TSTP Solution File: COM090_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM090_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 10:14:03 EDT 2023
% Result : Theorem 41.56s 27.45s
% Output : Refutation 42.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 177
% Syntax : Number of formulae : 312 ( 91 unt; 44 typ; 0 def)
% Number of atoms : 7815 ( 166 equ; 0 cnn)
% Maximal formula atoms : 553 ( 29 avg)
% Number of connectives : 23273 ( 101 ~; 36 |; 57 &;22851 @)
% ( 14 <=>; 214 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 12 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 11 con; 0-5 aty)
% Number of variables : 1179 ( 0 ^;1101 !; 26 ?;1179 :)
% ( 52 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(cl_Groups_Ominus_type,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(finite_finite1_type,type,
finite_finite1:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).
thf(combi_type,type,
combi:
!>[TA: $tType] : ( fun @ TA @ TA ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( fun @ TC @ TB ) @ ( fun @ TC @ TA ) ) ) ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ TA ) ) ).
thf(the_type,type,
the:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(iprod_type,type,
iprod:
!>[TA: $tType] : ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) ) ).
thf(zipwith0_type,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ ( list @ TC ) @ ( fun @ ( list @ TB ) @ ( list @ TA ) ) ) ) ).
thf(linord2118332866rt_key_type,type,
linord2118332866rt_key:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > ( list @ TB ) > ( list @ TB ) ) ).
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_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(set_type,type,
set:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ TA @ bool ) ) ).
thf(lbounds_type,type,
lbounds: ( list @ atom ) > ( list @ ( product_prod @ int @ ( list @ int ) ) ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( fun @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) ) ).
thf(product_curry_type,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ ( product_prod @ TC @ TB ) @ TA ) > ( fun @ TC @ ( fun @ TB @ TA ) ) ) ).
thf(produc1605651328_split_type,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TA ) ) ).
thf(product_prod_case_type,type,
product_prod_case:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TA ) ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(image_type,type,
image:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( fun @ TB @ bool ) > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fEx_type,type,
fEx:
!>[TA: $tType] : ( fun @ ( fun @ TA @ bool ) @ bool ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(fimplies_type,type,
fimplies: bool > ( fun @ bool @ bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(as_type,type,
as: list @ atom ).
thf(xs_type,type,
xs: list @ int ).
thf(11,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Ominus @ TA ) )
=> ( cl_Groups_Ominus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
thf(154,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Ominus @ TA ) )
=> ( cl_Groups_Ominus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( finite_finite @ TB @ ( image @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(518,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( finite_finite @ TB @ ( image @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
thf(481,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: product_prod @ TA @ TB,C: product_prod @ TA @ TB] :
( ( C = B )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ C )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_split__weak__cong) ).
thf(352,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: product_prod @ TA @ TB,C: product_prod @ TA @ TB] :
( ( C = B )
=> ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ C )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(94,axiom,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(408,plain,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TA @ TB,C: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( image @ TA @ TB @ B @ A ) ) )
<=> ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) )
& ( C
= ( aa @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_image__iff) ).
thf(523,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TA @ TB,C: TB] :
( ( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( image @ TA @ TB @ B @ A ) ) )
=> ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) )
& ( C
= ( aa @ TA @ TB @ B @ D ) ) ) )
& ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) )
& ( C
= ( aa @ TA @ TB @ B @ D ) ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( image @ TA @ TB @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( the @ ( product_prod @ TB @ TA ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ bool @ bool @ TA ) ) @ ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TB ) @ fconj ) @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( fequal @ TB ) @ B ) ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_The__split__eq) ).
thf(440,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( the @ ( product_prod @ TB @ TA ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ bool @ bool @ TA ) ) @ ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TB ) @ fconj ) @ ( aa @ TB @ ( fun @ TB @ bool ) @ ( fequal @ TB ) @ B ) ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ A @ C ) ) @ ( image @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_imageI) ).
thf(385,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ A @ C ) ) @ ( image @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(84,axiom,
finite_finite1 @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(384,plain,
finite_finite1 @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(5,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(142,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
cl_Groups_Ominus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
thf(153,plain,
cl_Groups_Ominus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(92,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(404,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(301,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)],[53]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(436,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( product_Pair @ TE @ TF ) @ G ) @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod__induct6) ).
thf(184,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( product_Pair @ TE @ TF ) @ G ) @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ bool,B: fun @ TA @ TC,C: fun @ TC @ TB] :
( ( image @ TC @ TB @ C @ ( image @ TA @ TC @ B @ A ) )
= ( image @ TA @ TB @ ( aa @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) @ ( aa @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) @ ( combb @ TC @ TB @ TA ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_image__image) ).
thf(460,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ bool,B: fun @ TA @ TC,C: fun @ TC @ TB] :
( ( image @ TC @ TB @ C @ ( image @ TA @ TC @ B @ A ) )
= ( image @ TA @ TB @ ( aa @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) @ ( aa @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) @ ( combb @ TC @ TB @ TA ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(51,axiom,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite) ).
thf(284,plain,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_mem__splitI) ).
thf(316,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
( ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ),C: product_prod @ TC @ TB] :
( ! [D: TC,E: TB] :
( ( ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ D ) @ E )
= C )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ B @ D ) @ E ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TC @ TB @ ( fun @ TA @ bool ) ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_splitI2_H) ).
thf(261,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ),C: product_prod @ TC @ TB] :
( ! [D: TC,E: TB] :
( ( ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ D ) @ E )
= C )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ B @ D ) @ E ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TC @ TB @ ( fun @ TA @ bool ) ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(27,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(216,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(108,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fdisj ) @ B ) ) @ A ) ) )
<=> ( ( finite_finite @ TA @ ( collect @ TA @ B ) )
& ( finite_finite @ TA @ ( collect @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__disjI) ).
thf(443,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fdisj ) @ B ) ) @ A ) ) )
=> ( ( finite_finite @ TA @ ( collect @ TA @ B ) )
& ( finite_finite @ TA @ ( collect @ TA @ A ) ) ) )
& ( ( ( finite_finite @ TA @ ( collect @ TA @ B ) )
& ( finite_finite @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fdisj ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( product_Pair @ TD @ TE ) @ F ) @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_prod__induct5) ).
thf(376,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( product_Pair @ TD @ TE ) @ F ) @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(348,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)],[70]) ).
thf(7,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(147,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(49,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(280,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(29,axiom,
cl_Groups_Ominus @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(221,plain,
cl_Groups_Ominus @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) ) @ ( minus_minus @ ( fun @ TA @ TB ) ) @ C ) @ B ) @ A )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( minus_minus @ TB ) @ ( aa @ TA @ TB @ C @ A ) ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_minus__apply) ).
thf(243,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) ) @ ( minus_minus @ ( fun @ TA @ TB ) ) @ C ) @ B ) @ A )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( minus_minus @ TB ) @ ( aa @ TA @ TB @ C @ A ) ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(44,axiom,
finite_finite @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096finite_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
thf(265,plain,
finite_finite @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_prod__cases4) ).
thf(507,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod_Oexhaust) ).
thf(307,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(34,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Diff__iff) ).
thf(233,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_curryD) ).
thf(201,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(82,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(381,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
( ( finite_finite @ TA @ ( collect @ TA @ B ) )
=> ( ( finite_finite @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) ) @ A ) ) ) )
<=> ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( finite_finite @ TB @ ( collect @ TB @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( combc @ TB @ TA @ bool ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__Collect__bounded__ex) ).
thf(334,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
( ( finite_finite @ TA @ ( collect @ TA @ B ) )
=> ( ( ( finite_finite @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) ) @ A ) ) ) )
=> ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( finite_finite @ TB @ ( collect @ TB @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( combc @ TB @ TA @ bool ) @ A ) @ C ) ) ) ) )
& ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( finite_finite @ TB @ ( collect @ TB @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( combc @ TB @ TA @ bool ) @ A ) @ C ) ) ) )
=> ( finite_finite @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ~ ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TB @ ( image @ TA @ TB @ A @ B ) )
=> ? [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( finite_finite @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ TB @ ( fun @ TB @ bool ) @ TA ) @ ( fequal @ TB ) ) @ A ) ) @ ( aa @ TA @ TB @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_pigeonhole__infinite) ).
thf(392,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ~ ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TB @ ( image @ TA @ TB @ A @ B ) )
=> ? [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( finite_finite @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ TB @ ( fun @ TB @ bool ) @ TA ) @ ( fequal @ TB ) ) @ A ) ) @ ( aa @ TA @ TB @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(102,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ fNot ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_set__diff__eq) ).
thf(429,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ fNot ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( the @ ( product_prod @ TA @ TB ) @ A )
= ( the @ ( product_prod @ TA @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ bool @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_split__paired__The) ).
thf(467,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( the @ ( product_prod @ TA @ TB ) @ A )
= ( the @ ( product_prod @ TA @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ bool @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(125,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( set @ TA @ A ) ) )
=> ( ( linord2118332866rt_key @ TA @ TA @ ( combi @ TA ) @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_insort__insert__triv) ).
thf(493,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( set @ TA @ A ) ) )
=> ( ( linord2118332866rt_key @ TA @ TA @ ( combi @ TA ) @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TB )
& ( zero @ TC ) )
=> ! [A: fun @ TB @ ( fun @ TC @ TA )] :
( ( aa @ ( list @ TC ) @ ( list @ TA ) @ ( aa @ ( list @ TB ) @ ( fun @ ( list @ TC ) @ ( list @ TA ) ) @ ( zipwith0 @ TB @ TC @ TA @ A ) @ ( nil @ TB ) ) @ ( nil @ TC ) )
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zipwith0_Osimps_I1_J) ).
thf(224,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TB )
& ( zero @ TC ) )
=> ! [A: fun @ TB @ ( fun @ TC @ TA )] :
( ( aa @ ( list @ TC ) @ ( list @ TA ) @ ( aa @ ( list @ TB ) @ ( fun @ ( list @ TC ) @ ( list @ TA ) ) @ ( zipwith0 @ TB @ TC @ TA @ A ) @ ( nil @ TB ) ) @ ( nil @ TC ) )
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( product_curry @ TA @ TB @ TC @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_split__curry) ).
thf(156,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( product_curry @ TA @ TB @ TC @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(356,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(99,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(420,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Pair__eq) ).
thf(193,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(119,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(476,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_prod__caseI) ).
thf(489,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(328,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(117,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(471,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(130,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_the__sym__eq__trivial) ).
thf(515,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(112,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite @ TA @ ( collect @ TA @ B ) )
| ( finite_finite @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__conjI) ).
thf(457,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite @ TA @ ( collect @ TA @ B ) )
| ( finite_finite @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_DiffE) ).
thf(371,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: TB,C: fun @ TA @ bool,D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ( B
= ( aa @ TA @ TB @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ B ) @ ( image @ TA @ TB @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rev__image__eqI) ).
thf(503,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: TB,C: fun @ TA @ bool,D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ( B
= ( aa @ TA @ TB @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ B ) @ ( image @ TA @ TB @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_splitD) ).
thf(266,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_split__paired__All) ).
thf(360,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(90,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_DiffD1) ).
thf(398,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(134,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ B ) )
& ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( C = B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_theI_H) ).
thf(530,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ B ) )
& ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( C = B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_splitI) ).
thf(343,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(35,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(237,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).
thf(166,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite1 @ TA )
& ( finite_finite1 @ TB ) )
=> ( finite_finite1 @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list__ex1__simps_I1_J) ).
thf(148,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( produc1605651328_split @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_internal__split__conv) ).
thf(423,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( produc1605651328_split @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_pred__equals__eq2) ).
thf(286,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(96,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(413,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ D ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_splitD_H) ).
thf(382,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ D ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(57,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ C ) @ A ) ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_iprod__left__diff__distrib) ).
thf(313,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ C ) @ A ) ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc1605651328_split @ TA @ TB @ TC )
= ( product_prod_case @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_internal__split__def) ).
thf(144,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc1605651328_split @ TA @ TB @ TC )
= ( product_prod_case @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_prod_Orecs) ).
thf(159,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( list_ex1 @ TA @ B @ A )
<=> ? [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ A ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_list__ex1__iff) ).
thf(172,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( list_ex1 @ TA @ B @ A )
=> ? [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ A ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( D = C ) ) ) )
& ( ? [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ A ) ) )
& ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( D = C ) ) )
=> ( list_ex1 @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ ( collect @ TA @ B ) )
=> ( finite_finite @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combs @ TA @ bool @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ TB ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ TB @ bool @ TA ) ) @ ( fequal @ TB ) ) ) @ A ) ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__image__set) ).
thf(219,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ ( collect @ TA @ B ) )
=> ( finite_finite @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combs @ TA @ bool @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ TB ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ TB @ bool @ TA ) ) @ ( fequal @ TB ) ) ) @ A ) ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_prod__cases3) ).
thf(230,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(110,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(451,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(59,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(318,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(104,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(434,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(86,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( finite_finite @ TA @ A )
=> ? [B: list @ TA] :
( ( set @ TA @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_finite__list) ).
thf(387,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( finite_finite @ TA @ A )
=> ? [B: list @ TA] :
( ( set @ TA @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ TB,D: TB] :
( ( D
= ( aa @ TA @ TB @ C @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ D ) @ ( image @ TA @ TB @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_image__eqI) ).
thf(323,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ TB,D: TB] :
( ( D
= ( aa @ TA @ TB @ C @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ D ) @ ( image @ TA @ TB @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ TC @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_split__eta) ).
thf(213,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TA @ TB ) @ TC @ TB ) @ A ) ) @ ( product_Pair @ TA @ TB ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(122,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) )
<=> ! [B: bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( pp @ B ) )
=> ( pp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Ex__def) ).
thf(483,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ! [B: bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( pp @ B ) )
=> ( pp @ B ) ) )
& ( ! [B: bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( pp @ B ) )
=> ( pp @ B ) )
=> ? [B: TA] : ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(132,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) @ A )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Diff__idemp) ).
thf(520,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) @ A )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(69,axiom,
( ( lbounds @ as )
!= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096lbounds_Aas_A_126_061_A_091_093_096) ).
thf(345,plain,
( ( lbounds @ as )
!= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(76,axiom,
( ( image @ ( product_prod @ int @ ( list @ int ) ) @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ int ) @ ( product_prod_case @ int @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( aa @ ( fun @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ int ) @ ( combb @ int @ int @ ( list @ int ) ) ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) )
= ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_I_F_Ii_M_Aks_J_O_Ai_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_J_A_092_096_Aset_A_Ilbounds_Aas_J_A_061_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
thf(367,plain,
( ( image @ ( product_prod @ int @ ( list @ int ) ) @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ int ) @ ( product_prod_case @ int @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( aa @ ( fun @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ int ) @ ( combb @ int @ int @ ( list @ int ) ) ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) )
= ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(48,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(278,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
finite_finite @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite_finite @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(135,plain,
~ ( finite_finite @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(106,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_DiffD2) ).
thf(438,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC )] :
( ( product_curry @ TA @ TB @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_curry__split) ).
thf(473,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC )] :
( ( product_curry @ TA @ TB @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_prod__cases6) ).
thf(426,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ B ) @ A ) )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_splitE) ).
thf(162,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ B ) @ A ) )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: fun @ ( product_prod @ TA @ TB ) @ bool,C: TB,D: TA] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ C ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ A @ D ) @ C ) ) @ ( image @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_pair__imageI) ).
thf(374,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: fun @ ( product_prod @ TA @ TB ) @ bool,C: TB,D: TA] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ C ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ A @ D ) @ C ) ) @ ( image @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_prod_Osimps_I2_J) ).
thf(255,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: bool,C: product_prod @ TA @ TB] :
( ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( combb @ bool @ bool @ TB ) @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) ) ) @ A ) ) @ C ) )
<=> ( ( pp @ B )
& ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_split__part) ).
thf(209,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: bool,C: product_prod @ TA @ TB] :
( ( ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( combb @ bool @ bool @ TB ) @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) ) ) @ A ) ) @ C ) )
=> ( ( pp @ B )
& ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ C ) ) ) )
& ( ( ( pp @ B )
& ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ C ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ TA ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( combb @ bool @ bool @ TB ) @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) ) ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( product_Pair @ TC @ TD ) @ E ) @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_prod__induct4) ).
thf(282,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( product_Pair @ TC @ TD ) @ E ) @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ),C: fun @ TE @ ( fun @ TD @ TC )] :
( ( aa @ ( product_prod @ TE @ TD ) @ TC @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) ) @ ( product_prod_case @ TA @ TB @ ( product_prod @ TE @ TD ) ) @ B ) @ A ) )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TE @ TD ) @ TC @ TB ) @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_split__twice) ).
thf(150,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ),C: fun @ TE @ ( fun @ TD @ TC )] :
( ( aa @ ( product_prod @ TE @ TD ) @ TC @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( product_prod @ TE @ TD ) ) @ ( product_prod_case @ TA @ TB @ ( product_prod @ TE @ TD ) ) @ B ) @ A ) )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( aa @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) ) @ ( fun @ TA @ ( fun @ TB @ TC ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) @ TA ) @ ( aa @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( fun @ ( fun @ TB @ ( product_prod @ TE @ TD ) ) @ ( fun @ TB @ TC ) ) @ ( combb @ ( product_prod @ TE @ TD ) @ TC @ TB ) @ ( aa @ ( fun @ TE @ ( fun @ TD @ TC ) ) @ ( fun @ ( product_prod @ TE @ TD ) @ TC ) @ ( product_prod_case @ TE @ TD @ TC ) @ C ) ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(62,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(327,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(56,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(310,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(64,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_the__eq__trivial) ).
thf(331,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_split__paired__Ex) ).
thf(463,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ C ) @ B ) @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_curry__conv) ).
thf(338,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ C ) @ B ) @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(116,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(470,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_the__equality) ).
thf(250,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] :
( ( B
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ C ) @ D ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_splitI2) ).
thf(203,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] :
( ( B
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ C ) @ D ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) ) @ ( product_prod_case @ TC @ TA @ ( fun @ TB @ bool ) ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mem__splitE) ).
thf(319,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) ) @ ( product_prod_case @ TC @ TA @ ( fun @ TB @ bool ) ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(304,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(42,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Ominus @ TA )
& ( zero @ TA ) )
=> ( ( minus_minus @ ( list @ TA ) )
= ( zipwith0 @ TA @ TA @ TA @ ( minus_minus @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_list__diff__def) ).
thf(258,plain,
! [TA: $tType] :
( ( ( cl_Groups_Ominus @ TA )
& ( zero @ TA ) )
=> ( ( minus_minus @ ( list @ TA ) )
= ( zipwith0 @ TA @ TA @ TA @ ( minus_minus @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(87,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(390,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TA @ TB,C: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( image @ TA @ TB @ B @ A ) ) )
=> ~ ! [D: TA] :
( ( C
= ( aa @ TA @ TB @ B @ D ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_imageE) ).
thf(186,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TA @ TB,C: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ C ) @ ( image @ TA @ TB @ B @ A ) ) )
=> ~ ! [D: TA] :
( ( C
= ( aa @ TA @ TB @ B @ D ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( image @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_image__ident) ).
thf(139,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( image @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(98,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(418,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_PairE) ).
thf(378,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_splitE2) ).
thf(246,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ B @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(129,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ? [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_the1__equality) ).
thf(510,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ? [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_curryI) ).
thf(207,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ C @ B ) ) @ ( image @ TA @ TB @ C @ ( set @ TA @ A ) ) ) )
=> ( ( linord2118332866rt_key @ TA @ TB @ C @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_insort__insert__key__triv) ).
thf(478,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ C @ B ) ) @ ( image @ TA @ TB @ C @ ( set @ TA @ A ) ) ) )
=> ( ( linord2118332866rt_key @ TA @ TB @ C @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: product_prod @ TB @ TC,C: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ C ) @ B ) @ A ) )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ C @ D ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_splitE_H) ).
thf(447,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: product_prod @ TB @ TC,C: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ C ) @ B ) @ A ) )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ C @ D ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(103,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( finite_finite @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__Diff) ).
thf(432,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( finite_finite @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) ) @ ( minus_minus @ ( fun @ TA @ TB ) ) @ B ) @ A ) @ C )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( minus_minus @ TB ) @ ( aa @ TA @ TB @ B @ C ) ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_fun__diff__def) ).
thf(410,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TB ) ) @ ( minus_minus @ ( fun @ TA @ TB ) ) @ B ) @ A ) @ C )
= ( aa @ TB @ TB @ ( aa @ TB @ ( fun @ TB @ TB ) @ ( minus_minus @ TB ) @ ( aa @ TA @ TB @ B @ C ) ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ ( the @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_theI) ).
thf(168,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ ( the @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ A ) @ B ) @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_curry__def) ).
thf(405,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ A ) @ B ) @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(20,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ A ) @ ( nil @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_list__diff__Nil2) ).
thf(190,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ A ) @ ( nil @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Pair__inject) ).
thf(273,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',fact_63_list_Osimps_I4_J) ).
thf(136,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)],[3]) ).
thf(67,axiom,
! [TA: $tType,A: list @ TA] : ( finite_finite @ TA @ ( set @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__set) ).
thf(341,plain,
! [TA: $tType,A: list @ TA] : ( finite_finite @ TA @ ( set @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(46,axiom,
! [TA: $tType,A: TA,B: TA,C: bool] :
( ( ( pp @ C )
=> ( B
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) )
& ( ~ ( pp @ C )
=> ( A
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_If__def) ).
thf(268,plain,
! [TA: $tType,A: TA,B: TA,C: bool] :
( ( ( pp @ C )
=> ( B
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) )
& ( ~ ( pp @ C )
=> ( A
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combb @ bool @ bool @ TA ) @ ( fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(73,axiom,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__code) ).
thf(358,plain,
! [TA: $tType] :
( ( finite_finite1 @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ),B: TC,C: product_prod @ TA @ TB] :
( ! [D: TA,E: TB] :
( ( C
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ E ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TA @ TB @ ( fun @ TC @ bool ) ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_mem__splitI2) ).
thf(400,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ),B: TC,C: product_prod @ TA @ TB] :
( ! [D: TA,E: TB] :
( ( C
= ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ E ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( fun @ TC @ bool ) @ bool @ ( aa @ TC @ ( fun @ ( fun @ TC @ bool ) @ bool ) @ ( member @ TC ) @ B ) @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TA @ TB @ ( fun @ TC @ bool ) ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(97,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( finite_finite @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ A ) @ B ) )
<=> ( finite_finite @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__Diff2) ).
thf(415,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite @ TA @ B )
=> ( ( ( finite_finite @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ A ) @ B ) )
=> ( finite_finite @ TA @ A ) )
& ( ( finite_finite @ TA @ A )
=> ( finite_finite @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_prod__cases5) ).
thf(239,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(37,axiom,
finite_finite @ int @ ( image @ ( product_prod @ int @ ( list @ int ) ) @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ int ) @ ( product_prod_case @ int @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( aa @ ( fun @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ int ) @ ( combb @ int @ int @ ( list @ int ) ) ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__096finite_A_I_I_F_Ii_M_Aks_J_O_Ai_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_J_A_092_096_Aset_A_Ilbounds_Aas_J_J_096) ).
thf(242,plain,
finite_finite @ int @ ( image @ ( product_prod @ int @ ( list @ int ) ) @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ int ) @ ( product_prod_case @ int @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ int @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( aa @ ( fun @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ int ) @ ( combb @ int @ int @ ( list @ int ) ) ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(395,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(77,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_DiffI) ).
thf(369,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(227,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)],[32]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_prod__induct3) ).
thf(491,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_curryE) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC,B: fun @ TA @ ( fun @ TB @ TC )] :
( ! [C: TA,D: TB] :
( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ C ) @ D )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ A @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) )
=> ( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_cond__split__eta) ).
thf(364,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC,B: fun @ TA @ ( fun @ TB @ TC )] :
( ! [C: TA,D: TB] :
( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ C ) @ D )
= ( aa @ ( product_prod @ TA @ TB ) @ TC @ A @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) )
=> ( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( D = C )
=> ( ! [E: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ C ) )
=> ( ( aa @ TA @ TB @ B @ E )
= ( aa @ TA @ TB @ A @ E ) ) )
=> ( ( image @ TA @ TB @ B @ D )
= ( image @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_image__cong) ).
thf(496,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( D = C )
=> ( ! [E: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ C ) )
=> ( ( aa @ TA @ TB @ B @ E )
= ( aa @ TA @ TB @ A @ E ) ) )
=> ( ( image @ TA @ TB @ B @ D )
= ( image @ TA @ TB @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_split__conv) ).
thf(454,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(534,plain,
$false,
inference(e,[status(thm)],[154,518,481,352,408,523,440,385,384,142,153,404,301,436,184,460,284,316,261,216,443,376,348,147,280,221,243,265,507,307,233,201,381,334,392,429,467,493,224,156,356,420,193,476,489,328,471,515,457,371,503,266,360,398,530,343,237,166,148,423,286,413,382,313,144,159,172,219,230,451,318,434,387,323,213,483,520,345,367,278,135,438,473,426,162,374,255,209,282,150,327,310,331,463,338,470,250,203,319,304,258,390,186,139,418,378,246,510,207,478,447,432,410,168,405,190,273,136,341,268,358,400,415,239,242,395,369,227,491,222,364,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM090_5 : TPTP v8.1.2. Released v6.0.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n021.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Fri May 19 03:23:13 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.14 % [INFO] Parsing done (250ms).
% 1.89/1.15 % [INFO] Running in sequential loop mode.
% 2.63/1.40 % [INFO] eprover registered as external prover.
% 2.63/1.40 % [INFO] cvc4 registered as external prover.
% 2.63/1.40 % [INFO] Scanning for conjecture ...
% 3.35/1.60 % [INFO] Found a conjecture and 132 axioms. Running axiom selection ...
% 3.76/1.71 % [INFO] Axiom selection finished. Selected 132 axioms (removed 0 axioms).
% 4.36/1.90 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.36/1.92 % [INFO] Type checking passed.
% 4.68/1.93 % [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 ...
% 41.56/27.44 % External prover 'e' found a proof!
% 41.56/27.44 % [INFO] Killing All external provers ...
% 41.56/27.44 % Time passed: 26894ms (effective reasoning time: 26292ms)
% 41.56/27.44 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 41.56/27.45 % Axioms used in derivation (132): arity_fun___Finite__Set_Ofinite, help_fdisj_2_1_U, fact_27_cond__split__eta, help_fimplies_2_1_U, arity_HOL_Obool___Finite__Set_Ofinite, fact_86_list__ex1__simps_I1_J, fact_16_split__conv, fact_65_prod__cases6, fact_78_list__diff__def, help_COMBS_1_1_U, fact_25_finite, fact_18_list__diff__Nil2, fact_35_splitI, fact_22_prod_Osimps_I2_J, help_fconj_3_1_U, fact_69_prod__cases4, fact_4_finite__Collect__conjI, fact_15_finite__imageI, fact_7_split__paired__All, fact_1__096lbounds_Aas_A_126_061_A_091_093_096, fact_36_prod__caseI, fact_80_zipwith0_Osimps_I1_J, arity_Int_Oint___Groups_Ominus, fact_61_fun__diff__def, fact_24_Pair__inject, fact_64_prod__induct6, help_COMBI_1_1_U, fact_50_internal__split__conv, fact_26_split__paired__Ex, fact_60_minus__apply, fact_81_curryE, fact_14_finite__Diff, arity_HOL_Obool___Groups_Ominus, fact_45_splitD, fact_11_finite__Collect__bounded__ex, arity_Int_Oint___Rings_Oring, fact_48_imageI, fact_87_The__split__eq, fact_83_curry__split, fact_52_imageE, fact_54_splitE, fact_67_prod__induct5, fact_97_Ex__def, fact_63_list_Osimps_I4_J, fact_57_split__part, fact_88_list__ex1__iff, fact_41_DiffE, help_fNot_2_1_U, fact_90_If__def, help_fNot_1_1_U, fact_9__096finite_A_I_I_F_Ii_M_Aks_J_O_Ai_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_J_A_092_096_Aset_A_Ilbounds_Aas_J_J_096, fact_2_finite__set, arity_HOL_Obool___Orderings_Olinorder, fact_82_curryD, fact_91_the__eq__trivial, fact_94_theI, fact_79_curryI, arity_List_Olist___Groups_Ominus, fact_39_Diff__idemp, fact_99_insort__insert__triv, help_COMBB_1_1_U, fact_34_image__image, fact_30_splitE2, fact_37_mem__splitI, fact_95_theI_H, fact_73_PairE, help_fdisj_1_1_U, fact_96_the1__equality, fact_66_prod__cases5, help_fconj_2_1_U, fact_42_set__diff__eq, fact_17_pair__imageI, fact_46_splitD_H, fact_71_prod__cases3, fact_3_finite__Collect__disjI, fact_31_finite__list, fact_8_Pair__eq, arity_Int_Oint___Orderings_Olinorder, fact_38_Diff__iff, fact_85_curry__def, help_fequal_1_1_T, fact_76_mem__def, fact_28_pigeonhole__infinite, fact_49_image__iff, fact_40_DiffI, arity_Int_Oint___Groups_Ogroup__add, fact_58_splitE_H, help_COMBC_1_1_U, fact_93_the__equality, fact_44_DiffD2, fact_20_split__weak__cong, fact_19_split__twice, fact_33_internal__split__def, fact_13_pred__equals__eq2, fact_68_prod__induct4, arity_prod___Finite__Set_Ofinite, fact_62_image__cong, fact_6_finite__code, help_fequal_2_1_T, fact_53_splitI2, help_fconj_1_1_U, help_fdisj_3_1_U, fact_21_finite__Diff2, fact_5__096_I_F_Ii_M_Aks_J_O_Ai_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_J_A_092_096_Aset_A_Ilbounds_Aas_J_A_061_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096, fact_32_prod_Orecs, fact_70_prod__induct3, fact_56_splitI2_H, fact_77_Collect__def, fact_98_insort__insert__key__triv, fact_84_split__curry, help_pp_1_1_U, fact_10_finite__image__set, fact_59_mem__splitE, help_fimplies_1_1_U, fact_43_DiffD1, fact_23_split__eta, fact_75_ext, fact_0__096finite_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096, fact_47_rev__image__eqI, arity_Int_Oint___Groups_Ozero, fact_92_the__sym__eq__trivial, help_fimplies_3_1_U, help_pp_2_1_U, fact_51_image__ident, fact_72_prod_Oexhaust, help_fEx_1_1_U, fact_29_image__eqI, fact_55_mem__splitI2, fact_12_iprod__left__diff__distrib, arity_fun___Groups_Ominus, fact_74_curry__conv, fact_89_split__paired__The
% 41.56/27.45 % No. of inferences in proof: 268
% 41.56/27.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26894 ms resp. 26292 ms w/o parsing
% 42.62/27.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.62/27.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------