TSTP Solution File: LCL763_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL763_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:31 EDT 2023
% Result : Theorem 15.54s 6.11s
% Output : Refutation 15.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 142
% Syntax : Number of formulae : 249 ( 92 unt; 37 typ; 0 def)
% Number of atoms : 855 ( 327 equ; 0 cnn)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 5188 ( 88 ~; 27 |; 112 &;4780 @)
% ( 25 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 9 con; 0-5 aty)
% Number of variables : 783 ( 0 ^; 678 !; 79 ?; 783 :)
% ( 26 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_type,type,
it: fun @ dB @ bool ).
thf(beta_type,type,
beta: fun @ dB @ ( fun @ dB @ bool ) ).
thf(abs_type,type,
abs: dB > dB ).
thf(app_type,type,
app: fun @ dB @ ( fun @ dB @ dB ) ).
thf(var_type,type,
var: nat > dB ).
thf(dB_case_type,type,
dB_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ TA ) ) > ( fun @ dB @ TA ) > dB > TA ) ).
thf(dB_size_type,type,
dB_size: dB > nat ).
thf(liftn_type,type,
liftn: nat > dB > nat > dB ).
thf(subst_type,type,
subst: dB > dB > nat > dB ).
thf(substn_type,type,
substn: dB > dB > nat > dB ).
thf(step1_type,type,
step1:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ bool ) ) > ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(foldl_type,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(list_rec_type,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) ) > ( list @ TA ) > TB ) ).
thf(list_size_type,type,
list_size:
!>[TA: $tType] : ( ( fun @ TA @ nat ) > ( list @ TA ) > nat ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(listsp_type,type,
listsp:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(sublist_type,type,
sublist:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ nat @ bool ) > ( list @ TA ) ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(conversep_type,type,
conversep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ TA @ ( fun @ TB @ bool ) ) ) ).
thf(accp_type,type,
accp:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ bool ) ) > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(n_type,type,
n: nat ).
thf(85,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ B ) @ A ) @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_not__step1__Nil) ).
thf(504,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ B ) @ A ) @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(40,axiom,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
<=> ( ? [C: dB,D: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ D ) )
& ( A
= ( subst @ C @ D @ ( zero_zero @ nat ) ) ) )
| ? [C: dB,D: dB,E: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ E ) )
& ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ E ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
| ? [C: dB,D: dB,E: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ E ) @ C ) )
& ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ E ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
| ? [C: dB,D: dB] :
( ( B
= ( abs @ C ) )
& ( A
= ( abs @ D ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_beta_Osimps) ).
thf(292,plain,
! [A: dB,B: dB] :
( ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
=> ( ? [C: dB,D: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ D ) )
& ( A
= ( subst @ C @ D @ ( zero_zero @ nat ) ) ) )
| ? [C: dB,D: dB,E: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ E ) )
& ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ E ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
| ? [C: dB,D: dB,E: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ E ) @ C ) )
& ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ E ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
| ? [C: dB,D: dB] :
( ( B
= ( abs @ C ) )
& ( A
= ( abs @ D ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) ) ) )
& ( ( ? [C: dB,D: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ D ) )
& ( A
= ( subst @ C @ D @ ( zero_zero @ nat ) ) ) )
| ? [C: dB,D: dB,E: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ E ) )
& ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ E ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
| ? [C: dB,D: dB,E: dB] :
( ( B
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ E ) @ C ) )
& ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ E ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
| ? [C: dB,D: dB] :
( ( B
= ( abs @ C ) )
& ( A
= ( abs @ D ) )
& ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(37,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
<=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_IT_Osimps) ).
thf(266,plain,
! [A: dB] :
( ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) )
& ( ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) )
=> ( pp @ ( aa @ dB @ bool @ it @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(88,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_list_Oexhaust) ).
thf(518,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(32,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Abs__eq__apps__conv) ).
thf(234,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) ) )
& ( ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) )
=> ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_list_Orecs_I2_J) ).
thf(352,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(104,axiom,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( append @ dB @ E @ ( cons @ dB @ C @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_App__eq__foldl__conv) ).
thf(582,plain,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( append @ dB @ E @ ( cons @ dB @ C @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) ) )
& ( ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( append @ dB @ E @ ( cons @ dB @ C @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(72,axiom,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_beta__cases_I2_J) ).
thf(449,plain,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_foldl__Nil) ).
thf(440,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_list_Osimps_I5_J) ).
thf(384,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(13,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zero__reorient) ).
thf(142,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_dB_Osimps_I1_J) ).
thf(340,plain,
! [A: nat,B: nat] :
( ( ( ( var @ B )
= ( var @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( var @ B )
= ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
<=> ? [D: TB,E: TA] :
( ( B = E )
& ( A = D )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_conversep_Osimps) ).
thf(538,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ? [D: TB,E: TA] :
( ( B = E )
& ( A = D )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ D ) @ E ) ) ) )
& ( ? [D: TB,E: TA] :
( ( B = E )
& ( A = D )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ D ) @ E ) ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_list_Osize_I1_J) ).
thf(174,plain,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( fun @ TB @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TB @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_conversep_Ointros) ).
thf(417,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( fun @ TB @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TB @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_list_Orecs_I1_J) ).
thf(559,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(24,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_apps__preserves__beta) ).
thf(189,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(68,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ D @ B ) ) )
=> ( ! [D: list @ dB] :
( ( pp @ ( aa @ ( list @ dB ) @ bool @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ bool ) @ ( step1 @ dB @ beta ) @ B ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ C @ D ) ) )
=> ~ ! [D: dB] :
( ( C
= ( abs @ D ) )
=> ! [E: dB,F: list @ dB] :
( ( B
= ( cons @ dB @ E @ F ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ ( subst @ D @ E @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_apps__betasE) ).
thf(421,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ D @ B ) ) )
=> ( ! [D: list @ dB] :
( ( pp @ ( aa @ ( list @ dB ) @ bool @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ bool ) @ ( step1 @ dB @ beta ) @ B ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ C @ D ) ) )
=> ~ ! [D: dB] :
( ( C
= ( abs @ D ) )
=> ! [E: dB,F: list @ dB] :
( ( B
= ( cons @ dB @ E @ F ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ ( subst @ D @ E @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(41,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_dB_Osimps_I5_J) ).
thf(325,plain,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(15,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( append @ TA @ ( cons @ TA @ C @ B ) @ A )
= ( cons @ TA @ C @ ( append @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_append__Cons) ).
thf(152,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( append @ TA @ ( cons @ TA @ C @ B ) @ A )
= ( cons @ TA @ C @ ( append @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_neq__Nil__conv) ).
thf(228,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Var__apps__neq__Abs__apps) ).
thf(179,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(71,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( append @ TA @ B @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_self__append__conv) ).
thf(443,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( append @ TA @ B @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( B
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(7,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_same__append__eq) ).
thf(121,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_conversepD) ).
thf(348,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(397,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(73,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(453,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(10,axiom,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_substn__subst__n) ).
thf(133,plain,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(243,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(76,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Beta) ).
thf(467,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(36,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ E ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) ) )
<=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Cons__step1__Cons) ).
thf(252,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ E ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) ) )
=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ E ) @ C ) @ A ) ) ) ) )
& ( ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ E ) @ C ) @ A ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ E ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_dB_Osize_I1_J) ).
thf(329,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(103,axiom,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ D ) )
=> ( ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ C ) )
=> ( ( C
= ( foldl @ dB @ dB @ app @ ( subst @ B @ D @ ( zero_zero @ nat ) ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_double__induction__lemma) ).
thf(578,plain,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ D ) )
=> ( ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ C ) )
=> ( ( C
= ( foldl @ dB @ dB @ app @ ( subst @ B @ D @ ( zero_zero @ nat ) ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(61,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_termi__implies__IT) ).
thf(403,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(83,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_substn_Osimps_I2_J) ).
thf(499,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(30,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_dB_Osimps_I11_J) ).
thf(225,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(26,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_apps__eq__tail__conv) ).
thf(193,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(79,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_list__ex1__simps_I1_J) ).
thf(476,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(95,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_dB_Osimps_I2_J) ).
thf(547,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_list_Osimps_I4_J) ).
thf(515,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(50,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_subst__preserves__beta) ).
thf(371,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(106,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(605,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(64,axiom,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_abs) ).
thf(412,plain,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_not__Cons__self) ).
thf(149,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(52,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subst__App) ).
thf(375,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(98,axiom,
! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_beta) ).
thf(562,plain,
! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(25,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Lambda) ).
thf(191,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_liftn__0) ).
thf(118,plain,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(57,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_liftn_Osimps_I2_J) ).
thf(391,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(54,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ B ) @ ( nil @ TA ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_not__Nil__step1) ).
thf(382,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ B ) @ ( nil @ TA ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(101,axiom,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_sublist__nil) ).
thf(572,plain,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(46,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
( ( listsp @ TA @ ( accp @ TA @ B ) @ A )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_ListOrder_Olists__accD) ).
thf(350,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
( ( listsp @ TA @ ( accp @ TA @ B ) @ A )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(67,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_IT__implies__termi) ).
thf(419,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( accp @ dB @ ( conversep @ dB @ dB @ beta ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_sublist__singleton) ).
thf(567,plain,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(56,axiom,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Abs__App__neq__Var__apps) ).
thf(387,plain,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(49,axiom,
! [A: dB,B: list @ dB,C: nat] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ? [D: list @ dB] :
( ( pp @ ( aa @ ( list @ dB ) @ bool @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ bool ) @ ( step1 @ dB @ beta ) @ B ) @ D ) )
& ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_head__Var__reduction) ).
thf(367,plain,
! [A: dB,B: list @ dB,C: nat] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ? [D: list @ dB] :
( ( pp @ ( aa @ ( list @ dB ) @ bool @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ bool ) @ ( step1 @ dB @ beta ) @ B ) @ D ) )
& ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(93,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_list_Osimps_I3_J) ).
thf(535,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(16,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_dB_Osimps_I3_J) ).
thf(155,plain,
! [A: dB,B: dB] :
( ( ( ( abs @ B )
= ( abs @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( abs @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool )] :
( ( conversep @ TB @ TA @ ( conversep @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_conversep__conversep) ).
thf(108,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool )] :
( ( conversep @ TB @ TA @ ( conversep @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(89,axiom,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Osimps_I8_J) ).
thf(521,plain,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(9,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ ( conversep @ TA @ TA @ A ) )
= ( conversep @ ( list @ TA ) @ ( list @ TA ) @ ( step1 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_step1__converse) ).
thf(130,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ ( conversep @ TA @ TA @ A ) )
= ( conversep @ ( list @ TA ) @ ( list @ TA ) @ ( step1 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(74,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ D ) @ C ) @ ( cons @ TA @ B @ A ) ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ A ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ D @ E ) @ B ) ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ B @ E ) )
=> ~ ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ D ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Cons__step1E) ).
thf(455,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ D ) @ C ) @ ( cons @ TA @ B @ A ) ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ A ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ D @ E ) @ B ) ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ B @ E ) )
=> ~ ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ D ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(58,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ C @ ( append @ dB @ B @ ( cons @ dB @ A @ ( nil @ dB ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_app__last) ).
thf(394,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ C @ ( append @ dB @ B @ ( cons @ dB @ A @ ( nil @ dB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(78,axiom,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_subst__eq) ).
thf(473,plain,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(92,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dB_Osimps_I7_J) ).
thf(531,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_append__same__eq) ).
thf(112,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_beta__cases_I3_J) ).
thf(355,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(28,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( listsp @ TA @ B @ A )
<=> ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_listsp_Osimps) ).
thf(209,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( listsp @ TA @ B @ A )
=> ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) ) )
& ( ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) )
=> ( listsp @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(81,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) )
<=> ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_apps__eq__Abs__conv) ).
thf(487,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) )
=> ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) ) )
& ( ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(525,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_foldl__Cons) ).
thf(414,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20,axiom,
! [A: dB,B: list @ dB,C: list @ dB] :
( ( pp @ ( aa @ ( list @ dB ) @ bool @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ bool ) @ ( step1 @ dB @ beta ) @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_apps__preserves__betas) ).
thf(177,plain,
! [A: dB,B: list @ dB,C: list @ dB] :
( ( pp @ ( aa @ ( list @ dB ) @ bool @ ( aa @ ( list @ dB ) @ ( fun @ ( list @ dB ) @ bool ) @ ( step1 @ dB @ beta ) @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(84,axiom,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_subst__Var__IT) ).
thf(502,plain,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(75,axiom,
! [A: dB] :
( ! [B: nat] :
( A
!= ( var @ B ) )
=> ( ! [B: dB,C: dB] :
( A
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ C ) )
=> ~ ! [B: dB] :
( A
!= ( abs @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_dB_Oexhaust) ).
thf(463,plain,
! [A: dB] :
( ! [B: nat] :
( A
!= ( var @ B ) )
=> ( ! [B: dB,C: dB] :
( A
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ C ) )
=> ~ ! [B: dB] :
( A
!= ( abs @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(8,axiom,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_substn__subst__0) ).
thf(127,plain,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( accp @ TA @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ C ) ) @ A ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ C ) ) @ ( cons @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Cons__acc__step1I) ).
thf(250,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( accp @ TA @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ C ) ) @ A ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ C ) ) @ ( cons @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(96,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ ( conversep @ TA @ TA @ C ) ) @ B ) @ A ) )
<=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( conversep @ ( list @ TA ) @ ( list @ TA ) @ ( step1 @ TA @ C ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_in__step1__converse) ).
thf(556,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ TA @ ( fun @ TA @ bool )] :
( ( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ ( conversep @ TA @ TA @ C ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( conversep @ ( list @ TA ) @ ( list @ TA ) @ ( step1 @ TA @ C ) ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( conversep @ ( list @ TA ) @ ( list @ TA ) @ ( step1 @ TA @ C ) ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ ( step1 @ TA @ ( conversep @ TA @ TA @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(23,axiom,
! [A: dB,B: nat] :
~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_beta__cases_I1_J) ).
thf(186,plain,
! [A: dB,B: nat] :
~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(60,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_appL) ).
thf(401,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(18,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_not__Cons__self2) ).
thf(171,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [TA: $tType] :
( ( conversep @ TA @ TA @ ( fequal @ TA ) )
= ( fequal @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_conversep__eq) ).
thf(139,plain,
! [TA: $tType] :
( ( conversep @ TA @ TA @ ( fequal @ TA ) )
= ( fequal @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_dB_Osimps_I6_J) ).
thf(246,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(80,axiom,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var__apps__eq__Var__apps__conv) ).
thf(478,plain,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_conversep__iff) ).
thf(287,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(39,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_listsp_ONil) ).
thf(290,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(53,axiom,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_dB_Osimps_I9_J) ).
thf(378,plain,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(63,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ B ) ) @ A ) )
=> ( listsp @ TA @ ( accp @ TA @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_ListOrder_Olists__accI) ).
thf(410,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ ( accp @ ( list @ TA ) @ ( step1 @ TA @ B ) ) @ A ) )
=> ( listsp @ TA @ ( accp @ TA @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(62,axiom,
! [A: dB] :
? [B: list @ dB,C: dB] :
( ( A
= ( foldl @ dB @ dB @ app @ C @ B ) )
& ( ? [D: nat] :
( C
= ( var @ D ) )
| ? [D: dB] :
( C
= ( abs @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_ex__head__tail) ).
thf(405,plain,
! [A: dB] :
? [B: list @ dB,C: dB] :
( ( A
= ( foldl @ dB @ dB @ app @ C @ B ) )
& ( ? [D: nat] :
( C
= ( var @ D ) )
| ? [D: dB] :
( C
= ( abs @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(22,axiom,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dB_Osize_I4_J) ).
thf(183,plain,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(51,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_appR) ).
thf(373,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(105,axiom,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_IT_OVar) ).
thf(603,plain,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_list_Osimps_I2_J) ).
thf(564,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1,conjecture,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ ( nil @ dB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ ( nil @ dB ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(107,plain,
~ ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ ( nil @ dB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ C @ B ) @ A )
= ( append @ TA @ C @ ( append @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_append__assoc) ).
thf(136,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ C @ B ) @ A )
= ( append @ TA @ C @ ( append @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(86,axiom,
! [A: list @ dB,B: dB,C: nat] :
( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Var__eq__apps__conv) ).
thf(506,plain,
! [A: list @ dB,B: dB,C: nat] :
( ( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) )
& ( ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) )
=> ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_foldl__fun__comm) ).
thf(437,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(43,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ B @ A ) )
<=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Nil__is__append__conv) ).
thf(332,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( nil @ TA )
= ( append @ TA @ B @ A ) )
=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) )
& ( ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) )
=> ( ( nil @ TA )
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(102,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_dB_Osimps_I12_J) ).
thf(575,plain,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(91,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(528,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(17,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_list_Oinject) ).
thf(163,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Abs__apps__eq__Abs__apps__conv) ).
thf(200,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(111,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(77,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_dB_Osimps_I4_J) ).
thf(469,plain,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_dB_Osimps_I10_J) ).
thf(222,plain,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(82,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_insert__Nil) ).
thf(496,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(606,plain,
$false,
inference(e,[status(thm)],[504,292,266,518,234,352,582,449,440,384,142,340,538,174,417,559,189,421,325,152,228,179,443,121,348,397,453,133,243,467,252,329,578,403,499,225,193,476,547,515,371,605,412,149,375,562,191,118,391,382,572,350,419,567,387,367,535,155,108,521,130,455,394,473,531,112,355,209,487,525,414,177,502,463,127,250,556,186,401,171,139,246,478,287,290,378,410,405,183,373,603,564,107,136,506,437,332,575,528,163,200,111,469,222,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL763_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.13 % Command : run_Leo-III %s %d
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu May 18 16:02:41 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.85/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.01 % [INFO] Parsing done (214ms).
% 1.56/1.02 % [INFO] Running in sequential loop mode.
% 2.14/1.25 % [INFO] eprover registered as external prover.
% 2.14/1.25 % [INFO] cvc4 registered as external prover.
% 2.14/1.26 % [INFO] Scanning for conjecture ...
% 2.40/1.38 % [INFO] Found a conjecture and 104 axioms. Running axiom selection ...
% 2.91/1.47 % [INFO] Axiom selection finished. Selected 104 axioms (removed 0 axioms).
% 3.42/1.66 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.57/1.70 % [INFO] Type checking passed.
% 3.57/1.70 % [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 ...
% 15.54/6.11 % External prover 'e' found a proof!
% 15.54/6.11 % [INFO] Killing All external provers ...
% 15.54/6.11 % Time passed: 5612ms (effective reasoning time: 5082ms)
% 15.54/6.11 % 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)>
% 15.54/6.11 % Axioms used in derivation (104): fact_38_list_Osize_I1_J, fact_44_subst__preserves__beta, fact_63_not__Nil__step1, fact_12_dB_Osimps_I3_J, fact_30_ex__head__tail, fact_91_app__last, fact_52_liftn__0, fact_3_dB_Osimps_I1_J, fact_42_abs, fact_89_conversep_Osimps, fact_15_Lambda, fact_11_subst__Var__IT, fact_21_subst__eq, fact_81_conversep_Ointros, fact_22_Var__apps__neq__Abs__apps, fact_79_list_Orecs_I2_J, fact_34_dB_Osize_I1_J, fact_8_IT_OVar, fact_72_list_Osimps_I5_J, fact_39_appR, fact_68_list_Oinject, fact_10_apps__eq__Abs__conv, fact_96_append__Cons, fact_62_not__step1__Nil, fact_55_double__induction__lemma, fact_47_apps__preserves__beta, fact_59_step1__converse, fact_75_mem__def, fact_6_dB_Osimps_I5_J, fact_67_apps__betasE, fact_97_Nil__is__append__conv, fact_32_dB_Osimps_I10_J, fact_66_conversep__eq, fact_33_dB_Osimps_I11_J, fact_70_Cons__acc__step1I, fact_25_foldl__fun__comm, fact_61_ListOrder_Olists__accD, fact_48_substn__subst__n, fact_40_appL, fact_95_append__assoc, fact_2_apps__eq__tail__conv, fact_74_ext, fact_58_termi__implies__IT, fact_20_dB_Osimps_I7_J, fact_78_list_Osimps_I3_J, fact_27_list_Osimps_I4_J, fact_86_Cons__step1E, fact_51_liftn_Osimps_I2_J, fact_54_head__Var__reduction, fact_83_listsp_Osimps, fact_90_sublist__nil, fact_7_foldl__Nil, fact_43_substn_Osimps_I2_J, fact_28_list__ex1__simps_I1_J, fact_35_beta, fact_36_dB_Osize_I4_J, fact_94_same__append__eq, fact_49_beta__cases_I3_J, fact_45_zero__reorient, fact_98_self__append__conv, fact_18_dB_Osimps_I9_J, help_fequal_1_1_T, fact_31_dB_Osimps_I12_J, fact_5_dB_Osimps_I4_J, arity_Nat_Onat___Groups_Ozero, fact_16_Abs__apps__eq__Abs__apps__conv, fact_88_sublist__singleton, fact_41_beta__cases_I1_J, fact_87_insert__Nil, fact_82_conversepD, fact_93_append__same__eq, fact_17_dB_Osimps_I8_J, fact_46_beta__cases_I2_J, fact_69_Cons__step1__Cons, fact_1_Var__apps__eq__Var__apps__conv, help_fequal_2_1_T, fact_71_foldl__Cons, fact_37_substn__subst__0, fact_4_dB_Osimps_I2_J, fact_65_conversep__iff, fact_19_dB_Osimps_I6_J, fact_85_list_Oexhaust, fact_80_conversep__conversep, fact_9_Abs__eq__apps__conv, fact_50_list_Orecs_I1_J, fact_53_apps__preserves__betas, fact_92_App__eq__foldl__conv, fact_23_Abs__App__neq__Var__apps, fact_60_in__step1__converse, fact_73_not__Cons__self2, help_pp_1_1_U, fact_13_listsp_ONil, fact_56_beta_Osimps, fact_57_IT__implies__termi, fact_76_not__Cons__self, fact_14_subst__App, help_pp_2_1_U, fact_84_neq__Nil__conv, fact_24_Beta, fact_26_IT_Osimps, fact_77_list_Osimps_I2_J, fact_64_ListOrder_Olists__accI, fact_29_dB_Oexhaust, fact_0_Var__eq__apps__conv
% 15.54/6.11 % No. of inferences in proof: 212
% 15.54/6.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5612 ms resp. 5082 ms w/o parsing
% 15.68/6.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.68/6.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------