TSTP Solution File: DAT136^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT136^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 : Tue May 7 07:39:34 EDT 2024
% Result : Theorem 106.17s 38.77s
% Output : Refutation 106.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 348
% Syntax : Number of formulae : 641 ( 285 unt; 57 typ; 0 def)
% Number of atoms : 1413 ( 600 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 5766 ( 170 ~; 20 |; 57 &;5017 @)
% ( 0 <=>; 502 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 149 ( 149 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 58 usr; 15 con; 0-4 aty)
% Number of variables : 1461 ( 53 ^1304 !; 62 ?;1461 :)
% ( 42 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_add_type,type,
semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere216010020id_add_type,type,
ordere216010020id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(strict797366125id_add_type,type,
strict797366125id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(strict2144017051up_add_type,type,
strict2144017051up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere516151231imp_le_type,type,
ordere516151231imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu493225792length_type,type,
coindu493225792length:
!>[TA: $tType] : ( nat > ( coindu1593790203_llist @ TA ) > extended_enat ) ).
thf(coindu441856546concat_type,type,
coindu441856546concat:
!>[TA: $tType] : ( ( coindu1593790203_llist @ ( coindu1593790203_llist @ TA ) ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu531130065ldropn_type,type,
coindu531130065ldropn:
!>[TA: $tType] : ( nat > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1213758845finite_type,type,
coindu1213758845finite:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1018505716length_type,type,
coindu1018505716length:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > extended_enat ) ).
thf(coindu1121789889_LCons_type,type,
coindu1121789889_LCons:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1598213697e_LNil_type,type,
coindu1598213697e_LNil:
!>[TA: $tType] : ( coindu1593790203_llist @ TA ) ).
thf(coindu335574135_lnull_type,type,
coindu335574135_lnull:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1079202755ist_of_type,type,
coindu1079202755ist_of:
!>[TA: $tType] : ( ( list @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu749330388e_lnth_type,type,
coindu749330388e_lnth:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > nat > TA ) ).
thf(extended_enat2_type,type,
extended_enat2: nat > extended_enat ).
thf(extended_size_enat_type,type,
extended_size_enat: extended_enat > nat ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(groups15040474setsum_type,type,
groups15040474setsum:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TA ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(set_ord_lessThan_type,type,
set_ord_lessThan:
!>[TA: $tType] : ( TA > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(n_type,type,
n: nat ).
thf(m_type,type,
m: nat ).
thf(n2_type,type,
n2: nat ).
thf(n3_type,type,
n3: nat ).
thf(na_type,type,
na: nat ).
thf(x_type,type,
x: a ).
thf(xs_type,type,
xs: coindu1593790203_llist @ a ).
thf(xss_type,type,
xss: coindu1593790203_llist @ ( coindu1593790203_llist @ a ) ).
thf(xss2_type,type,
xss2: list @ ( coindu1593790203_llist @ a ) ).
thf(xssa_type,type,
xssa: coindu1593790203_llist @ ( coindu1593790203_llist @ a ) ).
thf(248,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_less__Suc__eq__0__disj) ).
thf(1036,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(169,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Suc__neq__Zero) ).
thf(809,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(28,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_6) ).
thf(365,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(292,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
& ( ( plus_plus @ nat @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_less__imp__add__positive) ).
thf(1168,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
& ( ( plus_plus @ nat @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(264,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_less__zeroE) ).
thf(1083,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
thf(1110,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(68,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_n__not__Suc__n) ).
thf(481,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(23,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_lnull__imp__lfinite) ).
thf(352,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(41,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_neq__if__length__neq) ).
thf(408,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(289,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Suc__less__eq) ).
thf(1158,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(238,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_less__irrefl__nat) ).
thf(1005,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(138,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__strict__left__mono) ).
thf(730,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(104,axiom,
! [TA: $tType,A: nat] :
( ( coindu493225792length @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( extended_enat2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_gen__llength__code_I1_J) ).
thf(614,plain,
! [TA: $tType,A: nat] :
( ( coindu493225792length @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( extended_enat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(192,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add__strict__right__mono) ).
thf(878,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(52,axiom,
ordere779506340up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(440,plain,
ordere779506340up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(115,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add_Oright__cancel) ).
thf(655,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(78,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add__mono__thms__linordered__field_I2_J) ).
thf(511,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(251,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__antisym) ).
thf(1041,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(188,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ~ ! [C: nat] :
( ( A
= ( extended_enat2 @ C ) )
=> ~ ( ord_less @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_less__enatE) ).
thf(861,plain,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ~ ! [C: nat] :
( ( A
= ( extended_enat2 @ C ) )
=> ~ ( ord_less @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_llist_Odisc_I2_J) ).
thf(384,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(282,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zero__less__iff__neq__zero) ).
thf(1137,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TC @ ( type2 @ TC ) )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( groups15040474setsum @ TB @ TC
@ ^ [D: TB] : ( groups15040474setsum @ TA @ TC @ ( A @ D ) @ B )
@ C )
= ( groups15040474setsum @ TA @ TC
@ ^ [D: TA] :
( groups15040474setsum @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_setsum_Ocommute) ).
thf(533,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TC @ ( type2 @ TC ) )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( groups15040474setsum @ TB @ TC
@ ^ [D: TB] : ( groups15040474setsum @ TA @ TC @ ( A @ D ) @ B )
@ C )
= ( groups15040474setsum @ TA @ TC
@ ^ [D: TA] :
( groups15040474setsum @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_gr__implies__not0) ).
thf(550,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(74,axiom,
order @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_19) ).
thf(500,plain,
order @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(164,axiom,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) @ ( coindu1018505716length @ TA @ C ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu531130065ldropn @ TA @ A @ C ) @ B )
= ( coindu749330388e_lnth @ TA @ C @ ( plus_plus @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_lnth__ldropn) ).
thf(797,plain,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) @ ( coindu1018505716length @ TA @ C ) )
=> ( ( coindu749330388e_lnth @ TA @ ( coindu531130065ldropn @ TA @ A @ C ) @ B )
= ( coindu749330388e_lnth @ TA @ C @ ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(218,axiom,
! [TA: $tType] :
( ( coindu493225792length @ TA )
= ( ^ [A: nat,B: coindu1593790203_llist @ TA] : ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_gen__llength__def) ).
thf(945,plain,
! [TA: $tType] :
( ( coindu493225792length @ TA )
= ( ^ [A: nat,B: coindu1593790203_llist @ TA] : ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(122,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_add__less__same__cancel1) ).
thf(670,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(40,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_llist_OdiscI_I1_J) ).
thf(404,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(278,axiom,
! [TA: $tType,A: list @ TA] :
( ( coindu1018505716length @ TA @ ( coindu1079202755ist_of @ TA @ A ) )
= ( extended_enat2 @ ( size_size @ ( list @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_llength__llist__of) ).
thf(1127,plain,
! [TA: $tType,A: list @ TA] :
( ( coindu1018505716length @ TA @ ( coindu1079202755ist_of @ TA @ A ) )
= ( extended_enat2 @ ( size_size @ ( list @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(159,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add__mono__thms__linordered__field_I5_J) ).
thf(782,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(44,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_semiring__normalization__rules_I20_J) ).
thf(417,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(253,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__less__cancel__left) ).
thf(1046,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_nat__add__left__cancel__less) ).
thf(651,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(34,axiom,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_lfinite__code_I1_J) ).
thf(389,plain,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(97,axiom,
! [TA: $tType,A: coindu1593790203_llist @ ( coindu1593790203_llist @ TA )] :
( ( coindu1213758845finite @ ( coindu1593790203_llist @ TA ) @ A )
=> ( ( coindu1018505716length @ TA @ ( coindu441856546concat @ TA @ A ) )
= ( groups15040474setsum @ nat @ extended_enat
@ ^ [B: nat] : ( coindu1018505716length @ TA @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ TA ) @ A @ B ) )
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ TA ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_llength__lconcat__lfinite__conv__sum) ).
thf(570,plain,
! [TA: $tType,A: coindu1593790203_llist @ ( coindu1593790203_llist @ TA )] :
( ( coindu1213758845finite @ ( coindu1593790203_llist @ TA ) @ A )
=> ( ( coindu1018505716length @ TA @ ( coindu441856546concat @ TA @ A ) )
= ( groups15040474setsum @ nat @ extended_enat
@ ^ [B: nat] : ( coindu1018505716length @ TA @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ TA ) @ A @ B ) )
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ TA ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(76,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_measure__induct__rule) ).
thf(504,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(257,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__neg__neg) ).
thf(1059,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(60,axiom,
canoni770627133id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(460,plain,
canoni770627133id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(106,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_less__Suc__induct) ).
thf(619,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_less__not__refl2) ).
thf(838,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(129,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_not__less0) ).
thf(702,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(146,axiom,
zero @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(751,plain,
zero @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(214,axiom,
( ( extended_enat2 @ ( suc @ na ) )
= ( plus_plus @ extended_enat
@ ( groups15040474setsum @ nat @ extended_enat
@ ^ [A: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) )
@ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) )
@ ( extended_enat2 @ ( suc @ n3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062enat_A_ISuc_An_J_A_061_A_I_092_060Sum_062i_060length_Axss_H_O_Allength_A_Ilnth_Axss_Ai_J_J_A_L_Aenat_A_ISuc_An_H_J_092_060close_062) ).
thf(934,plain,
( ( extended_enat2 @ ( suc @ na ) )
= ( plus_plus @ extended_enat
@ ( groups15040474setsum @ nat @ extended_enat
@ ^ [A: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) )
@ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) )
@ ( extended_enat2 @ ( suc @ n3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(25,axiom,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_lfinite__LNil) ).
thf(357,plain,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(185,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_less__add__same__cancel1) ).
thf(853,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(286,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_add__Suc__right) ).
thf(1147,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(13,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_lfinite__LConsI) ).
thf(325,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(270,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_infinite__descent0__measure) ).
thf(1100,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(210,axiom,
ordere223160158up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(924,plain,
ordere223160158up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(71,axiom,
ord @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oord_20) ).
thf(492,plain,
ord @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(250,axiom,
monoid_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add) ).
thf(1040,plain,
monoid_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(173,axiom,
ord_less @ extended_enat @ ( extended_enat2 @ n2 ) @ ( coindu1018505716length @ a @ ( coindu441856546concat @ a @ xss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms) ).
thf(821,plain,
ord_less @ extended_enat @ ( extended_enat2 @ n2 ) @ ( coindu1018505716length @ a @ ( coindu441856546concat @ a @ xss ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(69,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat] :
( ( groups15040474setsum @ nat @ TA @ A @ ( set_ord_lessThan @ nat @ ( suc @ B ) ) )
= ( plus_plus @ TA @ ( groups15040474setsum @ nat @ TA @ A @ ( set_ord_lessThan @ nat @ B ) ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_setsum__lessThan__Suc) ).
thf(485,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat] :
( ( groups15040474setsum @ nat @ TA @ A @ ( set_ord_lessThan @ nat @ ( suc @ B ) ) )
= ( plus_plus @ TA @ ( groups15040474setsum @ nat @ TA @ A @ ( set_ord_lessThan @ nat @ B ) ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(178,axiom,
comm_monoid_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocomm__monoid__add_14) ).
thf(834,plain,
comm_monoid_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(230,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu749330388e_lnth @ TA @ B @ A ) @ ( coindu531130065ldropn @ TA @ ( suc @ A ) @ B ) )
= ( coindu531130065ldropn @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ldropn__Suc__conv__ldropn) ).
thf(981,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu749330388e_lnth @ TA @ B @ A ) @ ( coindu531130065ldropn @ TA @ ( suc @ A ) @ B ) )
= ( coindu531130065ldropn @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_linorder__neqE__nat) ).
thf(634,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(140,axiom,
! [A: nat] :
( ( extended_size_enat @ ( extended_enat2 @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_enat_Osize_I1_J) ).
thf(734,plain,
! [A: nat] :
( ( extended_size_enat @ ( extended_enat2 @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(261,axiom,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_enat__less__induct) ).
thf(1072,plain,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(275,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_not0__implies__Suc) ).
thf(1119,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Suc__less__SucD) ).
thf(428,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__mono__thms__linordered__semiring_I4_J) ).
thf(507,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(9,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_neq__LNil__conv) ).
thf(312,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
? [A: nat,B: nat] :
( ( ( coindu749330388e_lnth @ a @ ( coindu441856546concat @ a @ xssa ) @ ( suc @ na ) )
= ( coindu749330388e_lnth @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) @ B ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ a ) @ xssa ) )
& ( ( extended_enat2 @ ( suc @ na ) )
= ( plus_plus @ extended_enat
@ ( groups15040474setsum @ nat @ extended_enat
@ ^ [C: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ C ) )
@ ( set_ord_lessThan @ nat @ A ) )
@ ( extended_enat2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: nat,B: nat] :
( ( ( coindu749330388e_lnth @ a @ ( coindu441856546concat @ a @ xssa ) @ ( suc @ na ) )
= ( coindu749330388e_lnth @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) @ B ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ a ) @ xssa ) )
& ( ( extended_enat2 @ ( suc @ na ) )
= ( plus_plus @ extended_enat
@ ( groups15040474setsum @ nat @ extended_enat
@ ^ [C: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ C ) )
@ ( set_ord_lessThan @ nat @ A ) )
@ ( extended_enat2 @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(293,plain,
~ ? [A: nat,B: nat] :
( ( ( coindu749330388e_lnth @ a @ ( coindu441856546concat @ a @ xssa ) @ ( suc @ na ) )
= ( coindu749330388e_lnth @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) @ B ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ a ) @ xssa ) )
& ( ( extended_enat2 @ ( suc @ na ) )
= ( plus_plus @ extended_enat
@ ( groups15040474setsum @ nat @ extended_enat
@ ^ [C: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ C ) )
@ ( set_ord_lessThan @ nat @ A ) )
@ ( extended_enat2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(222,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add__strict__mono) ).
thf(956,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(7,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_3) ).
thf(307,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(51,axiom,
strict797366125id_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__comm__monoid__add_9) ).
thf(439,plain,
strict797366125id_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Suc__mono) ).
thf(529,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(117,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__less__same__cancel2) ).
thf(661,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_old_Onat_Oinject) ).
thf(925,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(29,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: nat] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu531130065ldropn @ TA @ B @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_ldropn__lnull) ).
thf(366,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: nat] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu531130065ldropn @ TA @ B @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(288,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: set @ nat,B: nat > TA,C: nat > TA] :
( ~ ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ! [D: nat] :
( ( member @ nat @ ( suc @ D ) @ A )
=> ( ( B @ ( suc @ D ) )
= ( C @ ( suc @ D ) ) ) )
=> ( ( groups15040474setsum @ nat @ TA @ B @ A )
= ( groups15040474setsum @ nat @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_setsum__cong__Suc) ).
thf(1153,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: set @ nat,B: nat > TA,C: nat > TA] :
( ~ ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ! [D: nat] :
( ( member @ nat @ ( suc @ D ) @ A )
=> ( ( B @ ( suc @ D ) )
= ( C @ ( suc @ D ) ) ) )
=> ( ( groups15040474setsum @ nat @ TA @ B @ A )
= ( groups15040474setsum @ nat @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(151,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_add__right__cancel) ).
thf(761,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(199,axiom,
ordere216010020id_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__comm__monoid__add_12) ).
thf(894,plain,
ordere216010020id_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(267,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_add__cancel__right__right) ).
thf(1091,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(157,axiom,
strict2144017051up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(778,plain,
strict2144017051up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_llist_Odistinct_I1_J) ).
thf(302,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Collect__mem__eq) ).
thf(349,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(36,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__cong) ).
thf(392,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(95,axiom,
ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_13) ).
thf(566,plain,
ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(246,axiom,
linorder @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_17) ).
thf(1032,plain,
linorder @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(119,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_measure__induct) ).
thf(665,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(176,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_lessThan__iff) ).
thf(830,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(61,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_semiring__normalization__rules_I6_J) ).
thf(461,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(72,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Zero__neq__Suc) ).
thf(493,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(127,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_less__not__refl3) ).
thf(682,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(181,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_semiring__normalization__rules_I21_J) ).
thf(842,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(227,axiom,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(974,plain,
ordere516151231imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(241,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_less__nat__zero__code) ).
thf(1012,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(207,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_add__lessD1) ).
thf(916,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TB] :
( ( groups15040474setsum @ TB @ TA
@ ^ [B: TB] : ( zero_zero @ TA )
@ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_setsum_Oneutral__const) ).
thf(467,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TB] :
( ( groups15040474setsum @ TB @ TA
@ ^ [B: TB] : ( zero_zero @ TA )
@ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(81,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_nat__induct) ).
thf(519,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(219,axiom,
( ( zero_zero @ extended_enat )
= ( extended_enat2 @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_zero__enat__def) ).
thf(948,plain,
( ( zero_zero @ extended_enat )
= ( extended_enat2 @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(259,axiom,
! [TA: $tType,A: TA > nat,B: set @ TA,C: nat] :
( ( ( groups15040474setsum @ TA @ nat @ A @ B )
= ( suc @ C ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_setsum__SucD) ).
thf(1064,plain,
! [TA: $tType,A: TA > nat,B: set @ TA,C: nat] :
( ( ( groups15040474setsum @ TA @ nat @ A @ B )
= ( suc @ C ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(136,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__iff__Suc__add) ).
thf(725,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(100,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ( plus_plus @ extended_enat @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( ( A
= ( zero_zero @ extended_enat ) )
& ( B
= ( zero_zero @ extended_enat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_plus__enat__eq__0__conv) ).
thf(593,plain,
! [A: extended_enat,B: extended_enat] :
( ( ( plus_plus @ extended_enat @ A @ B )
= ( zero_zero @ extended_enat ) )
= ( ( A
= ( zero_zero @ extended_enat ) )
& ( B
= ( zero_zero @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(45,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_lfinite__llength__enat) ).
thf(420,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(195,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add__is__0) ).
thf(884,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(70,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Zero__not__Suc) ).
thf(488,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__Suc__shift) ).
thf(554,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(121,axiom,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(669,plain,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(128,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_infinite__descent0) ).
thf(686,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(110,axiom,
! [A: nat,B: nat,C: extended_enat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_enat__less__enat__plusI) ).
thf(637,plain,
! [A: nat,B: nat,C: extended_enat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__Suc) ).
thf(590,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(89,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_not__less__eq) ).
thf(547,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(125,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_lift__Suc__mono__less) ).
thf(679,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(249,axiom,
ord_less @ extended_enat @ ( extended_enat2 @ ( suc @ n3 ) ) @ ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062enat_A_ISuc_An_H_J_A_060_Allength_A_Ilnth_Axss_A_Ilength_Axss_H_J_J_092_060close_062) ).
thf(1039,plain,
ord_less @ extended_enat @ ( extended_enat2 @ ( suc @ n3 ) ) @ ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__SucE) ).
thf(997,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(114,axiom,
monoid_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Omonoid__add_18) ).
thf(654,plain,
monoid_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [TA: $tType] :
( ( coindu1018505716length @ TA )
= ( coindu493225792length @ TA @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_llength__code) ).
thf(457,plain,
! [TA: $tType] :
( ( coindu1018505716length @ TA )
= ( coindu493225792length @ TA @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(134,axiom,
cancel1352612707id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(721,plain,
cancel1352612707id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(158,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ( coindu1018505716length @ TA @ A )
= ( zero_zero @ extended_enat ) )
= ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_llength__eq__0) ).
thf(779,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ( coindu1018505716length @ TA @ A )
= ( zero_zero @ extended_enat ) )
= ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(31,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( B @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_lfinite_Oinducts) ).
thf(371,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( B @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(79,axiom,
strict797366125id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add) ).
thf(515,plain,
strict797366125id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(287,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Suc__lessI) ).
thf(1150,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(231,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_add__left__cancel) ).
thf(984,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_enat__ord__simps_I2_J) ).
thf(911,plain,
! [A: nat,B: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(20,axiom,
! [TA: $tType,A: nat] :
( ( coindu531130065ldropn @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_ldropn__LNil) ).
thf(343,plain,
! [TA: $tType,A: nat] :
( ( coindu531130065ldropn @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Suc__lessD) ).
thf(792,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(265,axiom,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_False) ).
thf(1086,plain,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(209,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( suc @ ( zero_zero @ nat ) ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_add__is__1) ).
thf(921,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( suc @ ( zero_zero @ nat ) ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(87,axiom,
! [A: extended_enat] :
~ ( ord_less @ extended_enat @ A @ ( zero_zero @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_not__iless0) ).
thf(541,plain,
! [A: extended_enat] :
~ ( ord_less @ extended_enat @ A @ ( zero_zero @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(38,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1079202755ist_of @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_llist__of__inject) ).
thf(398,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1079202755ist_of @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(244,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1018505716length @ TA @ A )
= ( zero_zero @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_llength__lnull) ).
thf(1026,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1018505716length @ TA @ A )
= ( zero_zero @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(221,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) )
=> ( ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A )
= ( coindu1598213697e_LNil @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_lnth__prefix) ).
thf(953,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) )
=> ( ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A )
= ( coindu1598213697e_LNil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__Suc__eq) ).
thf(773,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(163,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add__0__iff) ).
thf(794,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(42,axiom,
! [TA: $tType,A: list @ TA] : ( coindu1213758845finite @ TA @ ( coindu1079202755ist_of @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_lfinite__llist__of) ).
thf(412,plain,
! [TA: $tType,A: list @ TA] : ( coindu1213758845finite @ TA @ ( coindu1079202755ist_of @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_add__eq__self__zero) ).
thf(430,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(186,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__cancel__left__left) ).
thf(856,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(144,axiom,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ A @ ( coindu531130065ldropn @ TA @ B @ C ) )
= ( coindu531130065ldropn @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_ldropn__ldropn) ).
thf(745,plain,
! [TA: $tType,A: nat,B: nat,C: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ A @ ( coindu531130065ldropn @ TA @ B @ C ) )
= ( coindu531130065ldropn @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TB @ ( type2 @ TB ) )
=> ! [A: set @ TC,B: TA > TC,C: TC > TA,D: set @ TA,E: TA > TB,F: TC > TB] :
( ! [G: TC] :
( ( member @ TC @ G @ A )
=> ( ( B @ ( C @ G ) )
= G ) )
=> ( ! [G: TC] :
( ( member @ TC @ G @ A )
=> ( member @ TA @ ( C @ G ) @ D ) )
=> ( ! [G: TA] :
( ( member @ TA @ G @ D )
=> ( ( C @ ( B @ G ) )
= G ) )
=> ( ! [G: TA] :
( ( member @ TA @ G @ D )
=> ( member @ TC @ ( B @ G ) @ A ) )
=> ( ! [G: TC] :
( ( member @ TC @ G @ A )
=> ( ( E @ ( C @ G ) )
= ( F @ G ) ) )
=> ( ( groups15040474setsum @ TC @ TB @ F @ A )
= ( groups15040474setsum @ TA @ TB @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_setsum_Oreindex__bij__witness) ).
thf(573,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TB @ ( type2 @ TB ) )
=> ! [A: set @ TC,B: TA > TC,C: TC > TA,D: set @ TA,E: TA > TB,F: TC > TB] :
( ! [G: TC] :
( ( member @ TC @ G @ A )
=> ( ( B @ ( C @ G ) )
= G ) )
=> ( ! [G: TC] :
( ( member @ TC @ G @ A )
=> ( member @ TA @ ( C @ G ) @ D ) )
=> ( ! [G: TA] :
( ( member @ TA @ G @ D )
=> ( ( C @ ( B @ G ) )
= G ) )
=> ( ! [G: TA] :
( ( member @ TA @ G @ D )
=> ( member @ TC @ ( B @ G ) @ A ) )
=> ( ! [G: TC] :
( ( member @ TC @ G @ A )
=> ( ( E @ ( C @ G ) )
= ( F @ G ) ) )
=> ( ( groups15040474setsum @ TC @ TB @ F @ A )
= ( groups15040474setsum @ TA @ TB @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_llist_Oinject) ).
thf(296,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_semiring__normalization__rules_I24_J) ).
thf(444,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(172,axiom,
( na
= ( plus_plus @ nat @ n @ n3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_n) ).
thf(819,plain,
( na
= ( plus_plus @ nat @ n @ n3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(228,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_not__gr__zero) ).
thf(975,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(46,axiom,
~ ! [A: a,B: coindu1593790203_llist @ a] :
( ( coindu441856546concat @ a @ xssa )
!= ( coindu1121789889_LCons @ a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_Axs_O_Alconcat_Axss_A_061_ALCons_Ax_Axs_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(423,plain,
~ ! [A: a,B: coindu1593790203_llist @ a] :
( ( coindu441856546concat @ a @ xssa )
!= ( coindu1121789889_LCons @ a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(139,axiom,
! [TA: $tType,A: TA > extended_enat,B: nat] :
( ! [C: TA] :
? [D: TA] : ( ord_less @ extended_enat @ ( A @ C ) @ ( A @ D ) )
=> ? [C: TA] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_chain__incr) ).
thf(732,plain,
! [TA: $tType,A: TA > extended_enat,B: nat] :
( ! [C: TA] :
? [D: TA] : ( ord_less @ extended_enat @ ( A @ C ) @ ( A @ D ) )
=> ? [C: TA] : ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(143,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__add__Suc2) ).
thf(743,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(223,axiom,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
= ( A
!= ( zero_zero @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_i0__less) ).
thf(958,plain,
! [A: extended_enat] :
( ( ord_less @ extended_enat @ ( zero_zero @ extended_enat ) @ A )
= ( A
!= ( zero_zero @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(277,axiom,
! [A: nat] :
( ( ( zero_zero @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_enat__0__iff_I2_J) ).
thf(1124,plain,
! [A: nat] :
( ( ( zero_zero @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(191,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_nat__add__right__cancel) ).
thf(875,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(175,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_gr__implies__not__zero) ).
thf(826,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(112,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_zero__induct) ).
thf(641,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(35,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_7) ).
thf(391,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(215,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__cancel__left__right) ).
thf(936,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__less__less__Suc__eq) ).
thf(713,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(271,axiom,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_lfinite__conv__llength__enat) ).
thf(1107,plain,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
? [B: nat] :
( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(17,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_5) ).
thf(335,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Suc__lessE) ).
thf(804,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_less__add__eq__less) ).
thf(764,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(126,axiom,
zero @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_21) ).
thf(681,plain,
zero @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(160,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_lessI) ).
thf(784,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(233,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_infinite__descent) ).
thf(990,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(285,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add_Oassoc) ).
thf(1144,plain,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(276,axiom,
( m
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242__092_060open_062m_A_061_A0_092_060close_062) ).
thf(1122,plain,
( m
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(102,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_old_Onat_Odistinct_I2_J) ).
thf(599,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_lfinite__LCons) ).
thf(362,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(57,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_plus__nat_Oadd__0) ).
thf(451,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu749330388e_lnth @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_lnth__0) ).
thf(567,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu749330388e_lnth @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(141,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_gr0I) ).
thf(737,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(11,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_llist_OdiscI_I2_J) ).
thf(318,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_add__gr__0) ).
thf(880,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TB,B: TB > TA] :
( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TA ) ) )
=> ( ( groups15040474setsum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_setsum_Oneutral) ).
thf(434,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: set @ TB,B: TB > TA] :
( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TA ) ) )
=> ( ( groups15040474setsum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(197,axiom,
comm_monoid_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(890,plain,
comm_monoid_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(263,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_nat__add__left__cancel) ).
thf(1080,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_double__add__less__zero__iff__single__add__less__zero) ).
thf(631,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(149,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(758,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(171,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_ldropn__0) ).
thf(816,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(183,axiom,
! [TA: $tType] :
( ( strict797366125id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_pos__add__strict) ).
thf(848,plain,
! [TA: $tType] :
( ( strict797366125id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(225,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_neq0__conv) ).
thf(964,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_nat_OdiscI) ).
thf(626,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(217,axiom,
~ ( coindu335574135_lnull @ a @ ( coindu441856546concat @ a @ xssa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117__092_060open_062_092_060not_062_Alnull_A_Ilconcat_Axss_J_092_060close_062) ).
thf(943,plain,
~ ( coindu335574135_lnull @ a @ ( coindu441856546concat @ a @ xssa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(120,axiom,
semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_16) ).
thf(668,plain,
semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(15,axiom,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_llist_Odisc_I1_J) ).
thf(330,plain,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(258,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_double__zero) ).
thf(1061,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(245,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1029,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(200,axiom,
canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_10) ).
thf(895,plain,
canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Suc__less__eq2) ).
thf(768,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(252,axiom,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_zero__less__Suc) ).
thf(1044,plain,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(194,axiom,
semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).
thf(883,plain,
semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(242,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_old_Onat_Oinducts) ).
thf(1015,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(236,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_old_Onat_Odistinct_I1_J) ).
thf(1000,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ~ ( coindu335574135_lnull @ TB @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_lzip_Oexhaust) ).
thf(299,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ~ ( coindu335574135_lnull @ TB @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(116,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_add__right__imp__eq) ).
thf(658,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(273,axiom,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_enat__0__iff_I1_J) ).
thf(1113,plain,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: nat] :
( ( coindu749330388e_lnth @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( suc @ C ) )
= ( coindu749330388e_lnth @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_lnth__Suc__LCons) ).
thf(563,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: nat] :
( ( coindu749330388e_lnth @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( suc @ C ) )
= ( coindu749330388e_lnth @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(65,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1) ).
thf(473,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(135,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__eq__0__iff__both__eq__0) ).
thf(722,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(83,axiom,
( ( coindu749330388e_lnth @ a @ ( coindu441856546concat @ a @ xssa ) @ ( suc @ na ) )
= ( coindu749330388e_lnth @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) @ ( suc @ n3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062lnth_A_Ilconcat_Axss_J_A_ISuc_An_J_A_061_Alnth_A_Ilnth_Axss_A_Ilength_Axss_H_J_J_A_ISuc_An_H_J_092_060close_062) ).
thf(531,plain,
( ( coindu749330388e_lnth @ a @ ( coindu441856546concat @ a @ xssa ) @ ( suc @ na ) )
= ( coindu749330388e_lnth @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) @ ( suc @ n3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(281,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat] :
( ( groups15040474setsum @ nat @ TA @ A @ ( set_ord_lessThan @ nat @ ( suc @ B ) ) )
= ( plus_plus @ TA @ ( A @ ( zero_zero @ nat ) )
@ ( groups15040474setsum @ nat @ TA
@ ^ [C: nat] : ( A @ ( suc @ C ) )
@ ( set_ord_lessThan @ nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_setsum__lessThan__Suc__shift) ).
thf(1134,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat] :
( ( groups15040474setsum @ nat @ TA @ A @ ( set_ord_lessThan @ nat @ ( suc @ B ) ) )
= ( plus_plus @ TA @ ( A @ ( zero_zero @ nat ) )
@ ( groups15040474setsum @ nat @ TA
@ ^ [C: nat] : ( A @ ( suc @ C ) )
@ ( set_ord_lessThan @ nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(216,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_enat__iless) ).
thf(939,plain,
! [A: extended_enat,B: nat] :
( ( ord_less @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(254,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_lift__Suc__mono__less__iff) ).
thf(1049,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(105,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__add__Suc1) ).
thf(617,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_less__add__same__cancel2) ).
thf(516,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__SucI) ).
thf(776,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(92,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zero__less__double__add__iff__zero__less__single__add) ).
thf(557,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(111,axiom,
comm_semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(640,plain,
comm_semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(243,axiom,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1025,plain,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(190,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_less__Suc0) ).
thf(872,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(130,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_trans__less__add2) ).
thf(705,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(196,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_length__induct) ).
thf(887,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(43,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add_Ocomm__neutral) ).
thf(414,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Ex__list__of__length) ).
thf(327,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(123,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_semiring__normalization__rules_I25_J) ).
thf(673,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(53,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add__left__imp__eq) ).
thf(441,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(19,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: coindu1593790203_llist @ TA] :
( ? [C: TA] :
( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
=> ~ ( coindu1213758845finite @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_lfinite_Ocases) ).
thf(338,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: coindu1593790203_llist @ TA] :
( ? [C: TA] :
( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
=> ~ ( coindu1213758845finite @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(64,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu531130065ldropn @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ldropn__eq__LConsD) ).
thf(470,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu531130065ldropn @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ ( coindu1018505716length @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(168,axiom,
ord_less @ extended_enat @ ( extended_enat2 @ ( suc @ na ) ) @ ( coindu1018505716length @ a @ ( coindu441856546concat @ a @ xssa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Suc_Oprems) ).
thf(808,plain,
ord_less @ extended_enat @ ( extended_enat2 @ ( suc @ na ) ) @ ( coindu1018505716length @ a @ ( coindu441856546concat @ a @ xssa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(26,axiom,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_lnull__def) ).
thf(359,plain,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(279,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_add_Ocommute) ).
thf(1130,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(88,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__cancel__right__left) ).
thf(544,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(336,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(284,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_not__add__less2) ).
thf(1141,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(255,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat] : ( A @ ( zero_zero @ nat ) @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_diff__induct) ).
thf(1052,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat] : ( A @ ( zero_zero @ nat ) @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(137,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add_Ogroup__left__neutral) ).
thf(727,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(239,axiom,
comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_15) ).
thf(1008,plain,
comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(73,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__trans__Suc) ).
thf(497,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(187,axiom,
( ( coindu441856546concat @ a @ xssa )
= ( coindu1121789889_LCons @ a @ x @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_concat__xss) ).
thf(859,plain,
( ( coindu441856546concat @ a @ xssa )
= ( coindu1121789889_LCons @ a @ x @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(33,axiom,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zero__reorient) ).
thf(386,plain,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(268,axiom,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_enat_Oinject) ).
thf(1094,plain,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__imp__Suc__add) ).
thf(978,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(283,axiom,
ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_11) ).
thf(1140,plain,
ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(182,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( set_ord_lessThan @ TA @ A )
= ( set_ord_lessThan @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_lessThan__eq__iff) ).
thf(845,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( set_ord_lessThan @ TA @ A )
= ( set_ord_lessThan @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(56,axiom,
ab_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(450,plain,
ab_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( groups15040474setsum @ TB @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ~ ! [C: TB] :
( ( member @ TB @ C @ B )
=> ( ( A @ C )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_setsum_Onot__neutral__contains__not__neutral) ).
thf(903,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( groups15040474setsum @ TB @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ~ ! [C: TB] :
( ( member @ TB @ C @ B )
=> ( ( A @ C )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(150,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_add__less__imp__less__left) ).
thf(759,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_nat__neq__iff) ).
thf(891,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(154,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__pos__pos) ).
thf(771,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(213,axiom,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B )
= ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_enat__add1__eq) ).
thf(931,plain,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B )
= ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(86,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__less__imp__less__right) ).
thf(539,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(39,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_llist_Oexhaust) ).
thf(401,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(161,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ~ ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ( A
!= ( zero_zero @ extended_enat ) )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ltake_Oexhaust) ).
thf(786,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ~ ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ( A
!= ( zero_zero @ extended_enat ) )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(234,axiom,
( ( groups15040474setsum @ nat @ extended_enat
@ ^ [A: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) )
@ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) )
= ( zero_zero @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062_I_092_060Sum_062i_060length_Axss_H_O_Allength_A_Ilnth_Axss_Ai_J_J_A_061_A0_092_060close_062) ).
thf(995,plain,
( ( groups15040474setsum @ nat @ extended_enat
@ ^ [A: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ xssa @ A ) )
@ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) )
= ( zero_zero @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(224,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add_Oleft__commute) ).
thf(961,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ A @ B ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_one__is__add) ).
thf(813,plain,
! [A: nat,B: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ A @ B ) )
= ( ( ( A
= ( suc @ ( zero_zero @ nat ) ) )
& ( B
= ( zero_zero @ nat ) ) )
| ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(201,axiom,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( ord_less @ extended_enat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_enat__add__mono) ).
thf(896,plain,
! [A: nat,B: extended_enat,C: extended_enat] :
( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ B ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ C ) )
= ( ord_less @ extended_enat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(145,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add_Oleft__cancel) ).
thf(748,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(206,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_not__less__zero) ).
thf(914,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(49,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_2) ).
thf(433,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(202,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_nat_Odistinct_I1_J) ).
thf(899,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(21,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_llist_Ocollapse_I1_J) ).
thf(346,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(85,axiom,
! [A: nat,B: extended_enat,C: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ C @ A ) ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_enat__less__enat__plusI2) ).
thf(536,plain,
! [A: nat,B: extended_enat,C: nat] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ A ) @ B )
=> ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ C @ A ) ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(262,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Nat_Oadd__0__right) ).
thf(1077,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ ( set @ TA ) @ ( set_ord_lessThan @ TA @ A ) @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_lessThan__strict__subset__iff) ).
thf(478,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ ( set @ TA ) @ ( set_ord_lessThan @ TA @ A ) @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(133,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_nat__less__induct) ).
thf(716,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(290,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_add__mono__thms__linordered__field_I1_J) ).
thf(1161,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(165,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_semiring__normalization__rules_I5_J) ).
thf(800,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(274,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_gr0__implies__Suc) ).
thf(1116,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(280,axiom,
ordere216010020id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(1133,plain,
ordere216010020id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(147,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__less__cancel__right) ).
thf(752,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(55,axiom,
! [A: extended_enat,B: nat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ A @ ( extended_enat2 @ B ) )
= ( plus_plus @ extended_enat @ C @ ( extended_enat2 @ B ) ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_enat__add2__eq) ).
thf(447,plain,
! [A: extended_enat,B: nat,C: extended_enat] :
( ( ( plus_plus @ extended_enat @ A @ ( extended_enat2 @ B ) )
= ( plus_plus @ extended_enat @ C @ ( extended_enat2 @ B ) ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_not__lnull__conv) ).
thf(315,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TB @ ( type2 @ TB ) )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( groups15040474setsum @ TA @ TB @ C @ A )
= ( groups15040474setsum @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_setsum_Ocong) ).
thf(865,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TB @ ( type2 @ TB ) )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( groups15040474setsum @ TA @ TB @ C @ A )
= ( groups15040474setsum @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(103,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_strict__inc__induct) ).
thf(603,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(177,axiom,
semiri456707255roduct @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(833,plain,
semiri456707255roduct @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(226,axiom,
! [A: coindu1593790203_llist @ ( coindu1593790203_llist @ a )] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ na ) @ ( coindu1018505716length @ a @ ( coindu441856546concat @ a @ A ) ) )
=> ? [B: nat,C: nat] :
( ( ( coindu749330388e_lnth @ a @ ( coindu441856546concat @ a @ A ) @ na )
= ( coindu749330388e_lnth @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ A @ B ) @ C ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ C ) @ ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ A @ B ) ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ a ) @ A ) )
& ( ( extended_enat2 @ na )
= ( plus_plus @ extended_enat
@ ( groups15040474setsum @ nat @ extended_enat
@ ^ [D: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ A @ D ) )
@ ( set_ord_lessThan @ nat @ B ) )
@ ( extended_enat2 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Suc_Ohyps) ).
thf(967,plain,
! [A: coindu1593790203_llist @ ( coindu1593790203_llist @ a )] :
( ( ord_less @ extended_enat @ ( extended_enat2 @ na ) @ ( coindu1018505716length @ a @ ( coindu441856546concat @ a @ A ) ) )
=> ? [B: nat,C: nat] :
( ( ( coindu749330388e_lnth @ a @ ( coindu441856546concat @ a @ A ) @ na )
= ( coindu749330388e_lnth @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ A @ B ) @ C ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ C ) @ ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ A @ B ) ) )
& ( ord_less @ extended_enat @ ( extended_enat2 @ B ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ a ) @ A ) )
& ( ( extended_enat2 @ na )
= ( plus_plus @ extended_enat
@ ( groups15040474setsum @ nat @ extended_enat
@ ^ [D: nat] : ( coindu1018505716length @ a @ ( coindu749330388e_lnth @ ( coindu1593790203_llist @ a ) @ A @ D ) )
@ ( set_ord_lessThan @ nat @ B ) )
@ ( extended_enat2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(220,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_not__gr0) ).
thf(950,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(269,axiom,
! [TA: $tType] :
( ( coindu1018505716length @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( zero_zero @ extended_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_llength__LNil) ).
thf(1097,plain,
! [TA: $tType] :
( ( coindu1018505716length @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( zero_zero @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(179,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_semiring__normalization__rules_I22_J) ).
thf(835,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(6,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_4) ).
thf(305,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: set @ TA] :
( ( groups15040474setsum @ TA @ TB
@ ^ [D: TA] : ( plus_plus @ TB @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus @ TB @ ( groups15040474setsum @ TA @ TB @ A @ C ) @ ( groups15040474setsum @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_setsum_Odistrib) ).
thf(918,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: set @ TA] :
( ( groups15040474setsum @ TA @ TB
@ ^ [D: TA] : ( plus_plus @ TB @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus @ TB @ ( groups15040474setsum @ TA @ TB @ A @ C ) @ ( groups15040474setsum @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Suc__inject) ).
thf(474,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(247,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_gr__zeroI) ).
thf(1033,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(291,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__monoid__add__class_Oadd__0) ).
thf(1165,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(212,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_plus__enat__simps_I1_J) ).
thf(928,plain,
! [A: nat,B: nat] :
( ( plus_plus @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(256,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_infinite__descent__measure) ).
thf(1056,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(118,axiom,
strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_8) ).
thf(664,plain,
strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(37,axiom,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_lfinite__ldropn) ).
thf(395,plain,
! [TA: $tType,A: nat,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu531130065ldropn @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(142,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_trans__less__add1) ).
thf(740,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(232,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_add__less__mono) ).
thf(987,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(62,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ( set_ord_lessThan @ TA )
= ( ^ [A: TA] :
( collect @ TA
@ ^ [B: TA] : ( ord_less @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_lessThan__def) ).
thf(464,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ( set_ord_lessThan @ TA )
= ( ^ [A: TA] :
( collect @ TA
@ ^ [B: TA] : ( ord_less @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_lfinite__code_I2_J) ).
thf(332,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(101,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: nat] :
( ( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_llength__eq__enat__lfiniteD) ).
thf(596,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: nat] :
( ( ( coindu1018505716length @ TA @ A )
= ( extended_enat2 @ B ) )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(204,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_not__add__less1) ).
thf(908,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(174,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_old_Onat_Oexhaust) ).
thf(822,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(184,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_semiring__normalization__rules_I23_J) ).
thf(850,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(237,axiom,
coindu335574135_lnull @ a @ ( coindu441856546concat @ a @ ( coindu1079202755ist_of @ ( coindu1593790203_llist @ a ) @ xss2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_concat__xss_H) ).
thf(1004,plain,
coindu335574135_lnull @ a @ ( coindu441856546concat @ a @ ( coindu1079202755ist_of @ ( coindu1593790203_llist @ a ) @ xss2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(75,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_less__not__refl) ).
thf(501,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(369,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(12,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_lappend_Oexhaust) ).
thf(322,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(166,axiom,
ord_less @ extended_enat @ ( extended_enat2 @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ a ) @ xssa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062enat_A_Ilength_Axss_H_J_A_060_Allength_Axss_092_060close_062) ).
thf(803,plain,
ord_less @ extended_enat @ ( extended_enat2 @ ( size_size @ ( list @ ( coindu1593790203_llist @ a ) ) @ xss2 ) ) @ ( coindu1018505716length @ ( coindu1593790203_llist @ a ) @ xssa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mem__Collect__eq) ).
thf(354,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_add__less__mono1) ).
thf(1009,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(8,axiom,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: coindu1593790203_llist @ TA,C: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
& ( coindu1213758845finite @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_lfinite_Osimps) ).
thf(309,plain,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: coindu1593790203_llist @ TA,C: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
& ( coindu1213758845finite @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_double__zero__sym) ).
thf(560,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(266,axiom,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_add_Oright__neutral) ).
thf(1088,plain,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_lessE) ).
thf(708,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(148,axiom,
! [TA: $tType,A: nat,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ ( suc @ A ) @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu531130065ldropn @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_ldropn__Suc__LCons) ).
thf(755,plain,
! [TA: $tType,A: nat,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu531130065ldropn @ TA @ ( suc @ A ) @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu531130065ldropn @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(124,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_gr0__conv__Suc) ).
thf(676,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(58,axiom,
! [TA: $tType] :
( ( coindu441856546concat @ TA @ ( coindu1598213697e_LNil @ ( coindu1593790203_llist @ TA ) ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_lconcat__LNil) ).
thf(454,plain,
! [TA: $tType] :
( ( coindu441856546concat @ TA @ ( coindu1598213697e_LNil @ ( coindu1593790203_llist @ TA ) ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(260,axiom,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_add_Oleft__neutral) ).
thf(1069,plain,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(3450,plain,
$false,
inference(cvc4,[status(thm)],[1036,809,365,1168,1083,1110,481,352,408,1158,1005,730,614,878,440,655,511,1041,861,384,1137,533,550,500,797,945,670,404,1127,782,417,1046,651,389,570,504,1059,460,619,838,702,751,934,357,853,1147,325,1100,924,492,1040,821,485,834,981,634,734,1072,1119,428,507,312,293,956,307,439,529,661,925,366,1153,761,894,1091,778,302,349,392,566,1032,665,830,461,493,682,842,974,1012,916,467,519,948,1064,725,593,420,884,488,554,669,686,637,590,547,679,1039,997,654,457,721,779,371,515,1150,984,911,343,792,1086,921,541,398,1026,953,773,794,412,430,856,745,573,296,444,819,975,423,732,743,958,1124,875,826,641,391,936,713,1107,335,804,764,681,784,990,1144,1122,599,362,451,567,737,318,880,434,890,1080,631,758,816,848,964,626,943,668,330,1061,1029,895,768,1044,883,1015,1000,299,658,1113,563,473,722,531,1134,939,1049,617,516,776,557,640,1025,872,705,887,414,327,673,441,338,470,808,359,1130,544,336,1141,1052,727,1008,497,859,386,1094,978,1140,845,450,903,759,891,771,931,539,401,786,995,961,813,896,748,914,433,899,346,536,1077,478,716,1161,800,1116,1133,752,447,315,865,603,833,967,950,1097,835,305,918,474,1033,1165,928,1056,664,395,740,987,464,332,596,908,822,850,1004,501,369,322,803,354,1009,309,560,1088,708,755,676,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT136^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n019.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 11:37:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.01/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.75/1.13 % [INFO] Parsing done (263ms).
% 1.75/1.14 % [INFO] Running in sequential loop mode.
% 2.62/1.36 % [INFO] eprover registered as external prover.
% 2.62/1.36 % [INFO] cvc4 registered as external prover.
% 2.78/1.37 % [INFO] Scanning for conjecture ...
% 2.99/1.48 % [INFO] Found a conjecture and 291 axioms. Running axiom selection ...
% 3.26/1.57 % [INFO] Axiom selection finished. Selected 290 axioms (removed 1 axioms).
% 3.75/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 3.75/1.73 % [INFO] Type checking passed.
% 3.75/1.74 % [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 ...
% 106.17/38.76 % External prover 'cvc4' found a proof!
% 106.17/38.76 % [INFO] Killing All external provers ...
% 106.17/38.77 % Time passed: 38235ms (effective reasoning time: 37620ms)
% 106.17/38.77 % 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)>
% 106.17/38.77 % Axioms used in derivation (290): tcon_Extended__Nat_Oenat___Groups_Oordered__comm__monoid__add_12, fact_168_measure__induct__rule, fact_159_trans__less__add1, fact_182_llist_Oexhaust, fact_81_add__pos__pos, fact_209_gr0__implies__Suc, fact_73_lessE, fact_234_length__induct, fact_195_nat_Odistinct_I1_J, fact_14__092_060open_062_I_092_060Sum_062i_060length_Axss_H_O_Allength_A_Ilnth_Axss_Ai_J_J_A_061_A0_092_060close_062, fact_156_gr__implies__not0, fact_82_add__neg__neg, fact_212_add__is__1, fact_134_lnth__0, fact_181_neq__LNil__conv, fact_215_llength__eq__enat__lfiniteD, fact_204_Zero__not__Suc, tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_10, fact_92_add_Oassoc, fact_4__092_060open_062lnth_A_Ilconcat_Axss_J_A_ISuc_An_J_A_061_Alnth_A_Ilnth_Axss_A_Ilength_Axss_H_J_J_A_ISuc_An_H_J_092_060close_062, fact_108_lessThan__strict__subset__iff, fact_135_lconcat__LNil, fact_122_False, fact_207_not0__implies__Suc, fact_59_not__less__less__Suc__eq, fact_85_enat__less__enat__plusI, tcon_Nat_Onat___Orderings_Olinorder, fact_160_trans__less__add2, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__comm__monoid__add_9, fact_238_ldropn__ldropn, fact_1_assms, fact_144_add__lessD1, fact_247_neq__if__length__neq, fact_237_ldropn__0, tcon_Extended__Nat_Oenat___Orderings_Olinorder_17, fact_25_old_Onat_Oinject, fact_101_add__strict__left__mono, fact_65_Suc__less__eq2, fact_50_zero__reorient, fact_5__092_060open_062enat_A_ISuc_An_J_A_061_A_I_092_060Sum_062i_060length_Axss_H_O_Allength_A_Ilnth_Axss_Ai_J_J_A_L_Aenat_A_ISuc_An_H_J_092_060close_062, fact_48_less__add__Suc1, fact_124_add__is__0, tcon_HOL_Obool___Orderings_Olinorder_5, fact_174_lfinite__LConsI, fact_103_add__mono__thms__linordered__field_I1_J, fact_153_less__not__refl3, fact_96_Suc__inject, fact_44_Collect__mem__eq, fact_80_pos__add__strict, fact_52_less__imp__Suc__add, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_171_less__imp__add__positive, fact_97_enat__less__induct, fact_194_ltake_Oexhaust, fact_210_gr0__conv__Suc, fact_120_setsum_Oneutral, fact_2__092_060open_062enat_A_ISuc_An_H_J_A_060_Allength_A_Ilnth_Axss_A_Ilength_Axss_H_J_J_092_060close_062, fact_94_ab__semigroup__add__class_Oadd__ac_I1_J, fact_79_plus__enat__eq__0__conv, fact_19_add__right__cancel, fact_119_setsum_Onot__neutral__contains__not__neutral, fact_138_llength__lnull, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_125_Nat_Oadd__0__right, fact_127_zero__less__Suc, tcon_fun___Orderings_Oord, fact_123_neq0__conv, fact_137_llength__eq__0, fact_126_llist_Oinject, tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_16, fact_32_double__zero, fact_8_enat__add__mono, fact_143_not__less0, fact_242__092_060open_062m_A_061_A0_092_060close_062, tcon_Set_Oset___Orderings_Oorder_3, fact_197_old_Onat_Odistinct_I1_J, fact_245_ldropn__lnull, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_239_ldropn__LNil, fact_113_lnth__prefix, fact_130_nat__add__left__cancel__less, fact_30_add__cancel__left__left, fact_28_add__cancel__right__left, fact_191_llist_Odisc_I2_J, fact_136_lnth__Suc__LCons, fact_16_lessThan__eq__iff, fact_21_add__Suc__right, fact_164_infinite__descent0, fact_249_ldropn__Suc__conv__ldropn, fact_26_not__gr__zero, fact_58_gr__zeroI, tcon_Nat_Onat___Groups_Ocomm__monoid__add, fact_157_less__irrefl__nat, fact_217_zero__enat__def, fact_152_less__not__refl2, fact_90_add_Oright__cancel, fact_69_less__SucE, fact_222_semiring__normalization__rules_I23_J, fact_7_setsum__lessThan__Suc, fact_43_mem__Collect__eq, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, fact_87_add__left__imp__eq, fact_208_less__Suc__eq__0__disj, fact_111_lessThan__def, fact_161_add__eq__self__zero, fact_72_Suc__lessD, fact_175_lfinite__LNil, fact_115_setsum_Odistrib, fact_83_less__enatE, fact_185_lzip_Oexhaust, tcon_Nat_Onat___Orderings_Oord_2, fact_114_llength__lconcat__lfinite__conv__sum, fact_183_lfinite_Osimps, tcon_Nat_Onat___Groups_Omonoid__add, fact_151_add__less__mono1, fact_51_less__iff__Suc__add, fact_118_gen__llength__def, fact_228_setsum_Ocommute, fact_246_Ex__list__of__length, fact_230_semiring__normalization__rules_I6_J, fact_169_nat__add__left__cancel, fact_225_semiring__normalization__rules_I20_J, fact_27_add__cancel__right__right, fact_24_lessI, fact_224_semiring__normalization__rules_I21_J, fact_233_enat_Osize_I1_J, fact_110_chain__incr, fact_56_gr__implies__not__zero, fact_98_add__less__imp__less__right, fact_54_add__Suc__shift, fact_121_add__0__iff, fact_66_not__less__eq, fact_132_lfinite__code_I2_J, fact_9_enat__add1__eq, fact_198_nat_OdiscI, fact_178_lfinite_Oinducts, fact_158_nat__less__induct, tcon_HOL_Obool___Orderings_Oorder_6, fact_148_less__not__refl, fact_170_nat__add__right__cancel, fact_57_not__less__zero, fact_186_llist_Odistinct_I1_J, fact_60_strict__inc__induct, fact_53_add__Suc, fact_206_old_Onat_Oinducts, fact_203_Zero__neq__Suc, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, tcon_Extended__Nat_Oenat___Groups_Ocomm__monoid__add_14, fact_37_plus__enat__simps_I1_J, tcon_Nat_Onat___Groups_Ozero, fact_139_llength__LNil, fact_104_add__mono__thms__linordered__field_I2_J, fact_189_llist_OdiscI_I2_J, fact_106_lift__Suc__mono__less__iff, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_13, fact_162_infinite__descent, fact_193_llength__code, fact_192_gen__llength__code_I1_J, fact_117__092_060open_062_092_060not_062_Alnull_A_Ilconcat_Axss_J_092_060close_062, fact_213_setsum__cong__Suc, fact_34_add_Oleft__neutral, fact_86_add__right__imp__eq, fact_140_concat__xss, fact_201_zero__induct, fact_75_add_Ogroup__left__neutral, fact_116__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_Axs_O_Alconcat_Axss_A_061_ALCons_Ax_Axs_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_63_Suc__less__SucD, fact_236_llist__of__inject, fact_226_setsum_Ocong, fact_163_less__add__eq__less, fact_102_add__strict__mono, fact_216_lfinite__conv__llength__enat, fact_241_ldropn__Suc__LCons, fact_49_less__add__Suc2, fact_202_Suc__neq__Zero, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add, tcon_HOL_Obool___Orderings_Oord_7, fact_166_setsum__SucD, fact_200_diff__induct, fact_39_double__add__less__zero__iff__single__add__less__zero, fact_129_add__gr__0, fact_227_setsum_Oreindex__bij__witness, fact_36_i0__less, fact_0__092_060open_062enat_A_Ilength_Axss_H_J_A_060_Allength_Axss_092_060close_062, fact_62_less__trans__Suc, fact_99_add__less__imp__less__left, fact_55_zero__less__iff__neq__zero, tcon_Extended__Nat_Oenat___Groups_Omonoid__add_18, fact_6_Suc_Ohyps, fact_180_not__lnull__conv, fact_154_measure__induct, fact_112_setsum_Oneutral__const, fact_68_less__SucI, fact_243_llength__llist__of, fact_29_add__cancel__left__right, fact_150_not__add__less2, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_64_less__antisym, fact_235_lnth__ldropn, fact_17_nat_Oinject, fact_61_less__Suc__induct, fact_22_Suc__less__eq, fact_95_n__not__Suc__n, fact_221_semiring__normalization__rules_I24_J, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_147_add__less__mono, fact_76_add_Ocomm__neutral, fact_20_add__left__cancel, fact_89_add_Ocommute, fact_142_not__gr0, fact_188_llist_OdiscI_I1_J, fact_15_enat_Oinject, fact_141_gr0I, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_223_semiring__normalization__rules_I22_J, fact_220_semiring__normalization__rules_I25_J, tcon_Extended__Nat_Oenat___Orderings_Oorder_19, fact_184_lfinite_Ocases, fact_107_lift__Suc__mono__less, fact_12_add__less__cancel__left, fact_40_less__add__same__cancel2, fact_45_Collect__cong, fact_219_enat__0__iff_I2_J, fact_146_nat__neq__iff, fact_13_add__less__cancel__right, fact_165_linorder__neqE__nat, fact_199_nat__induct, fact_248_ldropn__eq__LConsD, fact_240_lfinite__ldropn, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, tcon_fun___Orderings_Oorder, fact_88_add_Oleft__commute, fact_244_lfinite__llist__of, tcon_Nat_Onat___Groups_Osemigroup__add, fact_77_comm__monoid__add__class_Oadd__0, fact_133_lfinite__code_I1_J, fact_11_lessThan__iff, tcon_Extended__Nat_Oenat___Groups_Ozero_21, fact_10_enat__add2__eq, tcon_Nat_Onat___Orderings_Oorder_1, fact_149_not__add__less1, fact_84_enat__less__enat__plusI2, fact_105_add__mono__thms__linordered__field_I5_J, fact_229_setsum__lessThan__Suc__shift, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_8, fact_167_less__nat__zero__code, fact_18_n, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_176_lnull__imp__lfinite, fact_67_less__Suc__eq, fact_196_old_Onat_Odistinct_I2_J, fact_78_not__iless0, fact_3_Suc_Oprems, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_15, fact_100_add__strict__right__mono, fact_70_Suc__lessI, fact_38_zero__less__double__add__iff__zero__less__single__add, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_218_enat__0__iff_I1_J, fact_205_old_Onat_Oexhaust, fact_42_add__less__same__cancel2, fact_91_add_Oleft__cancel, fact_23_Suc__mono, fact_179_lappend_Oexhaust, fact_231_semiring__normalization__rules_I5_J, fact_177_lnull__def, fact_71_Suc__lessE, fact_232_concat__xss_H, fact_145_less__zeroE, tcon_Set_Oset___Orderings_Oord_4, tcon_Extended__Nat_Oenat___Orderings_Oord_20, fact_190_llist_Odisc_I1_J, fact_47_add__less__same__cancel1, fact_155_plus__nat_Oadd__0, fact_74_add__eq__0__iff__both__eq__0, fact_173_infinite__descent0__measure, fact_172_infinite__descent__measure, fact_93_add__mono__thms__linordered__semiring_I4_J, fact_33_add_Oright__neutral, fact_131_lfinite__LCons, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_35_enat__ord__simps_I2_J, fact_31_double__zero__sym, fact_214_lfinite__llength__enat, fact_187_llist_Ocollapse_I1_J, fact_128_less__Suc0, fact_109_enat__iless, fact_211_one__is__add, tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_11, fact_41_less__add__same__cancel1
% 106.17/38.77 % No. of inferences in proof: 584
% 106.17/38.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 38235 ms resp. 37620 ms w/o parsing
% 106.65/38.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 106.65/38.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------