TSTP Solution File: COM047_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM047_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 10:13:59 EDT 2023
% Result : Theorem 24.04s 12.07s
% Output : Refutation 24.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 183
% Syntax : Number of formulae : 309 ( 155 unt; 59 typ; 0 def)
% Number of atoms : 671 ( 264 equ; 0 cnn)
% Maximal formula atoms : 51 ( 2 avg)
% Number of connectives : 3502 ( 80 ~; 26 |; 61 &;3216 @)
% ( 19 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 57 usr; 13 con; 0-6 aty)
% Number of variables : 777 ( 0 ^; 712 !; 21 ?; 777 :)
% ( 44 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(semiring_div_type,type,
semiring_div:
!>[TA: $tType] : $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( fun @ TB @ ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(div_mod_type,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(equal_equal_type,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(iprod_type,type,
iprod:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > TA ) ).
thf(zipwith0_type,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( list @ TC ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(listMem_type,type,
listMem:
!>[TA: $tType] : ( TA > ( list @ TA ) > $o ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(list_rec_type,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) ) > ( list @ TA ) > TB ) ).
thf(list_size_type,type,
list_size:
!>[TA: $tType] : ( ( fun @ TA @ nat ) > ( list @ TA ) > nat ) ).
thf(list_all_type,type,
list_all:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(member1_type,type,
member1:
!>[TA: $tType] : ( ( list @ TA ) > TA > $o ) ).
thf(null_type,type,
null:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(sublist_type,type,
sublist:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ nat @ bool ) > ( list @ TA ) ) ).
thf(tl_type,type,
tl:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(i_Z_type,type,
i_Z: atom > ( list @ int ) > $o ).
thf(asubst_type,type,
asubst: int > ( list @ int ) > atom > atom ).
thf(dvd_type,type,
dvd: int > int > ( list @ int ) > atom ).
thf(c_PresArith_Oatom_OLe_type,type,
c_PresArith_Oatom_OLe: int > ( list @ int ) > atom ).
thf(nDvd_type,type,
nDvd: int > int > ( list @ int ) > atom ).
thf(atom_case_type,type,
atom_case:
!>[TA: $tType] : ( ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > atom > TA ) ).
thf(atom_rec_type,type,
atom_rec:
!>[TA: $tType] : ( ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > atom > TA ) ).
thf(atom_size_type,type,
atom_size: atom > nat ).
thf(decr_Z_type,type,
decr_Z: atom > atom ).
thf(divisor_type,type,
divisor: atom > int ).
thf(hd_coeff_type,type,
hd_coeff: atom > int ).
thf(hd_coeff1_type,type,
hd_coeff1: int > atom > atom ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(a_type,type,
a: atom ).
thf(e_type,type,
e: list @ int ).
thf(i_type,type,
i: int ).
thf(int1_type,type,
int1: int ).
thf(j_type,type,
j: int ).
thf(list1_type,type,
list1: list @ int ).
thf(56,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_atom_Osimps_I2_J) ).
thf(310,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(3,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(131,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(234,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_list_Osimps_I3_J) ).
thf(481,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(46,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_26_list_Osimps_I4_J) ).
thf(276,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)],[46]) ).
thf(55,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(308,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(115,axiom,
! [A: list @ int,B: int,C: int] :
( ( hd_coeff @ ( nDvd @ C @ B @ A ) )
= ( list_case @ int @ int @ ( zero_zero @ int ) @ ( combk @ int @ ( list @ int ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_hd__coeff_Osimps_I3_J) ).
thf(511,plain,
! [A: list @ int,B: int,C: int] :
( ( hd_coeff @ ( nDvd @ C @ B @ A ) )
= ( list_case @ int @ int @ ( zero_zero @ int ) @ ( combk @ int @ ( list @ int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( aa @ TA @ ( fun @ TB @ TA ) @ ( combk @ TA @ TB ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(202,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( aa @ TA @ ( fun @ TB @ TA ) @ ( combk @ TA @ TB ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(75,axiom,
! [A: int,B: int,C: int] :
( ( hd_coeff1 @ C @ ( dvd @ B @ A @ ( nil @ int ) ) )
= ( dvd @ B @ A @ ( nil @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_hd__coeff1_Osimps_I5_J) ).
thf(385,plain,
! [A: int,B: int,C: int] :
( ( hd_coeff1 @ C @ ( dvd @ B @ A @ ( nil @ int ) ) )
= ( dvd @ B @ A @ ( nil @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(118,axiom,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ F @ E @ D @ ( dvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ E @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_atom_Osimps_I11_J) ).
thf(533,plain,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ F @ E @ D @ ( dvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ E @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(125,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_null__rec_I1_J) ).
thf(550,plain,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(61,axiom,
! [A: list @ int,B: int,C: int] :
( ( atom_size @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_atom_Osize_I2_J) ).
thf(340,plain,
! [A: list @ int,B: int,C: int] :
( ( atom_size @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(84,axiom,
( ( hd_coeff @ a )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I2_J) ).
thf(417,plain,
( ( hd_coeff @ a )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(50,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(288,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(41,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__reorient) ).
thf(257,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(22,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mod__self) ).
thf(196,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(121,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(542,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(9,axiom,
! [A: list @ int,B: int,C: int] :
( ( size_size @ atom @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_atom_Osize_I5_J) ).
thf(157,plain,
! [A: list @ int,B: int,C: int] :
( ( size_size @ atom @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( nDvd @ F @ E @ D )
!= ( dvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_atom_Osimps_I9_J) ).
thf(189,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( nDvd @ F @ E @ D )
!= ( dvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(31,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(228,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(51,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(289,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)],[51]) ).
thf(96,axiom,
! [A: list @ int,B: int,C: int] :
( ( hd_coeff @ ( dvd @ C @ B @ A ) )
= ( list_case @ int @ int @ ( zero_zero @ int ) @ ( combk @ int @ ( list @ int ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_hd__coeff_Osimps_I2_J) ).
thf(448,plain,
! [A: list @ int,B: int,C: int] :
( ( hd_coeff @ ( dvd @ C @ B @ A ) )
= ( list_case @ int @ int @ ( zero_zero @ int ) @ ( combk @ int @ ( list @ int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(28,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(216,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(103,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( tl @ TA @ ( cons @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_tl_Osimps_I2_J) ).
thf(475,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( tl @ TA @ ( cons @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(26,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( list_all @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_list__all__simps_I2_J) ).
thf(211,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( list_all @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(116,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_splice_Osimps_I3_J) ).
thf(514,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(65,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mod__by__1) ).
thf(353,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(79,axiom,
! [A: list @ int,B: int,C: int] :
( ( decr_Z @ ( nDvd @ C @ B @ A ) )
= ( nDvd @ C @ B @ ( tl @ int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_decr_092_060_094isub_062Z_Osimps_I3_J) ).
thf(397,plain,
! [A: list @ int,B: int,C: int] :
( ( decr_Z @ ( nDvd @ C @ B @ A ) )
= ( nDvd @ C @ B @ ( tl @ int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(4,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( c_PresArith_Oatom_OLe @ E @ D )
!= ( nDvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_atom_Osimps_I6_J) ).
thf(132,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( c_PresArith_Oatom_OLe @ E @ D )
!= ( nDvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(243,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(88,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_list_Osimps_I2_J) ).
thf(428,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(113,axiom,
pp @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(507,plain,
pp @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(38,axiom,
! [A: list @ int,B: int,C: int] :
( ( atom_size @ ( nDvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_atom_Osize_I3_J) ).
thf(248,plain,
! [A: list @ int,B: int,C: int] :
( ( atom_size @ ( nDvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(44,axiom,
! [A: list @ int,B: int,C: int] :
( ( size_size @ atom @ ( nDvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_atom_Osize_I6_J) ).
thf(270,plain,
! [A: list @ int,B: int,C: int] :
( ( size_size @ atom @ ( nDvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(59,axiom,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( nDvd @ C @ B @ A ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_divisor_Osimps_I3_J) ).
thf(334,plain,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( nDvd @ C @ B @ A ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(10,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(160,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_list_Orecs_I1_J) ).
thf(137,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(102,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_list_Oinject) ).
thf(467,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(106,axiom,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list__nonempty__induct) ).
thf(484,plain,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,axiom,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_sublist__nil) ).
thf(361,plain,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(91,axiom,
! [A: int,B: int] :
( ( hd_coeff1 @ B @ ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) )
= ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_hd__coeff1_Osimps_I4_J) ).
thf(435,plain,
! [A: int,B: int] :
( ( hd_coeff1 @ B @ ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) )
= ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(101,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_neq__Nil__conv) ).
thf(461,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(108,axiom,
( a
= ( c_PresArith_Oatom_OLe @ int1 @ list1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Le) ).
thf(493,plain,
( a
= ( c_PresArith_Oatom_OLe @ int1 @ list1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(57,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_zero__reorient) ).
thf(324,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(49,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mod__by__0) ).
thf(285,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list_Oexhaust) ).
thf(403,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(76,axiom,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_atom_Osimps_I10_J) ).
thf(388,plain,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_list__ex1__simps_I1_J) ).
thf(356,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(30,axiom,
! [A: list @ int,B: int] :
( ( size_size @ atom @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_atom_Osize_I4_J) ).
thf(225,plain,
! [A: list @ int,B: int] :
( ( size_size @ atom @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(21,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mod__0) ).
thf(193,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list_Orecs_I2_J) ).
thf(547,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(62,axiom,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_list_Osize_I1_J) ).
thf(343,plain,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(68,axiom,
semiring_div @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Divides_Osemiring__div) ).
thf(360,plain,
semiring_div @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(25,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
= ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_eq__Nil__null) ).
thf(205,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(114,axiom,
! [A: list @ int,B: int] :
( ( decr_Z @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( c_PresArith_Oatom_OLe @ B @ ( tl @ int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_decr_092_060_094isub_062Z_Osimps_I1_J) ).
thf(508,plain,
! [A: list @ int,B: int] :
( ( decr_Z @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( c_PresArith_Oatom_OLe @ B @ ( tl @ int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__Cons__self) ).
thf(425,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(13,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(166,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)],[13]) ).
thf(42,axiom,
! [A: atom,B: list @ int,C: int] :
( ( divisor @ ( asubst @ C @ B @ A ) )
= ( divisor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_divisor__asubst) ).
thf(264,plain,
! [A: atom,B: list @ int,C: int] :
( ( divisor @ ( asubst @ C @ B @ A ) )
= ( divisor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(11,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(161,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,axiom,
! [A: list @ int,B: int,C: list @ int,D: int,E: int] :
( ( dvd @ E @ D @ C )
!= ( c_PresArith_Oatom_OLe @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_atom_Osimps_I5_J) ).
thf(279,plain,
! [A: list @ int,B: int,C: list @ int,D: int,E: int] :
( ( dvd @ E @ D @ C )
!= ( c_PresArith_Oatom_OLe @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ 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(180,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ 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)],[17]) ).
thf(94,axiom,
semiring_div @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(444,plain,
semiring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TB )
& ( zero @ TC ) )
=> ! [A: fun @ TB @ ( fun @ TC @ TA )] :
( ( zipwith0 @ TB @ TC @ TA @ A @ ( nil @ TB ) @ ( nil @ TC ) )
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zipwith0_Osimps_I1_J) ).
thf(291,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TB )
& ( zero @ TC ) )
=> ! [A: fun @ TB @ ( fun @ TC @ TA )] :
( ( zipwith0 @ TB @ TC @ TA @ A @ ( nil @ TB ) @ ( nil @ TC ) )
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(83,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) )
<=> ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
& ( list_all @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list__all__simps_I1_J) ).
thf(413,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) )
=> ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
& ( list_all @ TA @ C @ A ) ) )
& ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
& ( list_all @ TA @ C @ A ) )
=> ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(77,axiom,
! [A: int,B: int,C: int] :
( ( hd_coeff1 @ C @ ( nDvd @ B @ A @ ( nil @ int ) ) )
= ( nDvd @ B @ A @ ( nil @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_hd__coeff1_Osimps_I6_J) ).
thf(391,plain,
! [A: int,B: int,C: int] :
( ( hd_coeff1 @ C @ ( nDvd @ B @ A @ ( nil @ int ) ) )
= ( nDvd @ B @ A @ ( nil @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(95,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_not__Cons__self2) ).
thf(445,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(74,axiom,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zmod__self) ).
thf(382,plain,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
! [A: list @ int,B: int] :
( ( atom_size @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_atom_Osize_I1_J) ).
thf(236,plain,
! [A: list @ int,B: int] :
( ( atom_size @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(64,axiom,
! [TA: $tType,A: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_equal__Nil__null) ).
thf(350,plain,
! [TA: $tType,A: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member1 @ TA @ ( cons @ TA @ C @ B ) @ A )
<=> ( ( C = A )
| ( member1 @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_member__rec_I1_J) ).
thf(406,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( ( member1 @ TA @ ( cons @ TA @ C @ B ) @ A )
=> ( ( C = A )
| ( member1 @ TA @ B @ A ) ) )
& ( ( ( C = A )
| ( member1 @ TA @ B @ A ) )
=> ( member1 @ TA @ ( cons @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(29,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ B @ A )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_equal__list__def) ).
thf(219,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( equal_equal @ ( list @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(85,axiom,
! [A: list @ int,B: int,C: int] :
( ( decr_Z @ ( dvd @ C @ B @ A ) )
= ( dvd @ C @ B @ ( tl @ int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_decr_092_060_094isub_062Z_Osimps_I2_J) ).
thf(419,plain,
! [A: list @ int,B: int,C: int] :
( ( decr_Z @ ( dvd @ C @ B @ A ) )
= ( dvd @ C @ B @ ( tl @ int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(73,axiom,
! [A: list @ int,B: int,C: atom] :
( ( ( hd_coeff @ C )
= ( zero_zero @ int ) )
=> ( ( i_Z @ C @ ( cons @ int @ B @ A ) )
<=> ( i_Z @ ( decr_Z @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Z_Onot__dep__decr) ).
thf(377,plain,
! [A: list @ int,B: int,C: atom] :
( ( ( hd_coeff @ C )
= ( zero_zero @ int ) )
=> ( ( ( i_Z @ C @ ( cons @ int @ B @ A ) )
=> ( i_Z @ ( decr_Z @ C ) @ A ) )
& ( ( i_Z @ ( decr_Z @ C ) @ A )
=> ( i_Z @ C @ ( cons @ int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(32,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( dvd @ F @ E @ D )
!= ( nDvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_atom_Osimps_I8_J) ).
thf(230,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( dvd @ F @ E @ D )
!= ( nDvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(97,axiom,
! [A: int,B: list @ int,C: int] :
( ( asubst @ C @ B @ ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) )
= ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_asubst_Osimps_I4_J) ).
thf(451,plain,
! [A: int,B: list @ int,C: int] :
( ( asubst @ C @ B @ ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) )
= ( c_PresArith_Oatom_OLe @ A @ ( nil @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(37,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ ( nil @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_iprod__Nil) ).
thf(245,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ ( nil @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(71,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) )
<=> ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_ex1 @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list__ex1__simps_I2_J) ).
thf(367,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) )
=> ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_ex1 @ TA @ C @ A ) ) ) )
& ( ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_ex1 @ TA @ C @ A ) ) )
=> ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(7,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_splice__Nil2) ).
thf(140,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_iprod__Nil2) ).
thf(213,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(39,axiom,
! [A: list @ int,B: int,C: list @ int,D: int,E: int] :
( ( nDvd @ E @ D @ C )
!= ( c_PresArith_Oatom_OLe @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_atom_Osimps_I7_J) ).
thf(251,plain,
! [A: list @ int,B: int,C: list @ int,D: int,E: int] :
( ( nDvd @ E @ D @ C )
!= ( c_PresArith_Oatom_OLe @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_splice_Osimps_I2_J) ).
thf(455,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(78,axiom,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ F @ E @ D @ ( dvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ E @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_atom_Orecs_I2_J) ).
thf(394,plain,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ F @ E @ D @ ( dvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ E @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(43,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mod__mod__trivial) ).
thf(267,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(89,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(431,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(112,axiom,
! [TA: $tType,A: list @ TA,B: TA] : ( listMem @ TA @ B @ ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_elem) ).
thf(505,plain,
! [TA: $tType,A: list @ TA,B: TA] : ( listMem @ TA @ B @ ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(92,axiom,
! [A: list @ int,B: int] :
( ( divisor @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_divisor_Osimps_I1_J) ).
thf(438,plain,
! [A: list @ int,B: int] :
( ( divisor @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,axiom,
! [A: atom] :
( ! [B: int,C: list @ int] :
( A
!= ( c_PresArith_Oatom_OLe @ B @ C ) )
=> ( ! [B: int,C: int,D: list @ int] :
( A
!= ( dvd @ B @ C @ D ) )
=> ~ ! [B: int,C: int,D: list @ int] :
( A
!= ( nDvd @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_atom_Oexhaust) ).
thf(162,plain,
! [A: atom] :
( ! [B: int,C: list @ int] :
( A
!= ( c_PresArith_Oatom_OLe @ B @ C ) )
=> ( ! [B: int,C: int,D: list @ int] :
( A
!= ( dvd @ B @ C @ D ) )
=> ~ ! [B: int,C: int,D: list @ int] :
( A
!= ( nDvd @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(72,axiom,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_atom_Orecs_I1_J) ).
thf(374,plain,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(40,axiom,
! [TA: $tType,A: TA] :
~ ( member1 @ TA @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_member__rec_I2_J) ).
thf(255,plain,
! [TA: $tType,A: TA] :
~ ( member1 @ TA @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( zipwith0 @ TC @ TA @ TB @ C @ ( nil @ TC ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ ( zero_zero @ TC ) ) @ B ) @ ( zipwith0 @ TC @ TA @ TB @ C @ ( nil @ TC ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I4_J) ).
thf(458,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( zipwith0 @ TC @ TA @ TB @ C @ ( nil @ TC ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ ( zero_zero @ TC ) ) @ B ) @ ( zipwith0 @ TC @ TA @ TB @ C @ ( nil @ TC ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(23,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zero__neq__one) ).
thf(199,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_one__neq__zero) ).
thf(177,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,axiom,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( dvd @ C @ B @ A ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_divisor_Osimps_I2_J) ).
thf(331,plain,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( dvd @ C @ B @ A ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: list @ TC,D: TC,E: fun @ TC @ ( fun @ TA @ TB )] :
( ( zipwith0 @ TC @ TA @ TB @ E @ ( cons @ TC @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ E @ D ) @ B ) @ ( zipwith0 @ TC @ TA @ TB @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zipwith0_Osimps_I2_J) ).
thf(441,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: list @ TC,D: TC,E: fun @ TC @ ( fun @ TA @ TB )] :
( ( zipwith0 @ TC @ TA @ TB @ E @ ( cons @ TC @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ E @ D ) @ B ) @ ( zipwith0 @ TC @ TA @ TB @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_list_Osimps_I5_J) ).
thf(502,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(123,axiom,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zmod__zero) ).
thf(544,plain,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(8,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( nDvd @ F @ E @ D )
= ( nDvd @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_atom_Osimps_I3_J) ).
thf(143,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( ( nDvd @ F @ E @ D )
= ( nDvd @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( nDvd @ F @ E @ D )
= ( nDvd @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_sublist__singleton) ).
thf(497,plain,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(120,axiom,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_atom_Orecs_I3_J) ).
thf(539,plain,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( listMem @ TA @ C @ B )
=> ( listMem @ TA @ C @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_insert) ).
thf(495,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( listMem @ TA @ C @ B )
=> ( listMem @ TA @ C @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(117,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( listMem @ TA @ B @ A )
<=> ( ? [C: TA,D: list @ TA] :
( ( B = C )
& ( A
= ( cons @ TA @ C @ D ) ) )
| ? [C: TA,D: list @ TA,E: TA] :
( ( B = C )
& ( A
= ( cons @ TA @ E @ D ) )
& ( listMem @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_ListMem_Osimps) ).
thf(517,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( listMem @ TA @ B @ A )
=> ( ? [C: TA,D: list @ TA] :
( ( B = C )
& ( A
= ( cons @ TA @ C @ D ) ) )
| ? [C: TA,D: list @ TA,E: TA] :
( ( B = C )
& ( A
= ( cons @ TA @ E @ D ) )
& ( listMem @ TA @ C @ D ) ) ) )
& ( ( ? [C: TA,D: list @ TA] :
( ( B = C )
& ( A
= ( cons @ TA @ C @ D ) ) )
| ? [C: TA,D: list @ TA,E: TA] :
( ( B = C )
& ( A
= ( cons @ TA @ E @ D ) )
& ( listMem @ TA @ C @ D ) ) )
=> ( listMem @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(19,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(186,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [TA: $tType,A: list @ TA] :
( ( null @ TA @ A )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_List_Onull__def) ).
thf(171,plain,
! [TA: $tType,A: list @ TA] :
( ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TC,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( zipwith0 @ TC @ TA @ TB @ C @ ( cons @ TC @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ ( zero_zero @ TA ) ) @ ( zipwith0 @ TC @ TA @ TB @ C @ A @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zipwith0_Osimps_I3_J) ).
thf(478,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TC,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( zipwith0 @ TC @ TA @ TB @ C @ ( cons @ TC @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ ( zero_zero @ TA ) ) @ ( zipwith0 @ TC @ TA @ TB @ C @ A @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(346,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(119,axiom,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_atom_Osimps_I12_J) ).
thf(536,plain,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(90,axiom,
! [A: list @ int,B: int] :
( ( hd_coeff @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( list_case @ int @ int @ ( zero_zero @ int ) @ ( combk @ int @ ( list @ int ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_hd__coeff_Osimps_I1_J) ).
thf(432,plain,
! [A: list @ int,B: int] :
( ( hd_coeff @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( list_case @ int @ int @ ( zero_zero @ int ) @ ( combk @ int @ ( list @ int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ 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(168,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ 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)],[14]) ).
thf(18,axiom,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_tl_Osimps_I1_J) ).
thf(183,plain,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(86,axiom,
! [A: atom] :
( ( ( hd_coeff @ A )
= ( zero_zero @ int ) )
=> ( ( ( divisor @ A )
!= ( zero_zero @ int ) )
=> ( ( divisor @ ( decr_Z @ A ) )
!= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Z_Oanormal__decr) ).
thf(422,plain,
! [A: atom] :
( ( ( hd_coeff @ A )
= ( zero_zero @ int ) )
=> ( ( ( divisor @ A )
!= ( zero_zero @ int ) )
=> ( ( divisor @ ( decr_Z @ A ) )
!= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(45,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(273,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(54,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_splice_Osimps_I1_J) ).
thf(305,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(35,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( c_PresArith_Oatom_OLe @ E @ D )
!= ( dvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_atom_Osimps_I4_J) ).
thf(239,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( c_PresArith_Oatom_OLe @ E @ D )
!= ( dvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(67,axiom,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_null__rec_I2_J) ).
thf(358,plain,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(80,axiom,
! [A: int,B: int,C: list @ int,D: int] :
( ( asubst @ D @ C @ ( nDvd @ B @ A @ ( nil @ int ) ) )
= ( nDvd @ B @ A @ ( nil @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_asubst_Osimps_I6_J) ).
thf(400,plain,
! [A: int,B: int,C: list @ int,D: int] :
( ( asubst @ D @ C @ ( nDvd @ B @ A @ ( nil @ int ) ) )
= ( nDvd @ B @ A @ ( nil @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(48,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(283,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)],[48]) ).
thf(53,axiom,
! [A: list @ int,B: int,C: list @ int,D: int] :
( ( ( c_PresArith_Oatom_OLe @ D @ C )
= ( c_PresArith_Oatom_OLe @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_atom_Osimps_I1_J) ).
thf(294,plain,
! [A: list @ int,B: int,C: list @ int,D: int] :
( ( ( ( c_PresArith_Oatom_OLe @ D @ C )
= ( c_PresArith_Oatom_OLe @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_PresArith_Oatom_OLe @ D @ C )
= ( c_PresArith_Oatom_OLe @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1,conjecture,
( ( i_Z @ a @ ( cons @ int @ i @ e ) )
<=> ( i_Z @ a @ ( cons @ int @ j @ e ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( i_Z @ a @ ( cons @ int @ i @ e ) )
<=> ( i_Z @ a @ ( cons @ int @ j @ e ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(126,plain,
~ ( ( ( i_Z @ a @ ( cons @ int @ i @ e ) )
=> ( i_Z @ a @ ( cons @ int @ j @ e ) ) )
& ( ( i_Z @ a @ ( cons @ int @ j @ e ) )
=> ( i_Z @ a @ ( cons @ int @ i @ e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(136,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(337,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(122,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(543,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(107,axiom,
( ( div_mod @ int @ i @ ( divisor @ a ) )
= ( div_mod @ int @ j @ ( divisor @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
thf(491,plain,
( ( div_mod @ int @ i @ ( divisor @ a ) )
= ( div_mod @ int @ j @ ( divisor @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(98,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(454,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(70,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_insert__Nil) ).
thf(364,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(552,plain,
$false,
inference(e,[status(thm)],[310,131,234,481,276,308,511,202,385,533,550,340,417,288,257,196,542,157,189,228,289,448,216,475,211,514,353,397,132,243,428,507,248,270,334,160,137,467,484,361,435,461,493,324,285,403,388,356,225,193,547,343,360,205,508,425,166,264,161,279,180,444,291,413,391,445,382,236,350,406,219,419,377,230,451,245,367,140,213,251,455,394,267,431,505,438,162,374,255,458,199,177,331,441,502,544,143,497,539,495,517,186,171,478,346,536,432,168,183,422,273,305,239,358,400,283,294,126,136,337,543,491,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COM047_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 03:47:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.07 % [INFO] Parsing done (213ms).
% 1.72/1.08 % [INFO] Running in sequential loop mode.
% 2.06/1.29 % [INFO] eprover registered as external prover.
% 2.06/1.30 % [INFO] cvc4 registered as external prover.
% 2.06/1.30 % [INFO] Scanning for conjecture ...
% 2.28/1.40 % [INFO] Found a conjecture and 123 axioms. Running axiom selection ...
% 2.55/1.49 % [INFO] Axiom selection finished. Selected 123 axioms (removed 0 axioms).
% 3.07/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.07/1.65 % [INFO] Type checking passed.
% 3.07/1.65 % [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 ...
% 3.92/1.92 % [INFO] [Domain constraints] Detected constraint on bool
% 3.92/1.92 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 4.25/1.95 % [INFO] [Domain constraints] Detected constraint on bool
% 4.25/1.95 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 24.04/12.07 % External prover 'e' found a proof!
% 24.04/12.07 % [INFO] Killing All external provers ...
% 24.04/12.07 % Time passed: 11545ms (effective reasoning time: 10986ms)
% 24.04/12.07 % 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)>
% 24.04/12.07 % Axioms used in derivation (123): fact_35_insert__Nil, fact_26_list_Osimps_I4_J, fact_43_mod__self, help_COMBS_1_1_U, arity_Int_Oint___Groups_Oone, fact_63_atom_Osize_I2_J, fact_57_hd__coeff_Osimps_I2_J, fact_86_list__nonempty__induct, fact_17_mod__mod__trivial, fact_68_atom_Osimps_I9_J, fact_25_list_Osimps_I3_J, fact_88_tl_Osimps_I1_J, fact_71_atom_Osimps_I5_J, fact_2_list_Oinject, fact_50_atom_Osize_I4_J, fact_13_insert, help_fTrue_1_1_T, arity_Int_Oint___Rings_Oring, fact_23_member__rec_I2_J, fact_45_mod__by__1, fact_14_divisor_Osimps_I1_J, fact_19_ListMem_Osimps, fact_54_list__all__simps_I1_J, fact_69_atom_Osimps_I8_J, fact_85_atom_Orecs_I1_J, fact_61_sublist__nil, help_fNot_2_1_U, help_fTrue_1_1_U, fact_29_splice_Osimps_I1_J, fact_73_mem__def, arity_Nat_Onat___Divides_Osemiring__div, fact_60_atom_Osimps_I3_J, help_fNot_1_1_U, fact_4_assms_I2_J, fact_89_decr_092_060_094isub_062Z_Osimps_I1_J, help_fFalse_1_1_T, fact_18_one__reorient, fact_97_hd__coeff1_Osimps_I5_J, fact_12_elem, fact_27_eq__Nil__null, fact_76_atom_Osimps_I12_J, fact_34_list_Oexhaust, fact_59_atom_Osimps_I2_J, help_COMBB_1_1_U, fact_37_zipwith0_Osimps_I3_J, fact_93_hd__coeff1_Osimps_I6_J, fact_83_atom_Orecs_I3_J, fact_11_zipwith0_Osimps_I2_J, fact_9_list_Orecs_I2_J, fact_6_not__Cons__self2, fact_30_List_Onull__def, fact_46_zero__reorient, help_fdisj_1_1_U, fact_92_asubst_Osimps_I6_J, fact_75_atom_Osimps_I11_J, fact_41_zmod__self, fact_39_list__ex1__simps_I1_J, fact_55_list__all__simps_I2_J, fact_58_sublist__singleton, fact_66_divisor_Osimps_I2_J, fact_72_atom_Osimps_I6_J, fact_5_not__Cons__self, fact_33_neq__Nil__conv, fact_81_iprod__Nil2, fact_28_splice__Nil2, fact_20_member__rec_I1_J, fact_49_atom_Osize_I1_J, help_fequal_1_1_T, fact_94_divisor__asubst, fact_77_Z_Onot__dep__decr, fact_74_atom_Osimps_I7_J, fact_0_Le, fact_52_one__neq__zero, fact_47_equal__list__def, arity_Nat_Onat___Groups_Ozero, fact_40_zmod__zero, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_56_hd__coeff_Osimps_I3_J, fact_82_iprod__Nil, fact_15_atom_Osimps_I1_J, fact_1_assms_I3_J, fact_21_splice_Osimps_I2_J, fact_78_atom_Oexhaust, fact_96_asubst_Osimps_I4_J, fact_8_splice_Osimps_I3_J, fact_79_list_Osize_I1_J, fact_53_list__ex1__simps_I2_J, fact_7_list_Osimps_I5_J, fact_51_zero__neq__one, help_fequal_2_1_T, fact_3_assms_I1_J, fact_65_atom_Osize_I3_J, fact_24_list_Osimps_I2_J, fact_16_atom_Osimps_I10_J, help_fdisj_3_1_U, arity_Int_Oint___Rings_Ozero__neq__one, fact_32_list_Orecs_I1_J, fact_44_hd__coeff_Osimps_I1_J, fact_36_equal__Nil__null, arity_Nat_Onat___Groups_Oone, fact_67_divisor_Osimps_I3_J, fact_31_null__rec_I2_J, help_fFalse_1_1_U, fact_91_tl_Osimps_I2_J, fact_84_atom_Orecs_I2_J, fact_70_atom_Osimps_I4_J, fact_62_atom_Osize_I5_J, help_pp_1_1_U, fact_10_null__rec_I1_J, fact_48_mod__by__0, arity_Int_Oint___Divides_Osemiring__div, fact_90_decr_092_060_094isub_062Z_Osimps_I2_J, fact_42_mod__0, fact_22_zipwith0_Osimps_I1_J, fact_95_hd__coeff1_Osimps_I4_J, arity_Int_Oint___Groups_Ozero, help_pp_2_1_U, fact_87_decr_092_060_094isub_062Z_Osimps_I3_J, fact_38_zipwith0_Osimps_I4_J, arity_Nat_Onat___Rings_Ozero__neq__one, fact_80_Z_Oanormal__decr, fact_64_atom_Osize_I6_J
% 24.04/12.07 % No. of inferences in proof: 250
% 24.04/12.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11545 ms resp. 10986 ms w/o parsing
% 24.36/12.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.36/12.16 % [INFO] Killing All external provers ...
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