%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL838_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 : n004.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 07:53:10 AM UTC 2026
% Result : Theorem 19.42s 17.96s
% Output : Refutation 20.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 106
% Syntax : Number of formulae : 214 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 845 ( 177 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 5160 ( 84 ~; 14 |; 41 &;4829 @)
% ( 10 <=>; 182 =>; 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 : 44 ( 42 usr; 23 con; 0-5 aty)
% Number of variables : 630 ( 0 ^; 606 !; 24 ?; 630 :)
% 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(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(liftn_decl,type,
liftn: nat > dB > nat > dB ).
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(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(t1_decl,type,
t1: type ).
thf(t_a_decl,type,
t_a: type ).
thf(t_decl,type,
t: 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(t2_decl,type,
t2: dB ).
thf(thesis_decl,type,
thesis: $o ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(41,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_76_IT_OVar) ).
thf(269,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)],[41]) ).
thf(37,axiom,
t2 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(257,plain,
t2 @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(18,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_72_listsp__conj__eq) ).
thf(173,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)],[18]) ).
thf(72,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_33_type_Osimps_I2_J) ).
thf(347,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)],[72]) ).
thf(67,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(333,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)],[67]) ).
thf(103,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_49_beta__cases_I2_J) ).
thf(468,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)],[103]) ).
thf(76,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(365,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)],[76]) ).
thf(9,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Suc__not__Zero) ).
thf(138,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(81,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 ) ) ) ) @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t @ ( 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_23_SI1) ).
thf(384,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 ) ) ) ) @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t @ ( 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)],[81]) ).
thf(10,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_37_shift__commute) ).
thf(142,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)],[10]) ).
thf(13,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_n__not__Suc__n) ).
thf(153,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(73,axiom,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Beta_I5_J) ).
thf(357,plain,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(99,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_20_lift_Osimps_I2_J) ).
thf(460,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)],[99]) ).
thf(14,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_nat_Osimps_I2_J) ).
thf(157,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(64,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_12_shift__eq) ).
thf(325,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)],[64]) ).
thf(61,axiom,
t @ ( u @ ( e @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_uT) ).
thf(316,plain,
t @ ( u @ ( e @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(39,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_dB_Osimps_I6_J) ).
thf(261,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,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_67_nat__induct) ).
thf(216,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)],[28]) ).
thf(96,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_10_Abs__apps__eq__Abs__apps__conv) ).
thf(443,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)],[96]) ).
thf(63,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_84_dB_Osimps_I4_J) ).
thf(321,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)],[63]) ).
thf(79,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_80_typing_OVar) ).
thf(376,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)],[79]) ).
thf(97,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_73_ext) ).
thf(453,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)],[97]) ).
thf(40,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_68_zero__induct) ).
thf(265,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)],[40]) ).
thf(60,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_92_Abs__App__neq__Var__apps) ).
thf(312,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)],[60]) ).
thf(27,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_82_Var__apps__eq__Var__apps__conv) ).
thf(206,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)],[27]) ).
thf(51,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Var__IT) ).
thf(292,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(80,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( 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_27_MI2) ).
thf(380,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( 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)],[80]) ).
thf(94,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_35_appR) ).
thf(439,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)],[94]) ).
thf(29,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_52_foldl__map) ).
thf(220,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)],[29]) ).
thf(56,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_32__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(302,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)],[56]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_97_liftn__lift) ).
thf(297,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)],[54]) ).
thf(44,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_44_subst__preserves__beta) ).
thf(275,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)],[44]) ).
thf(102,axiom,
t @ ( ua @ ( ea @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Beta_I7_J) ).
thf(467,plain,
t @ ( ua @ ( ea @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(34,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_85_subst__eq) ).
thf(229,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)],[34]) ).
thf(65,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_55_substs__lemma) ).
thf(329,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)],[65]) ).
thf(98,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) ) )
=> ? [E: type @ list] :
( ( E @ ( B @ ( D @ typings ) ) )
& ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_list__app__typeD) ).
thf(456,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) ) )
=> ? [E: type @ list] :
( ( E @ ( B @ ( D @ typings ) ) )
& ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(48,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_26_IT_OBeta) ).
thf(285,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)],[48]) ).
thf(31,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_22__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096) ).
thf(224,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)],[31]) ).
thf(62,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_25_subst__lemma) ).
thf(317,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)],[62]) ).
thf(85,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_79_typing__elims_I1_J) ).
thf(403,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)],[85]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_dB_Osimps_I1_J) ).
thf(188,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)],[23]) ).
thf(17,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dB_Osimps_I7_J) ).
thf(169,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Zero__not__Suc) ).
thf(109,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,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(225,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)],[32]) ).
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_7_dB_Osimps_I8_J) ).
thf(339,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(107,axiom,
! [A: type] :
( ( A @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(489,plain,
! [A: type] :
( ( A @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(8,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_nat_Oexhaust) ).
thf(134,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(70,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(343,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
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 ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Beta_I1_J) ).
thf(205,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)],[26]) ).
thf(16,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_40_lift__map) ).
thf(166,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)],[16]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Suc__inject) ).
thf(161,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_map__ident) ).
thf(180,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Suc__neq__Zero) ).
thf(149,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(90,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_dB_Osimps_I3_J) ).
thf(423,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)],[90]) ).
thf(46,axiom,
a @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Beta_I3_J) ).
thf(281,plain,
a @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(86,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_13_apps__eq__tail__conv) ).
thf(406,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)],[86]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_nat_Oinject) ).
thf(113,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)],[4]) ).
thf(75,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_91_var__app__type__eq) ).
thf(362,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)],[75]) ).
thf(92,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_18_subst__App) ).
thf(434,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)],[92]) ).
thf(57,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_70_list__app__typeI) ).
thf(303,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)],[57]) ).
thf(42,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_60_lift__types) ).
thf(271,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)],[42]) ).
thf(105,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_6_dB_Osimps_I9_J) ).
thf(483,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)],[105]) ).
thf(24,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_77_var__app__types) ).
thf(198,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)],[24]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(108,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Suc__n__not__n) ).
thf(130,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(83,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_43_subject__reduction) ).
thf(399,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)],[83]) ).
thf(30,axiom,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_uIT) ).
thf(223,plain,
u @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(104,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_5_dB_Osimps_I2_J) ).
thf(473,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)],[104]) ).
thf(106,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( a @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t @ ( 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_19_SI2) ).
thf(487,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun )] :
( ( B @ ( a @ ( t @ ( C @ ( D @ ( type @ shift ) ) ) @ typing ) ) )
=> ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( t @ ( 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)],[106]) ).
thf(5,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Zero__neq__Suc) ).
thf(123,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_nat_Osimps_I3_J) ).
thf(145,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(53,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_21_lift__IT) ).
thf(295,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)],[53]) ).
thf(47,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_24_subst__lift) ).
thf(282,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)],[47]) ).
thf(87,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_83_dB_Osimps_I5_J) ).
thf(414,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)],[87]) ).
thf(66,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_38_App) ).
thf(331,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)],[66]) ).
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_15_lift__type) ).
thf(441,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(100,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_41_beta) ).
thf(463,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)],[100]) ).
thf(6,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_not0__implies__Suc) ).
thf(127,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,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(336,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)],[68]) ).
thf(82,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_54_beta__cases_I3_J) ).
thf(386,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)],[82]) ).
thf(101,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_abs) ).
thf(465,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(25,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_89_app__Var__IT) ).
thf(203,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)],[25]) ).
thf(77,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_47_typing__elims_I3_J) ).
thf(368,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)],[77]) ).
thf(38,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_39_subst__map) ).
thf(258,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)],[38]) ).
thf(22,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_51_apps__preserves__beta) ).
thf(186,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)],[22]) ).
thf(84,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_34_appL) ).
thf(401,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)],[84]) ).
thf(88,axiom,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typings ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_list__app__typeE) ).
thf(418,plain,
! [A: type,B: dB @ list,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typings ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
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_30_Lambda) ).
thf(290,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(36,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(235,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)],[36]) ).
thf(91,axiom,
t1 @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_T) ).
thf(433,plain,
t1 @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(71,axiom,
t1 @ ( 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 ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__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(346,plain,
t1 @ ( 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 ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(49,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_dB_Osize_I1_J) ).
thf(287,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(55,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_90_subst__Var__IT) ).
thf(300,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)],[55]) ).
thf(21,axiom,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_beta__cases_I1_J) ).
thf(183,plain,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(89,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_29__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(422,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)],[89]) ).
thf(43,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_71_lifts__IT) ).
thf(273,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)],[43]) ).
thf(78,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_31_abs__typeE) ).
thf(373,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)],[78]) ).
thf(58,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_93_Var__apps__neq__Abs__apps) ).
thf(305,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)],[58]) ).
thf(52,axiom,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Beta_I6_J) ).
thf(294,plain,
ua @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(74,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_48_typing__elims_I2_J) ).
thf(358,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)],[74]) ).
thf(93,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_42_Abs) ).
thf(437,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)],[93]) ).
thf(19,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(178,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)],[19]) ).
thf(45,axiom,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typings ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_var__app__typesE) ).
thf(277,plain,
! [A: type,B: dB @ list,C: nat,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type @ list] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ foldr ) ) ) ) @ ( C @ var @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typings ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(33,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_45_lift__preserves__beta) ).
thf(227,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)],[33]) ).
thf(59,axiom,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( 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_28_MI1) ).
thf(309,plain,
! [A: dB,B: type,C: nat,D: type @ ( nat @ fun ),E: dB,F: type,G: type] :
( ( t
= ( 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)],[59]) ).
thf(35,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(232,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)],[35]) ).
thf(510,plain,
$false,
inference(e,[status(thm)],[269,257,173,347,333,468,365,138,384,142,153,357,460,157,325,316,261,216,443,321,376,453,265,312,206,292,380,439,220,302,297,275,467,229,329,456,285,224,317,403,188,169,109,225,339,489,134,343,205,166,161,180,149,423,281,406,113,362,434,303,271,483,198,108,130,399,223,473,487,123,145,295,282,414,331,441,463,127,336,386,465,203,368,258,186,401,418,290,235,433,346,287,300,183,422,273,373,305,294,358,437,178,277,227,309,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL838_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.15/10.42 % Computer : n004.cluster.edu
% 0.15/10.42 % Model : x86_64 x86_64
% 0.15/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.42 % Memory : 8046.5625MB
% 0.15/10.42 % OS : Linux 6.8.0-71-generic
% 0.15/10.42 % CPULimit : 300
% 0.15/10.42 % WCLimit : 300
% 0.15/10.42 % DateTime : Fri Sep 25 23:42:17 UTC 2026
% 0.15/10.42 % CPUTime :
% 0.15/10.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/10.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/10.91 % [INFO] Parsing done (187ms).
% 0.18/10.92 % [INFO] Running in sequential loop mode.
% 1.85/11.12 % [INFO] eprover registered as external prover.
% 1.85/11.12 % [INFO] Scanning for conjecture ...
% 2.29/11.23 % [INFO] Found a conjecture (or negated_conjecture) and 109 axioms. Running axiom selection ...
% 2.69/11.32 % [INFO] Axiom selection finished. Selected 105 axioms (removed 4 axioms).
% 3.70/11.52 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.70/11.58 % [INFO] Type checking passed.
% 3.70/11.58 % [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 ...
% 19.42/17.95 % External prover 'e' found a proof!
% 19.42/17.95 % [INFO] Killing All external provers ...
% 19.42/17.95 % Time passed: 7442ms (effective reasoning time: 7035ms)
% 19.42/17.95 % 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)>
% 19.42/17.96 % Axioms used in derivation (105): fact_90_subst__Var__IT, fact_55_substs__lemma, fact_42_Abs, fact_54_beta__cases_I3_J, fact_61_Zero__not__Suc, help_COMBS_1_1_U, fact_27_MI2, fact_50_map__ident, help_fconj_3_1_U, fact_70_list__app__typeI, fact_32__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_97_liftn__lift, fact_59_n__not__Suc__n, fact_31_abs__typeE, fact_43_subject__reduction, fact_68_zero__induct, fact_57_Suc__inject, fact_26_IT_OBeta, help_COMBI_1_1_U, fact_14_Beta_I1_J, fact_38_App, fact_2_uT, fact_58_Suc__n__not__n, fact_20_lift_Osimps_I2_J, fact_45_lift__preserves__beta, fact_48_typing__elims_I2_J, fact_52_foldl__map, fact_81_beta__cases_I1_J, fact_17_Beta_I7_J, fact_66_not0__implies__Suc, fact_0__096IT_At_096, fact_18_subst__App, fact_23_SI1, fact_72_listsp__conj__eq, fact_5_dB_Osimps_I2_J, fact_15_lift__type, fact_25_subst__lemma, fact_11_Beta_I5_J, fact_89_app__Var__IT, help_COMBB_1_1_U, fact_80_typing_OVar, fact_44_subst__preserves__beta, fact_86_dB_Osimps_I6_J, fact_29__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_95_IT_Osimps, fact_10_Abs__apps__eq__Abs__apps__conv, fact_40_lift__map, fact_73_ext, help_fconj_2_1_U, fact_69_nat_Oexhaust, fact_37_shift__commute, fact_1_Beta_I3_J, fact_77_var__app__types, fact_76_IT_OVar, fact_3_T, fact_35_appR, fact_51_apps__preserves__beta, fact_74_list__app__typeD, fact_91_var__app__type__eq, fact_9_Beta_I6_J, fact_12_shift__eq, fact_30_Lambda, fact_4_dB_Osimps_I3_J, fact_94_var__app__typesE, fact_13_apps__eq__tail__conv, fact_41_beta, fact_28_MI1, fact_56_Suc__neq__Zero, fact_19_SI2, fact_83_dB_Osimps_I5_J, fact_64_nat_Osimps_I3_J, help_COMBC_1_1_U, fact_53_nat_Oinject, fact_47_typing__elims_I3_J, fact_34_appL, fact_65_Zero__neq__Suc, fact_71_lifts__IT, fact_49_beta__cases_I2_J, help_fconj_1_1_U, fact_22__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096, fact_87_dB_Osimps_I7_J, fact_7_dB_Osimps_I8_J, fact_93_Var__apps__neq__Abs__apps, fact_24_subst__lift, fact_62_nat_Osimps_I2_J, fact_85_subst__eq, fact_8__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_63_Suc__not__Zero, fact_82_Var__apps__eq__Var__apps__conv, fact_33_type_Osimps_I2_J, fact_75_list__app__typeE, fact_60_lift__types, fact_39_subst__map, fact_79_typing__elims_I1_J, fact_78_dB_Osimps_I1_J, fact_67_nat__induct, fact_96_dB_Osize_I1_J, fact_36_abs, conj_0, fact_84_dB_Osimps_I4_J, fact_6_dB_Osimps_I9_J, fact_88_Var__IT, fact_21_lift__IT, fact_16_uIT, fact_92_Abs__App__neq__Var__apps
% 19.42/17.96 % No. of inferences in proof: 214
% 19.42/17.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7442 ms resp. 7035 ms w/o parsing
% 20.18/18.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.18/18.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------