TSTP Solution File: COM080_5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM080_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 10:14:02 EDT 2023
% Result : Theorem 44.42s 20.06s
% Output : Refutation 44.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 174
% Syntax : Number of formulae : 299 ( 101 unt; 51 typ; 0 def)
% Number of atoms : 1024 ( 271 equ; 0 cnn)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 5063 ( 45 ~; 11 |; 63 &;4725 @)
% ( 24 <=>; 195 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 13 con; 0-5 aty)
% Number of variables : 656 ( 0 ^; 603 !; 14 ?; 656 :)
% ( 39 !>; 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(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Oplus_type,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ TA ) ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
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 ) ) > ( fun @ ( list @ TC ) @ ( fun @ ( list @ TB ) @ ( list @ TA ) ) ) ) ).
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_size_type,type,
list_size:
!>[TA: $tType] : ( ( fun @ TA @ nat ) > ( list @ TA ) > nat ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(set_type,type,
set:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ TA @ bool ) ) ).
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(interpret_type,type,
interpret:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ ( list @ TA ) @ bool ) ) > ( fm @ TB ) > ( list @ TA ) > $o ) ).
thf(list_conj_type,type,
list_conj:
!>[TA: $tType] : ( ( list @ ( fm @ TA ) ) > ( fm @ TA ) ) ).
thf(list_disj_type,type,
list_disj:
!>[TA: $tType] : ( ( list @ ( fm @ TA ) ) > ( fm @ TA ) ) ).
thf(map_fm_type,type,
map_fm:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( fm @ TB ) > ( fm @ TA ) ) ).
thf(neg_type,type,
neg:
!>[TA: $tType] : ( ( fm @ TA ) > ( fm @ TA ) ) ).
thf(qfree_type,type,
qfree:
!>[TA: $tType] : ( ( fm @ TA ) > $o ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(i_Z_type,type,
i_Z: fun @ atom @ ( fun @ ( list @ int ) @ bool ) ).
thf(asubst_type,type,
asubst: int > ( list @ int ) > ( fun @ atom @ atom ) ).
thf(divisor_type,type,
divisor: atom > int ).
thf(lbounds_type,type,
lbounds: ( list @ atom ) > ( list @ ( product_prod @ int @ ( list @ int ) ) ) ).
thf(qEpres896714165pres_1_type,type,
qEpres896714165pres_1: ( list @ atom ) > ( fm @ atom ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(as_type,type,
as: list @ atom ).
thf(il_type,type,
il: int ).
thf(ksl_type,type,
ksl: list @ int ).
thf(m_type,type,
m: int ).
thf(xs_type,type,
xs: list @ int ).
thf(88,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(420,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(112,axiom,
! [A: atom] :
( ( member @ atom @ A @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ ( aa @ atom @ atom @ ( asubst @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ il ) @ m ) @ ksl ) @ A ) ) @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096) ).
thf(503,plain,
! [A: atom] :
( ( member @ atom @ A @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ ( aa @ atom @ atom @ ( asubst @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ il ) @ m ) @ ksl ) @ A ) ) @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) )
<=> ( ( B = A )
| ( C
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__cancel1) ).
thf(138,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) )
=> ( ( B = A )
| ( C
= ( zero_zero @ nat ) ) ) )
& ( ( ( B = A )
| ( C
= ( zero_zero @ nat ) ) )
=> ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(69,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__imp__eq) ).
thf(347,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(83,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(408,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(115,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(511,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(76,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__left__imp__eq) ).
thf(384,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(111,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list_Osimps_I3_J) ).
thf(500,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(13,axiom,
cl_Groups_Oplus @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oplus) ).
thf(174,plain,
cl_Groups_Oplus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,axiom,
interpret @ atom @ int @ i_Z @ ( qEpres896714165pres_1 @ as ) @ xs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096) ).
thf(417,plain,
interpret @ atom @ int @ i_Z @ ( qEpres896714165pres_1 @ as ) @ xs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(94,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) )
& ( ~ ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= ( cons @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_List_Oinsert__def) ).
thf(436,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) )
& ( ~ ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(21,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_55_list_Osimps_I4_J) ).
thf(196,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)],[21]) ).
thf(1,conjecture,
! [A: atom] :
( ( member @ atom @ A @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ A ) @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ il ) @ m ) ) @ ( iprod @ int @ ksl @ xs ) ) @ xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: atom] :
( ( member @ atom @ A @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ A ) @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ il ) @ m ) ) @ ( iprod @ int @ ksl @ xs ) ) @ xs ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(125,plain,
~ ! [A: atom] :
( ( member @ atom @ A @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ A ) @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ il ) @ m ) ) @ ( iprod @ int @ ksl @ xs ) ) @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,axiom,
! [A: atom] :
( ( member @ atom @ A @ ( set @ atom @ as ) )
=> ( ( divisor @ A )
!= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_norm) ).
thf(344,plain,
! [A: atom] :
( ( member @ atom @ A @ ( set @ atom @ as ) )
=> ( ( divisor @ A )
!= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(17,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(189,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A ) )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__add__left__commute) ).
thf(421,plain,
! [A: nat,B: nat,C: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A ) )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(9,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_zero__reorient) ).
thf(152,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)],[9]) ).
thf(50,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_57_splice_Osimps_I3_J) ).
thf(289,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)],[50]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mult__is__0) ).
thf(179,plain,
! [A: nat,B: nat] :
( ( ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
| ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
| ( A
= ( zero_zero @ nat ) ) )
=> ( ( times_times @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TC,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ 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 ) ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ C ) @ A ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zipwith0_Osimps_I3_J) ).
thf(253,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TC,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ 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 ) ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ C ) @ A ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(238,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(116,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(514,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)],[116]) ).
thf(105,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_36_list_Oexhaust) ).
thf(480,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)],[105]) ).
thf(57,axiom,
! [A: list @ int,B: list @ ( fm @ atom )] :
( ( interpret @ atom @ int @ i_Z @ ( list_conj @ atom @ B ) @ A )
<=> ! [C: fm @ atom] :
( ( member @ ( fm @ atom ) @ C @ ( set @ ( fm @ atom ) @ B ) )
=> ( interpret @ atom @ int @ i_Z @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Z_OI__list__conj) ).
thf(312,plain,
! [A: list @ int,B: list @ ( fm @ atom )] :
( ( ( interpret @ atom @ int @ i_Z @ ( list_conj @ atom @ B ) @ A )
=> ! [C: fm @ atom] :
( ( member @ ( fm @ atom ) @ C @ ( set @ ( fm @ atom ) @ B ) )
=> ( interpret @ atom @ int @ i_Z @ C @ A ) ) )
& ( ! [C: fm @ atom] :
( ( member @ ( fm @ atom ) @ C @ ( set @ ( fm @ atom ) @ B ) )
=> ( interpret @ atom @ int @ i_Z @ C @ A ) )
=> ( interpret @ atom @ int @ i_Z @ ( list_conj @ atom @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(25,axiom,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_list_Osize_I1_J) ).
thf(206,plain,
! [TA: $tType,A: fun @ TA @ nat] :
( ( list_size @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(51,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_in__set__insert) ).
thf(292,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(75,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(381,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(121,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(534,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(28,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_54_splice_Osimps_I2_J) ).
thf(220,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)],[28]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add__is__0) ).
thf(366,plain,
! [A: nat,B: nat] :
( ( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(64,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insert__Nil) ).
thf(334,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(79,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_iprod__Nil2) ).
thf(392,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ A @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(90,axiom,
! [A: list @ int,B: list @ int,C: int,D: fm @ atom] :
( ( qfree @ atom @ D )
=> ( ( interpret @ atom @ int @ i_Z @ D @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ C ) @ ( iprod @ int @ B @ A ) ) @ A ) )
<=> ( interpret @ atom @ int @ i_Z @ ( map_fm @ atom @ atom @ ( asubst @ C @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_I__subst) ).
thf(424,plain,
! [A: list @ int,B: list @ int,C: int,D: fm @ atom] :
( ( qfree @ atom @ D )
=> ( ( ( interpret @ atom @ int @ i_Z @ D @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ C ) @ ( iprod @ int @ B @ A ) ) @ A ) )
=> ( interpret @ atom @ int @ i_Z @ ( map_fm @ atom @ atom @ ( asubst @ C @ B ) @ D ) @ A ) )
& ( ( interpret @ atom @ int @ i_Z @ ( map_fm @ atom @ atom @ ( asubst @ C @ B ) @ D ) @ A )
=> ( interpret @ atom @ int @ i_Z @ D @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ C ) @ ( iprod @ int @ B @ A ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(5,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(137,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
<=> ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_mult__eq__1__iff) ).
thf(165,plain,
! [A: nat,B: nat] :
( ( ( ( times_times @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
=> ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) )
& ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) )
=> ( ( times_times @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(100,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( zero_zero @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(467,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( zero_zero @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(62,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
thf(329,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(99,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__0__iff) ).
thf(461,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( B
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(108,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(493,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(39,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_double__eq__0__iff) ).
thf(256,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_list__ex1__simps_I1_J) ).
thf(193,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(103,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(476,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat_Oinject) ).
thf(128,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( suc @ B )
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(36,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_37_neq__Nil__conv) ).
thf(244,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)],[36]) ).
thf(114,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(508,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(123,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_56_list_Osimps_I5_J) ).
thf(541,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)],[123]) ).
thf(85,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ B ) )
=> ( C
= ( zero_zero @ TA ) ) )
=> ( ( iprod @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_iprod0__if__coeffs0) ).
thf(412,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ B ) )
=> ( C
= ( zero_zero @ TA ) ) )
=> ( ( iprod @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(92,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(430,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(7,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_splice__Nil2) ).
thf(148,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(74,axiom,
! [A: list @ int,B: list @ ( fm @ atom )] :
( ( interpret @ atom @ int @ i_Z @ ( list_disj @ atom @ B ) @ A )
<=> ? [C: fm @ atom] :
( ( member @ ( fm @ atom ) @ C @ ( set @ ( fm @ atom ) @ B ) )
& ( interpret @ atom @ int @ i_Z @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Z_OI__list__disj) ).
thf(375,plain,
! [A: list @ int,B: list @ ( fm @ atom )] :
( ( ( interpret @ atom @ int @ i_Z @ ( list_disj @ atom @ B ) @ A )
=> ? [C: fm @ atom] :
( ( member @ ( fm @ atom ) @ C @ ( set @ ( fm @ atom ) @ B ) )
& ( interpret @ atom @ int @ i_Z @ C @ A ) ) )
& ( ? [C: fm @ atom] :
( ( member @ ( fm @ atom ) @ C @ ( set @ ( fm @ atom ) @ B ) )
& ( interpret @ atom @ int @ i_Z @ C @ A ) )
=> ( interpret @ atom @ int @ i_Z @ ( list_disj @ atom @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(81,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( zero_zero @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__0) ).
thf(402,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( zero_zero @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(49,axiom,
! [TA: $tType,A: list @ ( fm @ TA )] :
( ! [B: fm @ TA] :
( ( member @ ( fm @ TA ) @ B @ ( set @ ( fm @ TA ) @ A ) )
=> ( qfree @ TA @ B ) )
=> ( qfree @ TA @ ( list_disj @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_qfree__list__disj) ).
thf(286,plain,
! [TA: $tType,A: list @ ( fm @ TA )] :
( ! [B: fm @ TA] :
( ( member @ ( fm @ TA ) @ B @ ( set @ ( fm @ TA ) @ A ) )
=> ( qfree @ TA @ B ) )
=> ( qfree @ TA @ ( list_disj @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(46,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(281,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(33,axiom,
! [TA: $tType,A: fun @ nat @ bool,B: list @ TA,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( sublist @ TA @ B @ A ) ) )
=> ( member @ TA @ C @ ( set @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_in__set__sublistD) ).
thf(236,plain,
! [TA: $tType,A: fun @ nat @ bool,B: list @ TA,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( sublist @ TA @ B @ A ) ) )
=> ( member @ TA @ C @ ( set @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(70,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(350,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_splice_Osimps_I1_J) ).
thf(159,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_not__Cons__self) ).
thf(274,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(54,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 )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ 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 ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_zipwith0_Osimps_I2_J) ).
thf(303,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 )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ 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 ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(42,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_43_zipwith0_Osimps_I1_J) ).
thf(271,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)],[42]) ).
thf(104,axiom,
( ( ( lbounds @ as )
= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) )
=> ? [A: int] :
! [B: atom] :
( ( member @ atom @ B @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ B ) @ ( cons @ int @ A @ xs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_calculation) ).
thf(477,plain,
( ( ( lbounds @ as )
= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) )
=> ? [A: int] :
! [B: atom] :
( ( member @ atom @ B @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ B ) @ ( cons @ int @ A @ xs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( suc @ B ) ) @ A )
= ( suc @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__Suc) ).
thf(387,plain,
! [A: nat,B: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( suc @ B ) ) @ A )
= ( suc @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(109,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ nat] :
( ( list_size @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( aa @ TA @ nat @ C @ B ) ) @ ( list_size @ TA @ C @ A ) ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_list_Osize_I2_J) ).
thf(494,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ nat] :
( ( list_size @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( aa @ TA @ nat @ C @ B ) ) @ ( list_size @ TA @ C @ A ) ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(122,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_double__zero__sym) ).
thf(535,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(60,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ ( nil @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_iprod__Nil) ).
thf(323,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( iprod @ TA @ ( nil @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(106,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ A ) @ ( nil @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list__add__Nil2) ).
thf(483,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ A ) @ ( nil @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(117,axiom,
~ ! [A: int,B: list @ int,C: int] :
~ ! [D: atom] :
( ( member @ atom @ D @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ ( aa @ atom @ atom @ ( asubst @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ A ) @ C ) @ B ) @ D ) ) @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_B_Bthesis_O_A_I_B_Bil_Aksl_Am_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(521,plain,
~ ! [A: int,B: list @ int,C: int] :
~ ! [D: atom] :
( ( member @ atom @ D @ ( set @ atom @ as ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ ( aa @ atom @ atom @ ( asubst @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ A ) @ C ) @ B ) @ D ) ) @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( times_times @ nat @ ( suc @ B ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ ( times_times @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_mult__Suc) ).
thf(278,plain,
! [A: nat,B: nat] :
( ( times_times @ nat @ ( suc @ B ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ ( times_times @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add_Ocomm__neutral) ).
thf(223,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(55,axiom,
! [A: nat,B: nat,C: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B ) ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__add__assoc) ).
thf(306,plain,
! [A: nat,B: nat,C: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B ) ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(30,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_add__right__cancel) ).
thf(226,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(113,axiom,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Nat_Oadd__0__right) ).
thf(505,plain,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( iprod @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( times_times @ TA @ D @ B ) ) @ ( iprod @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_iprod__Cons) ).
thf(241,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( iprod @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( times_times @ TA @ D @ B ) ) @ ( iprod @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(102,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( zero_zero @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__0__left) ).
thf(473,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( zero_zero @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(26,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(209,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(98,axiom,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( zero_zero @ nat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_plus__nat_Oadd__0) ).
thf(458,plain,
! [A: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ ( zero_zero @ nat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(11,axiom,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_mult__0) ).
thf(162,plain,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(120,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(531,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(118,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( nil @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__add__Nil) ).
thf(525,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( nil @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(52,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_64_sublist__singleton) ).
thf(295,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)],[52]) ).
thf(47,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(282,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(84,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(409,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(22,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(199,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
! [TA: $tType,A: list @ ( fm @ TA )] :
( ! [B: fm @ TA] :
( ( member @ ( fm @ TA ) @ B @ ( set @ ( fm @ TA ) @ A ) )
=> ( qfree @ TA @ B ) )
=> ( qfree @ TA @ ( list_conj @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_qfree__list__conj) ).
thf(331,plain,
! [TA: $tType,A: list @ ( fm @ TA )] :
( ! [B: fm @ TA] :
( ( member @ ( fm @ TA ) @ B @ ( set @ ( fm @ TA ) @ A ) )
=> ( qfree @ TA @ B ) )
=> ( qfree @ TA @ ( list_conj @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(95,axiom,
! [A: list @ int,B: atom,C: list @ int,D: int] :
( ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ ( aa @ atom @ atom @ ( asubst @ D @ C ) @ B ) ) @ A ) )
<=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ B ) @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ D ) @ ( iprod @ int @ C @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_IZ__asubst) ).
thf(441,plain,
! [A: list @ int,B: atom,C: list @ int,D: int] :
( ( ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ ( aa @ atom @ atom @ ( asubst @ D @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ B ) @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ D ) @ ( iprod @ int @ C @ A ) ) @ A ) ) ) )
& ( ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ B ) @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ D ) @ ( iprod @ int @ C @ A ) ) @ A ) ) )
=> ( pp @ ( aa @ ( list @ int ) @ bool @ ( aa @ atom @ ( fun @ ( list @ int ) @ bool ) @ i_Z @ ( aa @ atom @ atom @ ( asubst @ D @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(66,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_75_mem__def) ).
thf(338,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)],[66]) ).
thf(101,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( iprod @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( iprod @ TA @ C @ A ) ) @ ( iprod @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_iprod__left__add__distrib) ).
thf(470,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( iprod @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( iprod @ TA @ C @ A ) ) @ ( iprod @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(124,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list__add__assoc) ).
thf(544,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: fm @ TA,B: fun @ TA @ TB] :
( ( qfree @ TB @ ( map_fm @ TA @ TB @ B @ A ) )
<=> ( qfree @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_qfree__map__fm) ).
thf(175,plain,
! [TA: $tType,TB: $tType,A: fm @ TA,B: fun @ TA @ TB] :
( ( ( qfree @ TB @ ( map_fm @ TA @ TB @ B @ A ) )
=> ( qfree @ TA @ A ) )
& ( ( qfree @ TA @ A )
=> ( qfree @ TB @ ( map_fm @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__eq__self__zero) ).
thf(446,plain,
! [A: nat,B: nat] :
( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( times_times @ nat @ B @ ( suc @ A ) )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ ( times_times @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_mult__Suc__right) ).
thf(497,plain,
! [A: nat,B: nat] :
( ( times_times @ nat @ B @ ( suc @ A ) )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ ( times_times @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(37,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ( ( plus_plus @ ( list @ TA ) )
= ( zipwith0 @ TA @ TA @ TA @ ( plus_plus @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_list__add__def) ).
thf(250,plain,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ( ( plus_plus @ ( list @ TA ) )
= ( zipwith0 @ TA @ TA @ TA @ ( plus_plus @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(97,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_6_list_Oinject) ).
thf(450,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)],[97]) ).
thf(24,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mult__0__right) ).
thf(203,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_list_Osimps_I2_J) ).
thf(319,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(71,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_74_ext) ).
thf(351,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)],[71]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ nat @ bool,B: list @ TA,C: TA] :
( ~ ( member @ TA @ C @ ( set @ TA @ B ) )
=> ~ ( member @ TA @ C @ ( set @ TA @ ( sublist @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_notin__set__sublistI) ).
thf(390,plain,
! [TA: $tType,A: fun @ nat @ bool,B: list @ TA,C: TA] :
( ~ ( member @ TA @ C @ ( set @ TA @ B ) )
=> ~ ( member @ TA @ C @ ( set @ TA @ ( sublist @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(87,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(418,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(32,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(235,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(433,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(8,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(151,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_nat__add__commute) ).
thf(300,plain,
! [A: nat,B: nat] :
( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ B ) @ A )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(40,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_add__left__cancel) ).
thf(262,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(82,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_add__0__right) ).
thf(405,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(18,axiom,
! [TA: $tType,A: fm @ TA] :
( ( qfree @ TA @ ( neg @ TA @ A ) )
<=> ( qfree @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_qfree__neg) ).
thf(190,plain,
! [TA: $tType,A: fm @ TA] :
( ( ( qfree @ TA @ ( neg @ TA @ A ) )
=> ( qfree @ TA @ A ) )
& ( ( qfree @ TA @ A )
=> ( qfree @ TA @ ( neg @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ A @ B ) )
<=> ( ( C = A )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult__cancel2) ).
thf(210,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ A @ B ) )
=> ( ( C = A )
| ( B
= ( zero_zero @ nat ) ) ) )
& ( ( ( C = A )
| ( B
= ( zero_zero @ nat ) ) )
=> ( ( times_times @ nat @ C @ B )
= ( times_times @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(61,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_not__Cons__self2) ).
thf(326,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(4,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(136,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ 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 ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ C ) @ ( nil @ TC ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I4_J) ).
thf(341,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ 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 ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ C ) @ ( nil @ TC ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(41,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_add__right__imp__eq) ).
thf(268,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(195,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(48,axiom,
( ( lbounds @ as )
!= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096lbounds_Aas_A_126_061_A_091_093_096) ).
thf(283,plain,
( ( lbounds @ as )
!= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__cancel) ).
thf(395,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(91,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= ( cons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_not__in__set__insert) ).
thf(427,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ~ ( member @ TA @ B @ ( set @ TA @ A ) )
=> ( ( insert @ TA @ B @ A )
= ( cons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(119,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( cons @ TA @ B @ A ) ) )
=> ( ( C = B )
| ( member @ TA @ C @ ( set @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_set__ConsD) ).
thf(528,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( cons @ TA @ B @ A ) ) )
=> ( ( C = B )
| ( member @ TA @ C @ ( set @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_sublist__nil) ).
thf(200,plain,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(178,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(44,axiom,
cl_Groups_Oplus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(277,plain,
cl_Groups_Oplus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(59,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(322,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_nat__add__right__cancel) ).
thf(486,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ C ) @ B )
= ( aa @ nat @ nat @ ( aa @ nat @ ( fun @ nat @ nat ) @ ( plus_plus @ nat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(65,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(337,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(72,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( list_ex1 @ TA @ B @ A )
<=> ? [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ A ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( ( member @ TA @ D @ ( set @ TA @ A ) )
& ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_list__ex1__iff) ).
thf(354,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( list_ex1 @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ A ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( ( member @ TA @ D @ ( set @ TA @ A ) )
& ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ( D = C ) ) ) )
& ( ? [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ A ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( ( 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)],[72]) ).
thf(56,axiom,
! [A: atom,B: list @ int,C: int] :
( ( divisor @ ( aa @ atom @ atom @ ( asubst @ C @ B ) @ A ) )
= ( divisor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_divisor__asubst) ).
thf(309,plain,
! [A: atom,B: list @ int,C: int] :
( ( divisor @ ( aa @ atom @ atom @ ( asubst @ C @ B ) @ A ) )
= ( divisor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(31,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list__add__Cons) ).
thf(232,plain,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(547,plain,
$false,
inference(e,[status(thm)],[420,503,138,347,408,511,384,500,174,417,436,196,125,344,189,421,152,289,179,253,238,514,480,312,206,292,381,534,220,366,334,392,424,137,165,467,329,461,493,256,193,476,128,244,508,541,412,430,148,375,402,286,281,236,350,159,274,303,271,477,387,494,535,323,483,521,278,223,306,226,505,241,473,209,458,162,531,525,295,282,409,199,331,441,338,470,544,175,446,497,250,450,203,319,351,390,418,235,433,151,300,262,405,190,210,326,136,341,268,195,283,395,427,528,200,178,277,322,486,337,354,309,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COM080_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 02:43:31 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.91/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.05 % [INFO] Parsing done (203ms).
% 1.40/1.06 % [INFO] Running in sequential loop mode.
% 2.25/1.36 % [INFO] eprover registered as external prover.
% 2.40/1.36 % [INFO] cvc4 registered as external prover.
% 2.40/1.37 % [INFO] Scanning for conjecture ...
% 2.59/1.49 % [INFO] Found a conjecture and 122 axioms. Running axiom selection ...
% 2.84/1.57 % [INFO] Axiom selection finished. Selected 122 axioms (removed 0 axioms).
% 3.51/1.71 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.61/1.73 % [INFO] Type checking passed.
% 3.61/1.73 % [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 ...
% 44.42/20.05 % External prover 'e' found a proof!
% 44.42/20.05 % [INFO] Killing All external provers ...
% 44.42/20.05 % Time passed: 19527ms (effective reasoning time: 18990ms)
% 44.42/20.05 % 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)>
% 44.42/20.06 % Axioms used in derivation (122): arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_18_zero__reorient, fact_56_list_Osimps_I5_J, fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096, fact_72_qfree__list__conj, fact_53_insert__Nil, fact_43_zipwith0_Osimps_I1_J, fact_86_list__nonempty__induct, fact_66_sublist__nil, fact_7_add__left__cancel, fact_6_list_Oinject, fact_39_zipwith0_Osimps_I3_J, fact_73_nat__add__right__cancel, fact_4_IZ__asubst, arity_Int_Oint___Groups_Ocomm__monoid__add, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_79_nat__add__commute, fact_40_add__0__iff, fact_54_splice_Osimps_I2_J, fact_5__096lbounds_Aas_A_126_061_A_091_093_096, fact_97_add__Suc, fact_71_qfree__map__fm, fact_75_mem__def, arity_Int_Oint___Rings_Oring, fact_42_zipwith0_Osimps_I2_J, fact_52_Z_OI__list__disj, fact_29_add__left__imp__eq, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_93_mult__0, fact_10_calculation, fact_68_in__set__sublistD, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, arity_Nat_Onat___Groups_Oplus, fact_16_iprod__Nil, fact_32_not__Cons__self, fact_1__096_B_Bthesis_O_A_I_B_Bil_Aksl_Am_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_77_nat__add__assoc, arity_Int_Oint___Groups_Oplus, fact_25_add__0, fact_74_ext, fact_96_mult__Suc, fact_34_iprod0__if__coeffs0, fact_88_iprod__Cons, fact_87_list_Osize_I2_J, fact_64_sublist__singleton, fact_95_mult__eq__1__iff, fact_20_list__add__assoc, fact_89_mult__cancel2, fact_92_mult__0__right, fact_58_in__set__insert, arity_List_Olist___Groups_Oplus, fact_19_list__add__Nil2, fact_27_add__right__imp__eq, fact_98_mult__Suc__right, fact_33_double__eq__0__iff, fact_50_list__add__def, fact_8_add__right__cancel, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_67_notin__set__sublistI, fact_12_norm, fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_81_Nat_Oadd__0__right, arity_Nat_Onat___Groups_Ozero, fact_17_list__add__Nil, fact_9_iprod__left__add__distrib, arity_Int_Oint___Groups_Omonoid__add, fact_21_list_Osimps_I3_J, fact_94_nat_Oinject, fact_78_nat__add__left__commute, fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_62_List_Oinsert__def, fact_36_list_Oexhaust, fact_37_neq__Nil__conv, fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_65_I__subst, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_83_qfree__list__disj, fact_3_list__add__Cons, fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096, fact_80_plus__nat_Oadd__0, fact_14_divisor__asubst, fact_35_Z_OI__list__conj, fact_11_set__ConsD, fact_61_not__in__set__insert, fact_57_splice_Osimps_I3_J, fact_24_add__0__right, fact_82_add__eq__self__zero, fact_69_list__ex1__iff, arity_Int_Oint___Groups_Oab__semigroup__add, fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_60_splice__Nil2, fact_55_list_Osimps_I4_J, fact_84_qfree__neg, help_pp_1_1_U, fact_76_nat__add__left__cancel, fact_59_splice_Osimps_I1_J, fact_70_add__is__0, fact_31_not__Cons__self2, arity_Nat_Onat___Groups_Omonoid__add, fact_23_add_Ocomm__neutral, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Int_Oint___Groups_Ozero, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, help_pp_2_1_U, fact_26_add__0__left, fact_15_iprod__Nil2, fact_90_mult__cancel1, fact_30_ab__semigroup__add__class_Oadd__ac_I1_J, fact_63_list__ex1__simps_I1_J, fact_38_zipwith0_Osimps_I4_J, fact_13_double__zero__sym, fact_91_mult__is__0, fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_28_add__imp__eq, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_85_list_Osize_I1_J, fact_22_list_Osimps_I2_J
% 44.42/20.06 % No. of inferences in proof: 248
% 44.42/20.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19527 ms resp. 18990 ms w/o parsing
% 44.42/20.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 44.42/20.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------