @ list] :
( ( H @ ( D @ ( G @ typings ) ) )
& ( A
= ( C @ ( H @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,axiom,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_beta) ).
thf(437,plain,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_70_lift__map) ).
thf(474,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)],[105]) ).
thf(53,axiom,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) ) )
=> ~ ! [D: type,E: type] :
~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_abs__typeE) ).
thf(283,plain,
! [A: type,B: dB,C: type @ ( nat @ fun )] :
( ( A @ ( B @ abs @ ( C @ typing ) ) )
=> ~ ! [D: type,E: type] :
~ ( E @ ( B @ ( D @ ( nat @ zero_zero @ ( C @ ( type @ shift ) ) ) @ typing ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(94,axiom,
! [A: type,B: type,C: type,D: type] :
( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_type_Osimps_I2_J) ).
thf(415,plain,
! [A: type,B: type,C: type,D: type] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_60_subst__lift) ).
thf(395,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)],[91]) ).
thf(96,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(427,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)],[96]) ).
thf(23,axiom,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Beta_I6_J) ).
thf(200,plain,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(49,axiom,
ua1 @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096) ).
thf(277,plain,
ua1 @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1,conjecture,
i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( i @ ( u @ ( a @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(111,plain,
~ ( i @ ( u @ ( a @ ( 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)],[2]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',fact_62_Abs__App__neq__Var__apps) ).
thf(469,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)],[103]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_43_apps__eq__tail__conv) ).
thf(491,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)],[110]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_39_lift_Osimps_I2_J) ).
thf(364,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)],[81]) ).
thf(35,axiom,
~ ! [A: type] :
~ ( A @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(232,plain,
~ ! [A: type] :
~ ( A @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t1 @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(502,plain,
$false,
inference(e,[status(thm)],[481,261,393,217,120,269,202,385,153,301,320,389,372,164,179,443,485,238,353,211,253,280,221,293,411,265,312,206,307,117,439,201,349,160,297,329,324,317,169,124,339,193,489,134,266,311,398,425,430,264,149,375,286,291,281,335,236,187,219,230,362,303,477,367,213,251,278,135,226,241,167,473,255,112,355,194,295,310,331,370,359,465,368,304,258,158,390,139,290,207,315,432,190,273,326,195,437,474,283,415,395,427,200,277,111,469,491,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL840_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 23:40:23 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 1.27/1.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.19/1.66 % [INFO] Parsing done (445ms).
% 2.19/1.68 % [INFO] Running in sequential loop mode.
% 3.53/2.27 % [INFO] eprover registered as external prover.
% 3.53/2.28 % [INFO] Scanning for conjecture ...
% 4.17/2.55 % [INFO] Found a conjecture (or negated_conjecture) and 108 axioms. Running axiom selection ...
% 4.85/2.74 % [INFO] Axiom selection finished. Selected 108 axioms (removed 0 axioms).
% 5.91/3.10 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.91/3.15 % [INFO] Type checking passed.
% 6.14/3.16 % [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 ...
% 37.66/18.43 % External prover 'e' found a proof!
% 37.66/18.43 % [INFO] Killing All external provers ...
% 37.66/18.44 % Time passed: 17893ms (effective reasoning time: 16748ms)
% 37.66/18.44 % 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)>
% 37.66/18.44 % Axioms used in derivation (108): fact_44_appR, help_COMBS_1_1_U, fact_35__096Abs_Ar_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_092_060rightarrow_062_092_060_094sub_062_092_060beta_062r_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_096, fact_54_dB_Osimps_I9_J, help_fconj_1_1_U, help_fconj_3_1_U, fact_15__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096, fact_36_Var__apps__eq__Var__apps__conv, fact_66__096IT_A_Ir_091lift_Au_A0_PSuc_Ai_093_091a_091u_Pi_093_P0_093_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_096, fact_30_var__app__type__eq, fact_75_Suc__n__not__n, fact_58_dB_Osimps_I6_J, fact_80_nat_Osimps_I3_J, fact_26_Abs, fact_69_subst__map, help_COMBI_1_1_U, fact_14_subst__lemma, fact_85_zero__reorient, fact_93_lift__types, fact_61_Var__apps__neq__Abs__apps, fact_17_Beta_I1_J, fact_46_subst__App, fact_96_list__app__typeI, fact_88_nat__induct, fact_22_App, fact_70_lift__map, fact_64_abs__typeE, fact_31_app__Var__IT, fact_71_map__ident, fact_45_appL, fact_2_uIT, fact_40_dB_Osimps_I2_J, fact_59_dB_Osimps_I7_J, fact_43_apps__eq__tail__conv, fact_5__096e_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_096, fact_89_dB_Osize_I1_J, fact_73_Suc__inject, fact_0__096IT_At_096, fact_12_SI2, fact_72_nat_Oinject, fact_74_ext, fact_92_listsp__conj__eq, fact_91_substs__lemma, fact_41_dB_Osimps_I3_J, fact_84_not0__implies__Suc, fact_27_Beta_I5_J, fact_77_Zero__not__Suc, fact_8_MI2, help_COMBB_1_1_U, fact_3_uT, fact_78_nat_Osimps_I2_J, fact_95_IT_Osimps, fact_97_var__app__types, fact_67_beta__cases_I3_J, fact_47_abs, fact_21_typing__elims_I1_J, fact_62_Abs__App__neq__Var__apps, fact_52_subject__reduction, help_fconj_2_1_U, fact_28__096e_060i_058T_062_A_092_060turnstile_062_Ar_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096, fact_25_SI1, fact_51_lift__preserves__beta, fact_9_subst__Var__IT, fact_1_Beta_I6_J, fact_57_subst__eq, fact_42_dB_Osimps_I1_J, fact_37_Abs__apps__eq__Abs__apps__conv, arity_Nat_Onat___Groups_Ozero, fact_24_lift__type, fact_19_type_Osimps_I2_J, fact_55_dB_Osimps_I5_J, fact_6__096_B_Bthesis_O_A_I_B_BT_H_H_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_90_IT_OVar, fact_4_Beta_I3_J, fact_39_lift_Osimps_I2_J, fact_38_Lambda, fact_23_T, fact_79_Suc__not__Zero, fact_29_shift__eq, help_COMBC_1_1_U, fact_65_apps__preserves__beta, fact_86_nat_Oexhaust, fact_87_zero__induct, fact_11__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096, fact_76_n__not__Suc__n, fact_34_typing__elims_I2_J, fact_56_dB_Osimps_I4_J, fact_83_foldl__map, fact_10_lift__IT, fact_33_typing__elims_I3_J, fact_20_typing_OVar, fact_13_Var__IT, fact_32_IT_OBeta, fact_16__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, help_pp_1_1_U, fact_18_Beta_I7_J, fact_81_Zero__neq__Suc, fact_7_MI1, fact_48_beta__cases_I1_J, fact_68_shift__commute, fact_60_subst__lift, fact_63_beta__cases_I2_J, fact_49_beta, help_pp_2_1_U, fact_94_lifts__IT, fact_50_subst__preserves__beta, fact_82_Suc__neq__Zero, fact_53_dB_Osimps_I8_J
% 37.66/18.44 % No. of inferences in proof: 220
% 37.66/18.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17893 ms resp. 16748 ms w/o parsing
% 38.60/18.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.60/18.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------