TSTP Solution File: ITP126^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP126^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 : Mon May 20 22:23:10 EDT 2024
% Result : Theorem 78.78s 38.08s
% Output : Refutation 79.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 376
% Syntax : Number of formulae : 689 ( 332 unt; 65 typ; 0 def)
% Number of atoms : 1512 ( 675 equ; 4 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 5588 ( 194 ~; 26 |; 103 &;4757 @)
% ( 0 <=>; 508 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 166 ( 166 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 16 con; 0-6 aty)
% Number of variables : 1624 ( 46 ^1452 !; 72 ?;1624 :)
% ( 54 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(i_type,type,
i: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(size_type,type,
size:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(semigroup_add_type,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_type,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(archim1804426504_field_type,type,
archim1804426504_field:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(strict797366125id_add_type,type,
strict797366125id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(strict2144017051up_add_type,type,
strict2144017051up_add:
!>[TA: $tType] : $o ).
thf(ordere516151231imp_le_type,type,
ordere516151231imp_le:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(bNF_Greatest_shift_type,type,
bNF_Greatest_shift:
!>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(drop_type,type,
drop:
!>[TA: $tType] : ( nat > ( list @ TA ) > ( list @ TA ) ) ).
thf(find_type,type,
find:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > ( option @ TA ) ) ).
thf(gen_length_type,type,
gen_length:
!>[TA: $tType] : ( nat > ( list @ TA ) > nat ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(list_ex_type,type,
list_ex:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(nth_type,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(c_MFOTL_Oformula_OEq_type,type,
c_MFOTL_Oformula_OEq:
!>[TA: $tType] : ( ( trm @ TA ) > ( trm @ TA ) > ( formula @ TA ) ) ).
thf(fvi_type,type,
fvi:
!>[TA: $tType] : ( nat > ( formula @ TA ) > ( set @ nat ) ) ).
thf(monito518325957Exists_type,type,
monito518325957Exists:
!>[TA: $tType] : ( ( monito748960549ormula @ TA ) > ( monito748960549ormula @ TA ) ) ).
thf(monito320348316_MNext_type,type,
monito320348316_MNext:
!>[TA: $tType] : ( i > ( monito748960549ormula @ TA ) > $o > ( list @ nat ) > ( monito748960549ormula @ TA ) ) ).
thf(monito1987675900_MPrev_type,type,
monito1987675900_MPrev:
!>[TA: $tType] : ( i > ( monito748960549ormula @ TA ) > $o > ( list @ ( set @ ( list @ ( option @ TA ) ) ) ) > ( list @ nat ) > ( monito748960549ormula @ TA ) ) ).
thf(monito1197352414ormula_type,type,
monito1197352414ormula:
!>[TA: $tType] : ( ( TA > nat ) > ( monito748960549ormula @ TA ) > nat ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(nat_triangle_type,type,
nat_triangle: nat > nat ).
thf(none_type,type,
none:
!>[TA: $tType] : ( option @ TA ) ).
thf(some_type,type,
some:
!>[TA: $tType] : ( TA > ( option @ TA ) ) ).
thf(size_option_type,type,
size_option:
!>[TA: $tType] : ( ( TA > nat ) > ( option @ TA ) > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(phi_type,type,
phi: formula @ a ).
thf(b2_type,type,
b2: nat ).
thf(n_type,type,
n: nat ).
thf(v_type,type,
v: list @ ( option @ b ) ).
thf(x_type,type,
x: b ).
thf(182,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Ex__less__Suc) ).
thf(809,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(251,axiom,
strict2144017051up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_4) ).
thf(1024,plain,
strict2144017051up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(164,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_All__less__Suc2) ).
thf(760,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(312,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: nat] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( suc @ C ) )
= ( nth @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nth__Cons__Suc) ).
thf(1237,plain,
! [TA: $tType,A: TA,B: list @ TA,C: nat] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( suc @ C ) )
= ( nth @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(231,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_85_less__Suc__eq__0__disj) ).
thf(962,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)],[231]) ).
thf(99,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_of__nat__0__eq__iff) ).
thf(555,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(75,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_zero__reorient) ).
thf(479,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(278,axiom,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Skolem__list__nth) ).
thf(1105,plain,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(307,axiom,
! [TA: $tType] :
( ( strict797366125id_add @ 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_205_pos__add__strict) ).
thf(1211,plain,
! [TA: $tType] :
( ( strict797366125id_add @ 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)],[307]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ 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_180_add__mono__thms__linordered__field_I1_J) ).
thf(523,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ 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)],[89]) ).
thf(157,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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_176_add__less__imp__less__left) ).
thf(741,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[157]) ).
thf(304,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_measure__induct) ).
thf(1205,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(29,axiom,
! [TA: $tType,A: monito748960549ormula @ TA,B: monito748960549ormula @ TA] :
( ( ( monito518325957Exists @ TA @ A )
= ( monito518325957Exists @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_mformula_Oinject_I5_J) ).
thf(379,plain,
! [TA: $tType,A: monito748960549ormula @ TA,B: monito748960549ormula @ TA] :
( ( ( monito518325957Exists @ TA @ A )
= ( monito518325957Exists @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(137,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_167_add__less__mono) ).
thf(677,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)],[137]) ).
thf(257,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_20) ).
thf(1041,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(203,axiom,
! [TA: $tType,A: option @ TA,B: TA] :
( ( A
= ( some @ TA @ B ) )
=> ( A
!= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_option_OdiscI) ).
thf(878,plain,
! [TA: $tType,A: option @ TA,B: TA] :
( ( A
= ( some @ TA @ B ) )
=> ( A
!= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(129,axiom,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_zero__less__Suc) ).
thf(655,plain,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(32,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add_Ocomm__neutral) ).
thf(384,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(151,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_not0__implies__Suc) ).
thf(715,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(72,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_add__cancel__right__right) ).
thf(472,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(145,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_140_add__is__0) ).
thf(698,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)],[145]) ).
thf(135,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Zero__not__Suc) ).
thf(670,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(294,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_less__zeroE) ).
thf(1164,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(178,axiom,
! [TA: $tType,A: nat,B: nat,C: formula @ TA] :
( ( member @ nat @ A @ ( fvi @ TA @ ( suc @ B ) @ C ) )
= ( member @ nat @ ( suc @ A ) @ ( fvi @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_fvi__Suc) ).
thf(797,plain,
! [TA: $tType,A: nat,B: nat,C: formula @ TA] :
( ( member @ nat @ A @ ( fvi @ TA @ ( suc @ B ) @ C ) )
= ( member @ nat @ ( suc @ A ) @ ( fvi @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(171,axiom,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_option_Odistinct_I1_J) ).
thf(782,plain,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(149,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_71_Suc__lessI) ).
thf(709,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)],[149]) ).
thf(5,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(320,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(54,axiom,
! [TA: $tType] :
( ( group_add @ 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_192_add_Oleft__cancel) ).
thf(436,plain,
! [TA: $tType] :
( ( group_add @ 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)],[54]) ).
thf(189,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_164_add__less__mono1) ).
thf(829,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)],[189]) ).
thf(275,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_210_less__natE) ).
thf(1095,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)],[275]) ).
thf(40,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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_196_add__left__imp__eq) ).
thf(404,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[40]) ).
thf(206,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( some @ TA @ A )
= ( some @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_option_Oinject) ).
thf(885,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( some @ TA @ A )
= ( some @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(260,axiom,
! [TA: $tType,A: trm @ TA,B: trm @ TA] :
( ( size_size @ ( formula @ TA ) @ ( c_MFOTL_Oformula_OEq @ TA @ A @ B ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( trm @ TA ) @ A ) @ ( size_size @ ( trm @ TA ) @ B ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_formula_Osize_I11_J) ).
thf(1046,plain,
! [TA: $tType,A: trm @ TA,B: trm @ TA] :
( ( size_size @ ( formula @ TA ) @ ( c_MFOTL_Oformula_OEq @ TA @ A @ B ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( trm @ TA ) @ A ) @ ( size_size @ ( trm @ TA ) @ B ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(172,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_less__add__Suc1) ).
thf(785,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(83,axiom,
! [TA: $tType,A: TA > nat] :
( ( size_option @ TA @ A @ ( none @ TA ) )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_option_Osize__gen_I1_J) ).
thf(504,plain,
! [TA: $tType,A: TA > nat] :
( ( size_option @ TA @ A @ ( none @ TA ) )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(117,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_plus__nat_Oadd__0) ).
thf(619,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(160,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_19) ).
thf(751,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(14,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(344,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(222,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ 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_179_add__strict__mono) ).
thf(934,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ 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(226,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_31_neq__if__length__neq) ).
thf(949,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)],[226]) ).
thf(264,axiom,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_list__ex__length) ).
thf(1059,plain,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(286,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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_175_add__less__imp__less__right) ).
thf(1132,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[286]) ).
thf(212,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_BNF__Greatest__Fixpoint_Oshift__def) ).
thf(902,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(47,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_comm__monoid__add__class_Oadd__0) ).
thf(421,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(234,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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_147_add__less__same__cancel1) ).
thf(969,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[234]) ).
thf(281,axiom,
member @ nat @ ( zero_zero @ nat ) @ ( fvi @ a @ b2 @ phi ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1115,plain,
member @ nat @ ( zero_zero @ nat ) @ ( fvi @ a @ b2 @ phi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_of__nat__0__less__iff) ).
thf(638,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(195,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_162_trans__less__add2) ).
thf(853,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)],[195]) ).
thf(73,axiom,
ordere779506340up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(475,plain,
ordere779506340up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(174,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_verit__comp__simplify1_I1_J) ).
thf(789,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(57,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(443,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(6,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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_197_add__right__imp__eq) ).
thf(321,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[6]) ).
thf(27,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add) ).
thf(376,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(288,axiom,
! [A: nat,B: nat,C: int] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ C ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_zadd__int__left) ).
thf(1136,plain,
! [A: nat,B: nat,C: int] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ C ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(16,axiom,
! [TA: $tType,A: monito748960549ormula @ TA,B: i,C: monito748960549ormula @ TA,D: $o,E: list @ ( set @ ( list @ ( option @ TA ) ) ),F: list @ nat] :
( ( monito518325957Exists @ TA @ A )
!= ( monito1987675900_MPrev @ TA @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_mformula_Odistinct_I53_J) ).
thf(348,plain,
! [TA: $tType,A: monito748960549ormula @ TA,B: i,C: monito748960549ormula @ TA,D: $o,E: list @ ( set @ ( list @ ( option @ TA ) ) ),F: list @ nat] :
( ( monito518325957Exists @ TA @ A )
!= ( monito1987675900_MPrev @ TA @ B @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_nat_Oinject) ).
thf(806,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__SucI) ).
thf(905,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(121,axiom,
semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_15) ).
thf(634,plain,
semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ 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_178_add__strict__left__mono) ).
thf(734,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ 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)],[155]) ).
thf(268,axiom,
! [TA: $tType,A: list @ TA,B: nat] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( suc @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_length__Suc__conv) ).
thf(1072,plain,
! [TA: $tType,A: list @ TA,B: nat] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( suc @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(283,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_34_old_Onat_Oinducts) ).
thf(1119,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)],[283]) ).
thf(131,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_18) ).
thf(660,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(43,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_verit__sum__simplify) ).
thf(411,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_measure__induct__rule) ).
thf(507,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(90,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(527,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(238,axiom,
! [TA: $tType,A: trm @ TA] :
( ( size_size @ ( trm @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_trm_Osize__neq) ).
thf(981,plain,
! [TA: $tType,A: trm @ TA] :
( ( size_size @ ( trm @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(166,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__gr0) ).
thf(766,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(62,axiom,
! [TA: $tType] : ( size @ ( formula @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_MFOTL_Oformula___Nat_Osize_26) ).
thf(452,plain,
! [TA: $tType] : ( size @ ( formula @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(55,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ ( zero_zero @ int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_plus__int__code_I1_J) ).
thf(439,plain,
! [A: int] :
( ( plus_plus @ int @ A @ ( zero_zero @ int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_int__ops_I5_J) ).
thf(661,plain,
! [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(291,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(1153,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)],[291]) ).
thf(23,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ 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_195_add_Oleft__commute) ).
thf(366,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ 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)],[23]) ).
thf(93,axiom,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( some @ TA @ B ) ) )
= ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__Some__eq) ).
thf(534,plain,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( some @ TA @ B ) ) )
= ( A
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(159,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_24_nat__less__induct) ).
thf(746,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)],[159]) ).
thf(250,axiom,
! [TA: $tType,A: TA > nat,B: monito748960549ormula @ TA] :
( ( monito1197352414ormula @ TA @ A @ ( monito518325957Exists @ TA @ B ) )
= ( plus_plus @ nat @ ( monito1197352414ormula @ TA @ A @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_mformula_Osize__gen_I5_J) ).
thf(1021,plain,
! [TA: $tType,A: TA > nat,B: monito748960549ormula @ TA] :
( ( monito1197352414ormula @ TA @ A @ ( monito518325957Exists @ TA @ B ) )
= ( plus_plus @ nat @ ( monito1197352414ormula @ TA @ A @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(258,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_16) ).
thf(1042,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(198,axiom,
! [TA: $tType] :
( ( '?' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
| ? [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_split__option__ex) ).
thf(862,plain,
! [TA: $tType] :
( ( '?' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
| ? [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Suc__inject) ).
thf(820,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(35,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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_125_add__left__cancel) ).
thf(392,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[35]) ).
thf(48,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(424,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_add__0__iff) ).
thf(407,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(51,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_add_Ogroup__left__neutral) ).
thf(429,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(184,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Zero__neq__Suc) ).
thf(815,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(229,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_of__nat__less__imp__less) ).
thf(957,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(209,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_not__less0) ).
thf(894,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(309,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_61_less__trans__Suc) ).
thf(1217,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)],[309]) ).
thf(110,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_bot__nat__0_Onot__eq__extremum) ).
thf(598,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(215,axiom,
! [TA: $tType,A: TA > nat,B: i,C: monito748960549ormula @ TA,D: $o,E: list @ nat] :
( ( monito1197352414ormula @ TA @ A @ ( monito320348316_MNext @ TA @ B @ C @ D @ E ) )
= ( plus_plus @ nat @ ( monito1197352414ormula @ TA @ A @ C ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_mformula_Osize__gen_I7_J) ).
thf(916,plain,
! [TA: $tType,A: TA > nat,B: i,C: monito748960549ormula @ TA,D: $o,E: list @ nat] :
( ( monito1197352414ormula @ TA @ A @ ( monito320348316_MNext @ TA @ B @ C @ D @ E ) )
= ( plus_plus @ nat @ ( monito1197352414ormula @ TA @ A @ C ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(77,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_group__cancel_Oadd2) ).
thf(484,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(254,axiom,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ nat] :
( ( size_size @ ( monito748960549ormula @ TA ) @ ( monito320348316_MNext @ TA @ A @ B @ C @ D ) )
= ( plus_plus @ nat @ ( size_size @ ( monito748960549ormula @ TA ) @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mformula_Osize_I16_J) ).
thf(1032,plain,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ nat] :
( ( size_size @ ( monito748960549ormula @ TA ) @ ( monito320348316_MNext @ TA @ A @ B @ C @ D ) )
= ( plus_plus @ nat @ ( size_size @ ( monito748960549ormula @ TA ) @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(119,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Euclid__induct) ).
thf(625,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(297,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_208_one__is__add) ).
thf(1178,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)],[297]) ).
thf(293,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ! [C: TA] :
( ( B
= ( plus_plus @ TA @ A @ C ) )
=> ( C
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_canonically__ordered__monoid__add__class_OlessE) ).
thf(1159,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ! [C: TA] :
( ( B
= ( plus_plus @ TA @ A @ C ) )
=> ( C
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(306,axiom,
ordere779506340up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_9) ).
thf(1210,plain,
ordere779506340up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(163,axiom,
! [TA: $tType,A: monito748960549ormula @ TA] :
( ( size_size @ ( monito748960549ormula @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mformula_Osize__neq) ).
thf(757,plain,
! [TA: $tType,A: monito748960549ormula @ TA] :
( ( size_size @ ( monito748960549ormula @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(139,axiom,
( ( nat_triangle @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_triangle__0) ).
thf(682,plain,
( ( nat_triangle @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(65,axiom,
ordere223160158up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(456,plain,
ordere223160158up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(7,axiom,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ ( set @ ( list @ ( option @ TA ) ) ),E: list @ nat,F: i,G: monito748960549ormula @ TA,H: $o,I: list @ nat] :
( ( monito1987675900_MPrev @ TA @ A @ B @ C @ D @ E )
!= ( monito320348316_MNext @ TA @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_mformula_Odistinct_I61_J) ).
thf(324,plain,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ ( set @ ( list @ ( option @ TA ) ) ),E: list @ nat,F: i,G: monito748960549ormula @ TA,H: $o,I: list @ nat] :
( ( monito1987675900_MPrev @ TA @ A @ B @ C @ D @ E )
!= ( monito320348316_MNext @ TA @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(290,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_41_nat__induct) ).
thf(1143,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)],[290]) ).
thf(249,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_72_Suc__lessE) ).
thf(1017,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)],[249]) ).
thf(154,axiom,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_int__if) ).
thf(725,plain,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(39,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_22) ).
thf(403,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(244,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_62_Suc__less__SucD) ).
thf(1006,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)],[244]) ).
thf(108,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_158_add__gr__0) ).
thf(593,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)],[108]) ).
thf(200,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_of__nat__0) ).
thf(869,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(114,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ 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_151_double__add__less__zero__iff__single__add__less__zero) ).
thf(610,plain,
! [TA: $tType] :
( ( linord219039673up_add @ 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)],[114]) ).
thf(205,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_5) ).
thf(884,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(253,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_less__not__refl2) ).
thf(1028,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ 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_152_zero__less__double__add__iff__zero__less__single__add) ).
thf(488,plain,
! [TA: $tType] :
( ( linord219039673up_add @ 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)],[78]) ).
thf(94,axiom,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ ( set @ ( list @ ( option @ TA ) ) ),E: list @ nat] :
( ( size_size @ ( monito748960549ormula @ TA ) @ ( monito1987675900_MPrev @ TA @ A @ B @ C @ D @ E ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( list @ ( set @ ( list @ ( option @ TA ) ) ) ) @ D ) @ ( size_size @ ( monito748960549ormula @ TA ) @ B ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_mformula_Osize_I15_J) ).
thf(537,plain,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ ( set @ ( list @ ( option @ TA ) ) ),E: list @ nat] :
( ( size_size @ ( monito748960549ormula @ TA ) @ ( monito1987675900_MPrev @ TA @ A @ B @ C @ D @ E ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( list @ ( set @ ( list @ ( option @ TA ) ) ) ) @ D ) @ ( size_size @ ( monito748960549ormula @ TA ) @ B ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(96,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_23) ).
thf(547,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(148,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_zero__less__iff__neq__zero) ).
thf(706,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(269,axiom,
strict797366125id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_7) ).
thf(1075,plain,
strict797366125id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(74,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_44_Collect__cong) ).
thf(476,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)],[74]) ).
thf(248,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(1016,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(107,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_gr0I) ).
thf(590,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(118,axiom,
! [TA: $tType,A: TA > nat,B: TA] :
( ( size_option @ TA @ A @ ( some @ TA @ B ) )
= ( plus_plus @ nat @ ( A @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_option_Osize__gen_I2_J) ).
thf(622,plain,
! [TA: $tType,A: TA > nat,B: TA] :
( ( size_option @ TA @ A @ ( some @ TA @ B ) )
= ( plus_plus @ nat @ ( A @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(126,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ 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_203_add__pos__pos) ).
thf(647,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ 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)],[126]) ).
thf(276,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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_150_less__add__same__cancel2) ).
thf(1099,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[276]) ).
thf(146,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_of__nat__less__0__iff) ).
thf(701,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(66,axiom,
! [TA: $tType] : ( size @ ( monito748960549ormula @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Monitor__Mirabelle__pzlrlsievl_Omformula___Nat_Osize_28) ).
thf(457,plain,
! [TA: $tType] : ( size @ ( monito748960549ormula @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(239,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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_148_add__less__same__cancel2) ).
thf(984,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[239]) ).
thf(153,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_nat_Odistinct_I1_J) ).
thf(721,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(104,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_old_Onat_Odistinct_I2_J) ).
thf(569,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(170,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_207_add__is__1) ).
thf(779,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)],[170]) ).
thf(303,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_not__add__less1) ).
thf(1202,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(21,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_double__zero__sym) ).
thf(360,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(130,axiom,
! [TA: $tType,A: TA] :
( ( size_size @ ( option @ TA ) @ ( some @ TA @ A ) )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_option_Osize_I4_J) ).
thf(657,plain,
! [TA: $tType,A: TA] :
( ( size_size @ ( option @ TA ) @ ( some @ TA @ A ) )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(255,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_option_Oexhaust) ).
thf(1035,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(100,axiom,
! [TA: $tType] :
( ( order @ 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_84_lift__Suc__mono__less) ).
thf(558,plain,
! [TA: $tType] :
( ( order @ 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)],[100]) ).
thf(136,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_63_less__antisym) ).
thf(674,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)],[136]) ).
thf(295,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_old_Onat_Odistinct_I1_J) ).
thf(1167,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(227,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_17) ).
thf(953,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(176,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_12) ).
thf(794,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(218,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_reals__Archimedean2) ).
thf(926,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(152,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_less__nat__zero__code) ).
thf(718,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(207,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_less__add__Suc2) ).
thf(888,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(232,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_75_length__induct) ).
thf(965,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)],[232]) ).
thf(49,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0) ).
thf(425,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(86,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_pos__int__cases) ).
thf(513,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(187,axiom,
! [TA: $tType,A: TA > $o,B: list @ TA,C: TA] :
( ( ( find @ TA @ A @ B )
= ( some @ TA @ C ) )
= ( ? [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ D ) )
& ( C
= ( nth @ TA @ B @ D ) )
& ! [E: nat] :
( ( ord_less @ nat @ E @ D )
=> ~ ( A @ ( nth @ TA @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_find__Some__iff) ).
thf(824,plain,
! [TA: $tType,A: TA > $o,B: list @ TA,C: TA] :
( ( ( find @ TA @ A @ B )
= ( some @ TA @ C ) )
= ( ? [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ D ) )
& ( C
= ( nth @ TA @ B @ D ) )
& ! [E: nat] :
( ( ord_less @ nat @ E @ D )
=> ~ ( A @ ( nth @ TA @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(196,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_171_add__Suc__shift) ).
thf(856,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)],[196]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: option @ TB,B: ( option @ TB ) > ( option @ TA ) > $o,C: option @ TA] :
( ( ( A
= ( none @ TB ) )
=> ( B @ A @ C ) )
=> ( ( ( C
= ( none @ TA ) )
=> ( B @ A @ C ) )
=> ( ! [D: TB,E: TA] :
( ( A
= ( some @ TB @ D ) )
=> ( ( C
= ( some @ TA @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_combine__options__cases) ).
thf(573,plain,
! [TA: $tType,TB: $tType,A: option @ TB,B: ( option @ TB ) > ( option @ TA ) > $o,C: option @ TA] :
( ( ( A
= ( none @ TB ) )
=> ( B @ A @ C ) )
=> ( ( ( C
= ( none @ TA ) )
=> ( B @ A @ C ) )
=> ( ! [D: TB,E: TA] :
( ( A
= ( some @ TB @ D ) )
=> ( ( C
= ( some @ TA @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(141,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_213_less__iff__Suc__add) ).
thf(689,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)],[141]) ).
thf(58,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_add_Ocommute) ).
thf(444,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(111,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_linorder__neqE__linordered__idom) ).
thf(601,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(185,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_8) ).
thf(819,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(236,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_143_nat__add__left__cancel__less) ).
thf(975,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)],[236]) ).
thf(143,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_less__imp__of__nat__less) ).
thf(694,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(193,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: list @ TA] :
( ( ( A @ B )
=> ( ( find @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( some @ TA @ B ) ) )
& ( ~ ( A @ B )
=> ( ( find @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( find @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_find_Osimps_I2_J) ).
thf(843,plain,
! [TA: $tType,A: TA > $o,B: TA,C: list @ TA] :
( ( ( A @ B )
=> ( ( find @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( some @ TA @ B ) ) )
& ( ~ ( A @ B )
=> ( ( find @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( find @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(168,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_64_Suc__less__eq2) ).
thf(772,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)],[168]) ).
thf(158,axiom,
! [TA: $tType] :
( ( '!' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
& ! [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_split__option__all) ).
thf(743,plain,
! [TA: $tType] :
( ( '!' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
& ! [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mem__Collect__eq) ).
thf(875,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(124,axiom,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( gen_length @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( gen_length @ TA @ ( suc @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_gen__length__code_I2_J) ).
thf(641,plain,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( gen_length @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( gen_length @ TA @ ( suc @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(289,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ 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_181_add__mono__thms__linordered__field_I2_J) ).
thf(1139,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ 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)],[289]) ).
thf(223,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_60_less__Suc__induct) ).
thf(936,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)],[223]) ).
thf(30,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(382,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
( ( ( size_size @ ( list @ ( option @ b ) ) @ ( cons @ ( option @ b ) @ ( some @ b @ x ) @ v ) )
= ( suc @ n ) )
& ! [A: nat] :
( ~ ( ord_less @ nat @ A @ ( suc @ n ) )
| ( ( ( nth @ ( option @ b ) @ ( cons @ ( option @ b ) @ ( some @ b @ x ) @ v ) @ A )
= ( none @ b ) )
= ( ~ ( member @ nat @ A @ ( fvi @ a @ b2 @ phi ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( ( ( size_size @ ( list @ ( option @ b ) ) @ ( cons @ ( option @ b ) @ ( some @ b @ x ) @ v ) )
= ( suc @ n ) )
& ! [A: nat] :
( ~ ( ord_less @ nat @ A @ ( suc @ n ) )
| ( ( ( nth @ ( option @ b ) @ ( cons @ ( option @ b ) @ ( some @ b @ x ) @ v ) @ A )
= ( none @ b ) )
= ( ~ ( member @ nat @ A @ ( fvi @ a @ b2 @ phi ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(313,plain,
~ ( ( ( size_size @ ( list @ ( option @ b ) ) @ ( cons @ ( option @ b ) @ ( some @ b @ x ) @ v ) )
= ( suc @ n ) )
& ! [A: nat] :
( ~ ( ord_less @ nat @ A @ ( suc @ n ) )
| ( ( ( nth @ ( option @ b ) @ ( cons @ ( option @ b ) @ ( some @ b @ x ) @ v ) @ A )
= ( none @ b ) )
= ( ~ ( member @ nat @ A @ ( fvi @ a @ b2 @ phi ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(173,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_not__less__zero) ).
thf(787,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(70,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_add__cancel__left__right) ).
thf(466,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(335,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(216,axiom,
! [TA: $tType] :
( ( gen_length @ TA )
= ( ^ [A: nat,B: list @ TA] : ( plus_plus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_gen__length__def) ).
thf(919,plain,
! [TA: $tType] :
( ( gen_length @ TA )
= ( ^ [A: nat,B: list @ TA] : ( plus_plus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(95,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_50_infinite__descent0__measure) ).
thf(540,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)],[95]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( cons @ TA @ A @ B ) )
= ( suc @ ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_length__Cons) ).
thf(604,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( cons @ TA @ A @ B ) )
= ( suc @ ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(246,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Collect__mem__eq) ).
thf(1011,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nat_OdiscI) ).
thf(736,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(61,axiom,
cancel1352612707id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(451,plain,
cancel1352612707id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(3,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(318,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(116,axiom,
! [TA: $tType,A: formula @ TA] :
( ( size_size @ ( formula @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_formula_Osize__neq) ).
thf(616,plain,
! [TA: $tType,A: formula @ TA] :
( ( size_size @ ( formula @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(28,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_nat__int__comparison_I1_J) ).
thf(377,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(241,axiom,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_less__int__code_I1_J) ).
thf(990,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(127,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_gr0__implies__Suc) ).
thf(649,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(259,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ A @ B ) )
= ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_of__nat__add) ).
thf(1043,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ A @ B ) )
= ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(208,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_old_Onat_Oexhaust) ).
thf(890,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(33,axiom,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ nat,E: i,F: monito748960549ormula @ TA,G: $o,H: list @ nat] :
( ( ( monito320348316_MNext @ TA @ A @ B @ C @ D )
= ( monito320348316_MNext @ TA @ E @ F @ G @ H ) )
= ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_mformula_Oinject_I7_J) ).
thf(387,plain,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ nat,E: i,F: monito748960549ormula @ TA,G: $o,H: list @ nat] :
( ( ( monito320348316_MNext @ TA @ A @ B @ C @ D )
= ( monito320348316_MNext @ TA @ E @ F @ G @ H ) )
= ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(120,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: nat] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( drop @ TA @ A @ B ) @ C )
= ( nth @ TA @ B @ ( plus_plus @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_nth__drop) ).
thf(631,plain,
! [TA: $tType,A: nat,B: list @ TA,C: nat] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( drop @ TA @ A @ B ) @ C )
= ( nth @ TA @ B @ ( plus_plus @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(167,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_less__Suc0) ).
thf(769,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(224,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_29_nat__neq__iff) ).
thf(943,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)],[224]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(330,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(280,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_not__add__less2) ).
thf(1112,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(80,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_bot__nat__0_Oextremum__strict) ).
thf(494,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__not__refl3) ).
thf(1080,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(15,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_add_Oright__neutral) ).
thf(345,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(98,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( gen_length @ TA @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_length__code) ).
thf(552,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( gen_length @ TA @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(194,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_23_infinite__descent) ).
thf(848,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)],[194]) ).
thf(88,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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_139_add__less__cancel__left) ).
thf(520,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[88]) ).
thf(68,axiom,
! [TA: $tType] :
( ( group_add @ 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_193_add_Oright__cancel) ).
thf(462,plain,
! [TA: $tType] :
( ( group_add @ 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)],[68]) ).
thf(221,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_less__numeral__extra_I3_J) ).
thf(932,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(296,axiom,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_dependent__nat__choice) ).
thf(1171,plain,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(37,axiom,
strict2144017051up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(399,plain,
strict2144017051up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(230,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_add__eq__self__zero) ).
thf(959,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(64,axiom,
ordere216010020id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__comm__monoid__add) ).
thf(455,plain,
ordere216010020id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(277,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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_149_less__add__same__cancel1) ).
thf(1102,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[277]) ).
thf(217,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_zero__less__imp__eq__int) ).
thf(922,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(308,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_209_less__imp__add__positive) ).
thf(1213,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)],[308]) ).
thf(188,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_lessI) ).
thf(827,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(270,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_11) ).
thf(1076,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(50,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(426,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(92,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( semiring_1_of_nat @ TA @ ( suc @ A ) )
!= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_of__nat__neq__0) ).
thf(531,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( semiring_1_of_nat @ TA @ ( suc @ A ) )
!= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(287,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ 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_177_add__strict__right__mono) ).
thf(1134,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ 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)],[287]) ).
thf(183,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_not__Cons__self2) ).
thf(812,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(162,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Nat_Oadd__0__right) ).
thf(754,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(261,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( drop @ TA @ A @ ( drop @ TA @ B @ C ) )
= ( drop @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_drop__drop) ).
thf(1049,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( drop @ TA @ A @ ( drop @ TA @ B @ C ) )
= ( drop @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(305,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_nat__int__comparison_I2_J) ).
thf(1208,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(106,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(589,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Suc__lessD) ).
thf(795,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(138,axiom,
! [TA: $tType] : ( size @ ( option @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Nat_Osize_27) ).
thf(680,plain,
! [TA: $tType] : ( size @ ( option @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(233,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_6) ).
thf(968,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(298,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_21_infinite__descent__measure) ).
thf(1181,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)],[298]) ).
thf(150,axiom,
! [A: nat] :
( ( nat_triangle @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_triangle @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_triangle__Suc) ).
thf(712,plain,
! [A: nat] :
( ( nat_triangle @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_triangle @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(252,axiom,
! [TA: $tType,A: monito748960549ormula @ TA] :
( ( size_size @ ( monito748960549ormula @ TA ) @ ( monito518325957Exists @ TA @ A ) )
= ( plus_plus @ nat @ ( size_size @ ( monito748960549ormula @ TA ) @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_mformula_Osize_I14_J) ).
thf(1025,plain,
! [TA: $tType,A: monito748960549ormula @ TA] :
( ( size_size @ ( monito748960549ormula @ TA ) @ ( monito518325957Exists @ TA @ A ) )
= ( plus_plus @ nat @ ( size_size @ ( monito748960549ormula @ TA ) @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(201,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( cons @ TA @ ( nth @ TA @ B @ A ) @ ( drop @ TA @ ( suc @ A ) @ B ) )
= ( drop @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Cons__nth__drop__Suc) ).
thf(872,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( cons @ TA @ ( nth @ TA @ B @ A ) @ ( drop @ TA @ ( suc @ A ) @ B ) )
= ( drop @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(292,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: list @ TA] :
( ( list_ex @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( A @ B )
| ( list_ex @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_list__ex__simps_I1_J) ).
thf(1156,plain,
! [TA: $tType,A: TA > $o,B: TA,C: list @ TA] :
( ( list_ex @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( A @ B )
| ( list_ex @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(44,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(414,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(8,axiom,
! [TA: $tType,A: monito748960549ormula @ TA,B: i,C: monito748960549ormula @ TA,D: $o,E: list @ nat] :
( ( monito518325957Exists @ TA @ A )
!= ( monito320348316_MNext @ TA @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_mformula_Odistinct_I55_J) ).
thf(327,plain,
! [TA: $tType,A: monito748960549ormula @ TA,B: i,C: monito748960549ormula @ TA,D: $o,E: list @ nat] :
( ( monito518325957Exists @ TA @ A )
!= ( monito320348316_MNext @ TA @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(228,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( ? [B: TA] :
( A
= ( some @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_not__None__eq) ).
thf(954,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( ? [B: TA] :
( A
= ( some @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_of__nat__less__iff) ).
thf(791,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(300,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nth__equalityI) ).
thf(1188,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(192,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Ex__list__of__length) ).
thf(840,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(12,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_double__zero) ).
thf(338,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(359,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(285,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
| ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_add__less__zeroD) ).
thf(1130,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
| ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(310,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_14) ).
thf(1220,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(214,axiom,
! [A: nat > $o] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_exists__least__lemma) ).
thf(907,plain,
! [A: nat > $o] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(256,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_not__gr__zero) ).
thf(1038,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(25,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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_126_add__right__cancel) ).
thf(370,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[25]) ).
thf(147,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( suc @ A )
= ( size_size @ ( list @ TA ) @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Suc__length__conv) ).
thf(703,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( suc @ A )
= ( size_size @ ( list @ TA ) @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(115,axiom,
! [TA: $tType] :
( ( order @ 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_83_lift__Suc__mono__less__iff) ).
thf(613,plain,
! [TA: $tType] :
( ( order @ 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)],[115]) ).
thf(311,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_52_infinite__descent0) ).
thf(1221,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)],[311]) ).
thf(262,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_40_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)],[262]) ).
thf(245,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( cons @ TA @ A @ B ) )
= ( plus_plus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_list_Osize_I4_J) ).
thf(1008,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( cons @ TA @ A @ B ) )
= ( plus_plus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(81,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_161_less__add__eq__less) ).
thf(497,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)],[81]) ).
thf(197,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list_Oinject) ).
thf(859,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(274,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_2) ).
thf(1094,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(237,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_58_not__less__less__Suc__eq) ).
thf(978,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)],[237]) ).
thf(69,axiom,
linord1659791738miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(465,plain,
linord1659791738miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(22,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add__cancel__right__left) ).
thf(363,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(220,axiom,
ordere216010020id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_10) ).
thf(931,plain,
ordere216010020id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(76,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_21) ).
thf(482,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(279,axiom,
! [A: nat,B: nat,C: nat] :
( ( A
= ( plus_plus @ nat @ B @ C ) )
=> ( ( suc @ A )
= ( plus_plus @ nat @ B @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_nat__arith_Osuc1) ).
thf(1108,plain,
! [A: nat,B: nat,C: nat] :
( ( A
= ( plus_plus @ nat @ B @ C ) )
=> ( ( suc @ A )
= ( plus_plus @ nat @ B @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(60,axiom,
semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add) ).
thf(450,plain,
semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(273,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_39_zero__induct) ).
thf(1084,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)],[273]) ).
thf(87,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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_138_add__less__cancel__right) ).
thf(517,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[87]) ).
thf(4,axiom,
order @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_1) ).
thf(319,plain,
order @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(265,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_214_less__imp__Suc__add) ).
thf(1062,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)],[265]) ).
thf(225,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_22_linorder__neqE__nat) ).
thf(946,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)],[225]) ).
thf(34,axiom,
! [TA: $tType] : ( size @ ( trm @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_MFOTL_Otrm___Nat_Osize_24) ).
thf(390,plain,
! [TA: $tType] : ( size @ ( trm @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_int__int__eq) ).
thf(418,plain,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(243,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_59_strict__inc__induct) ).
thf(995,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)],[243]) ).
thf(128,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_70_less__SucE) ).
thf(652,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)],[128]) ).
thf(17,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ 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_187_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(351,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ 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)],[17]) ).
thf(103,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_13) ).
thf(568,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(134,axiom,
! [TA: $tType,A: option @ TA] :
( ( size_size @ ( option @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_option_Osize__neq) ).
thf(667,plain,
! [TA: $tType,A: option @ TA] :
( ( size_size @ ( option @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(301,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Suc__neq__Zero) ).
thf(1193,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(271,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(1077,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(165,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_8_Suc__less__eq) ).
thf(763,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)],[165]) ).
thf(31,axiom,
order @ i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Interval_O_092_060I_062___Orderings_Oorder_25) ).
thf(383,plain,
order @ i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(211,axiom,
! [TA: $tType] :
( ( drop @ TA @ ( zero_zero @ nat ) )
= ( ^ [A: list @ TA] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_drop0) ).
thf(899,plain,
! [TA: $tType] :
( ( drop @ TA @ ( zero_zero @ nat ) )
= ( ^ [A: list @ TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(97,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_169_add__Suc) ).
thf(549,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)],[97]) ).
thf(179,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_of__nat__eq__0__iff) ).
thf(800,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(53,axiom,
! [A: int] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_plus__int__code_I2_J) ).
thf(433,plain,
! [A: int] :
( ( plus_plus @ int @ ( zero_zero @ int ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(85,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nth__Cons__0) ).
thf(510,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(190,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_neq0__conv) ).
thf(832,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(140,axiom,
! [TA: $tType,A: ( option @ TA ) > $o,B: option @ TA] :
( ( A @ ( none @ TA ) )
=> ( ! [C: TA] : ( A @ ( some @ TA @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_option_Oinducts) ).
thf(684,plain,
! [TA: $tType,A: ( option @ TA ) > $o,B: option @ TA] :
( ( A @ ( none @ TA ) )
=> ( ! [C: TA] : ( A @ ( some @ TA @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(282,axiom,
! [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_int__plus) ).
thf(1116,plain,
! [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ A @ B ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(161,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ 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_202_add__neg__neg) ).
thf(752,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ 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)],[161]) ).
thf(59,axiom,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ ( set @ ( list @ ( option @ TA ) ) ),E: list @ nat,F: i,G: monito748960549ormula @ TA,H: $o,I: list @ ( set @ ( list @ ( option @ TA ) ) ),J: list @ nat] :
( ( ( monito1987675900_MPrev @ TA @ A @ B @ C @ D @ E )
= ( monito1987675900_MPrev @ TA @ F @ G @ H @ I @ J ) )
= ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_mformula_Oinject_I6_J) ).
thf(447,plain,
! [TA: $tType,A: i,B: monito748960549ormula @ TA,C: $o,D: list @ ( set @ ( list @ ( option @ TA ) ) ),E: list @ nat,F: i,G: monito748960549ormula @ TA,H: $o,I: list @ ( set @ ( list @ ( option @ TA ) ) ),J: list @ nat] :
( ( ( monito1987675900_MPrev @ TA @ A @ B @ C @ D @ E )
= ( monito1987675900_MPrev @ TA @ F @ G @ H @ I @ J ) )
= ( ( A = F )
& ( B = G )
& ( C = H )
& ( D = I )
& ( E = J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(52,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(432,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(42,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add) ).
thf(410,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(191,axiom,
( ( ( size_size @ ( list @ ( option @ b ) ) @ v )
= n )
& ! [A: nat] :
( ( ord_less @ nat @ A @ n )
=> ( ( ( nth @ ( option @ b ) @ v @ A )
= ( none @ b ) )
= ( ~ ( member @ nat @ A @ ( fvi @ a @ ( suc @ b2 ) @ phi ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(835,plain,
( ( ( size_size @ ( list @ ( option @ b ) ) @ v )
= n )
& ! [A: nat] :
( ( ord_less @ nat @ A @ n )
=> ( ( ( nth @ ( option @ b ) @ v @ A )
= ( none @ b ) )
= ( ~ ( member @ nat @ A @ ( fvi @ a @ ( suc @ b2 ) @ phi ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(199,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n__not__Suc__n) ).
thf(865,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(26,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ 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_129_add__eq__0__iff__both__eq__0) ).
thf(373,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ 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)],[26]) ).
thf(102,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_gr__implies__not__zero) ).
thf(564,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(13,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_add_Oleft__neutral) ).
thf(341,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
strict797366125id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ostrict__ordered__comm__monoid__add) ).
thf(358,plain,
strict797366125id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(210,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_168_add__lessD1) ).
thf(897,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)],[210]) ).
thf(122,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_142_add__Suc__right) ).
thf(635,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)],[122]) ).
thf(266,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_list__decode_Ocases) ).
thf(1065,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(144,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ 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_182_add__mono__thms__linordered__field_I5_J) ).
thf(696,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ 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)],[144]) ).
thf(263,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Ex__less__Suc2) ).
thf(1056,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(133,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: TA,D: list @ TA] :
( ( ( drop @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( nth @ TA @ B @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_nth__via__drop) ).
thf(664,plain,
! [TA: $tType,A: nat,B: list @ TA,C: TA,D: list @ TA] :
( ( ( drop @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( nth @ TA @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(38,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_of__nat__eq__iff) ).
thf(400,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(302,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_74_Nat_OlessE) ).
thf(1197,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)],[302]) ).
thf(219,axiom,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( drop @ TA @ ( suc @ A ) @ ( cons @ TA @ B @ C ) )
= ( drop @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_drop__Suc__Cons) ).
thf(928,plain,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( drop @ TA @ ( suc @ A ) @ ( cons @ TA @ B @ C ) )
= ( drop @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(45,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_add__cancel__left__left) ).
thf(415,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(36,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ 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_188_add__mono__thms__linordered__semiring_I4_J) ).
thf(395,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ 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)],[36]) ).
thf(240,axiom,
! [TA: $tType,A: nat,B: formula @ TA,C: nat] :
( ! [D: nat] :
( ( member @ nat @ D @ ( fvi @ TA @ ( suc @ A ) @ B ) )
=> ( ord_less @ nat @ D @ C ) )
=> ! [D: nat] :
( ( member @ nat @ D @ ( fvi @ TA @ A @ B ) )
=> ( ord_less @ nat @ D @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_fvi__Suc__bound) ).
thf(987,plain,
! [TA: $tType,A: nat,B: formula @ TA,C: nat] :
( ! [D: nat] :
( ( member @ nat @ D @ ( fvi @ TA @ ( suc @ A ) @ B ) )
=> ( ord_less @ nat @ D @ C ) )
=> ! [D: nat] :
( ( member @ nat @ D @ ( fvi @ TA @ A @ B ) )
=> ( ord_less @ nat @ D @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(109,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_7_Suc__mono) ).
thf(596,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)],[109]) ).
thf(91,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_163_trans__less__add1) ).
thf(528,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)],[91]) ).
thf(125,axiom,
! [TA: $tType,A: list @ TA] :
( ( drop @ TA @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_drop__0) ).
thf(644,plain,
! [TA: $tType,A: list @ TA] :
( ( drop @ TA @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(67,axiom,
! [TA: $tType] :
( ( neg_numeral @ 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_160_is__num__normalize_I1_J) ).
thf(459,plain,
! [TA: $tType] :
( ( neg_numeral @ 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)],[67]) ).
thf(242,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_gr0__conv__Suc) ).
thf(992,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(142,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_less__irrefl__nat) ).
thf(691,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(56,axiom,
ordere516151231imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(442,plain,
ordere516151231imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(82,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_All__less__Suc) ).
thf(501,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(10,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_zero__eq__add__iff__both__eq__0) ).
thf(332,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(284,axiom,
ordere516151231imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_3) ).
thf(1129,plain,
ordere516151231imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(24,axiom,
neg_numeral @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Oneg__numeral) ).
thf(369,plain,
neg_numeral @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(113,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_gr__zeroI) ).
thf(607,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(180,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_list__eq__iff__nth__eq) ).
thf(803,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(71,axiom,
! [TA: $tType] :
( ( semigroup_add @ 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_191_add_Oassoc) ).
thf(469,plain,
! [TA: $tType] :
( ( semigroup_add @ 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)],[71]) ).
thf(18,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_group__cancel_Oadd1) ).
thf(354,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(299,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_field__lbound__gt__zero) ).
thf(1184,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(79,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_less__not__refl) ).
thf(491,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(204,axiom,
( ( ord_less @ int )
= ( ^ [A: int,B: int] :
? [C: nat] :
( B
= ( plus_plus @ int @ A @ ( semiring_1_of_nat @ int @ ( suc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_zless__iff__Suc__zadd) ).
thf(882,plain,
( ( ord_less @ int )
= ( ^ [A: int,B: int] :
? [C: nat] :
( B
= ( plus_plus @ int @ A @ ( semiring_1_of_nat @ int @ ( suc @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_gr__implies__not0) ).
thf(775,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(101,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_size__neq__size__imp__neq) ).
thf(560,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(63,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(454,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(267,axiom,
! [TA: $tType] :
( ( size_size @ ( option @ TA ) @ ( none @ TA ) )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_option_Osize_I3_J) ).
thf(1069,plain,
! [TA: $tType] :
( ( size_size @ ( option @ TA ) @ ( none @ TA ) )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(247,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_int__ops_I1_J) ).
thf(1014,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_old_Onat_Oinject) ).
thf(972,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1240,plain,
$false,
inference(cvc4,[status(thm)],[809,1024,760,1237,962,555,479,1105,1211,523,741,1205,379,677,1041,878,655,384,715,472,698,670,1164,797,782,709,320,436,829,1095,404,885,1046,785,504,619,751,344,934,949,1059,1132,902,421,969,1115,638,853,475,789,443,321,376,1136,348,806,905,634,734,1072,1119,660,411,507,527,981,766,452,439,661,1153,366,534,746,1021,1042,862,820,392,424,407,429,815,957,894,1217,598,916,484,1032,625,1178,1159,1210,757,682,456,324,1143,1017,725,403,1006,593,869,610,884,1028,488,537,547,706,1075,476,1016,590,622,647,1099,701,457,984,721,569,779,1202,360,657,1035,558,674,1167,953,794,926,718,888,965,425,513,824,856,573,689,444,601,819,975,694,843,772,743,875,641,1139,936,382,313,787,466,335,919,540,604,1011,736,451,318,616,377,990,649,1043,890,387,631,769,943,330,1112,494,1080,345,552,848,520,462,932,1171,399,959,455,1102,922,1213,827,1076,426,531,1134,812,754,1049,1208,589,795,680,968,1181,712,1025,872,1156,414,327,954,791,1188,840,338,359,1130,1220,907,1038,370,703,613,1221,1052,1008,497,859,1094,978,465,363,931,482,1108,450,1084,517,319,1062,946,390,418,995,652,351,568,667,1193,1077,763,383,899,549,800,433,510,832,684,1116,752,447,432,410,835,865,373,564,341,358,897,635,1065,696,1056,664,400,1197,928,415,395,987,596,528,644,459,992,691,442,501,332,1129,369,607,803,469,354,1184,491,882,775,560,454,1069,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ITP126^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 18:31:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.03/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.97/1.35 % [INFO] Parsing done (364ms).
% 2.18/1.36 % [INFO] Running in sequential loop mode.
% 3.16/1.73 % [INFO] eprover registered as external prover.
% 3.16/1.73 % [INFO] cvc4 registered as external prover.
% 3.16/1.74 % [INFO] Scanning for conjecture ...
% 3.51/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 311 axioms. Running axiom selection ...
% 3.87/2.03 % [INFO] Axiom selection finished. Selected 310 axioms (removed 1 axioms).
% 4.85/2.24 % [INFO] Problem is higher-order (TPTP THF).
% 4.85/2.26 % [INFO] Type checking passed.
% 4.85/2.26 % [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 ...
% 78.78/38.07 % External prover 'cvc4' found a proof!
% 78.78/38.07 % [INFO] Killing All external provers ...
% 78.78/38.08 % Time passed: 37577ms (effective reasoning time: 36710ms)
% 78.78/38.08 % 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)>
% 78.78/38.08 % Axioms used in derivation (310): fact_207_add__is__1, fact_46_nat_OdiscI, fact_216_list_Osize_I4_J, tcon_Monitor__Mirabelle__pzlrlsievl_Omformula___Nat_Osize_28, fact_68_Ex__less__Suc, fact_231_nat__int__comparison_I1_J, fact_219_pos__int__cases, fact_96_fvi__Suc__bound, fact_142_add__Suc__right, fact_71_Suc__lessI, fact_93_Skolem__list__nth, fact_174_drop__0, tcon_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_171_add__Suc__shift, fact_144_drop0, fact_159_drop__Suc__Cons, fact_85_less__Suc__eq__0__disj, tcon_Nat_Onat___Groups_Oab__semigroup__add_13, fact_238_triangle__0, tcon_Nat_Onat___Nat_Osize, fact_128_zero__eq__add__iff__both__eq__0, fact_206_nth__via__drop, fact_37_Zero__neq__Suc, fact_94_nth__equalityI, fact_209_less__imp__add__positive, tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add, fact_244_mformula_Osize__gen_I7_J, fact_24_nat__less__induct, fact_76_combine__options__cases, fact_81_option_OdiscI, fact_80_option_Oexhaust, fact_129_add__eq__0__iff__both__eq__0, fact_246_mformula_Oinject_I5_J, tcon_Int_Oint___Groups_Ozero, fact_169_add__Suc, fact_0_nth__Cons__Suc, fact_5_not__Some__eq, fact_224_plus__int__code_I1_J, tcon_MFOTL_Oformula___Nat_Osize_26, fact_54_less__zeroE, fact_53_gr__implies__not0, tcon_Interval_O_092_060I_062___Orderings_Oorder_25, fact_16_measure__induct__rule, fact_184_add_Ocomm__neutral, fact_195_add_Oleft__commute, fact_90_length__Suc__conv, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_5, fact_9_neq0__conv, fact_39_zero__induct, fact_84_lift__Suc__mono__less, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_10, fact_208_one__is__add, fact_201_of__nat__less__imp__less, fact_10_less__nat__zero__code, tcon_Nat_Onat___Groups_Ozero_20, fact_177_add__strict__right__mono, fact_167_add__less__mono, fact_139_add__less__cancel__left, fact_127_of__nat__eq__iff, fact_23_infinite__descent, fact_27_less__not__refl2, fact_214_less__imp__Suc__add, fact_19_n__not__Suc__n, fact_88_gr0__conv__Suc, fact_162_trans__less__add2, fact_136_add_Oright__neutral, fact_189_group__cancel_Oadd1, fact_187_ab__semigroup__add__class_Oadd__ac_I1_J, fact_197_add__right__imp__eq, fact_14_nat_Oinject, fact_186_reals__Archimedean2, fact_69_less__SucI, fact_92_list__eq__iff__nth__eq, fact_192_add_Oleft__cancel, fact_217_add__less__zeroD, fact_239_mformula_Osize_I15_J, fact_149_less__add__same__cancel1, fact_212_less__add__Suc2, fact_155_of__nat__eq__0__iff, fact_104_dependent__nat__choice, fact_191_add_Oassoc, tcon_Int_Oint___Groups_Oordered__comm__monoid__add, fact_196_add__left__imp__eq, fact_202_add__neg__neg, fact_204_canonically__ordered__monoid__add__class_OlessE, fact_30_size__neq__size__imp__neq, fact_55_not__less0, fact_225_zless__iff__Suc__zadd, fact_156_of__nat__less__iff, tcon_Int_Oint___Groups_Ocancel__semigroup__add, fact_3_zero__less__Suc, fact_138_add__less__cancel__right, fact_241_mformula_Oinject_I6_J, fact_109_zero__reorient, fact_15_option_Oinject, fact_99_fvi__Suc, tcon_Int_Oint___Groups_Omonoid__add, tcon_Int_Oint___Orderings_Oorder_1, fact_41_nat__induct, fact_73_Suc__lessD, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_6, tcon_Int_Oint___Groups_Osemigroup__add, fact_215_gen__length__def, fact_117_less__numeral__extra_I3_J, tcon_Int_Oint___Groups_Oab__semigroup__add, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_7, tcon_HOL_Obool___Orderings_Oorder_22, tcon_Nat_Onat___Groups_Osemigroup__add_15, fact_131_add__cancel__right__left, fact_12_list_Oinject, fact_130_add__cancel__right__right, fact_163_trans__less__add1, fact_106_trm_Osize__neq, fact_52_infinite__descent0, fact_235_int__plus, fact_33_not0__implies__Suc, fact_44_Collect__cong, fact_133_add__cancel__left__left, fact_89_Ex__less__Suc2, fact_111_gr__zeroI, fact_32_Ex__list__of__length, fact_181_add__mono__thms__linordered__field_I2_J, fact_74_Nat_OlessE, fact_26_less__not__refl3, fact_124_of__nat__0__less__iff, help_If_1_1_T, fact_122_Cons__nth__drop__Suc, fact_123_list__ex__length, fact_79_option_Oinducts, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_9, fact_56_not__gr0, fact_105_formula_Osize__neq, fact_226_less__int__code_I1_J, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, fact_194_add_Ocommute, fact_112_not__less__zero, tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_83_lift__Suc__mono__less__iff, fact_121_option_Osize__gen_I2_J, fact_151_double__add__less__zero__iff__single__add__less__zero, fact_114_zero__less__iff__neq__zero, fact_211_less__add__Suc1, fact_66_not__less__eq, fact_120_gen__length__code_I2_J, tcon_MFOTL_Otrm___Nat_Osize_24, fact_102_find__Some__iff, fact_145_drop__drop, tcon_Int_Oint___Rings_Olinordered__idom, fact_8_Suc__less__eq, fact_86_gr0__implies__Suc, fact_4_not__None__eq, fact_59_strict__inc__induct, tcon_Nat_Onat___Orderings_Owellorder, fact_7_Suc__mono, fact_60_less__Suc__induct, fact_178_add__strict__left__mono, fact_98_option_Osize__gen_I1_J, fact_249_mformula_Osize__gen_I5_J, fact_61_less__trans__Suc, fact_140_add__is__0, fact_242_mformula_Oinject_I7_J, fact_232_int__if, fact_166_not__add__less1, fact_17_measure__induct, fact_175_add__less__imp__less__right, fact_218_Euclid__induct, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_4, tcon_Nat_Onat___Nat_Osemiring__char__0_16, tcon_List_Olist___Nat_Osize_23, fact_240_mformula_Osize_I16_J, fact_150_less__add__same__cancel2, fact_126_add__right__cancel, fact_64_Suc__less__eq2, fact_223_plus__int__code_I2_J, fact_25_less__irrefl__nat, fact_75_length__induct, fact_62_Suc__less__SucD, fact_152_zero__less__double__add__iff__zero__less__single__add, fact_108_option_Osize__neq, fact_43_Collect__mem__eq, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, fact_172_add__eq__self__zero, tcon_Option_Ooption___Nat_Osize_27, fact_193_add_Oright__cancel, tcon_Int_Oint___Rings_Osemiring__1, fact_157_of__nat__add, fact_248_mformula_Odistinct_I55_J, fact_18_not__Cons__self2, tcon_Int_Oint___Groups_Ocomm__monoid__add, fact_134_double__zero__sym, fact_35_old_Onat_Oexhaust, fact_29_nat__neq__iff, fact_143_nat__add__left__cancel__less, fact_91_Suc__length__conv, fact_78_split__option__ex, fact_77_split__option__all, fact_135_double__zero, fact_168_add__lessD1, fact_119_length__code, tcon_Int_Oint___Groups_Ogroup__add, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_11, fact_243_mformula_Odistinct_I61_J, fact_22_linorder__neqE__nat, fact_179_add__strict__mono, fact_36_Zero__not__Suc, fact_227_linorder__neqE__linordered__idom, fact_229_int__ops_I1_J, help_If_3_1_T, fact_13_old_Onat_Oinject, fact_228_nat__int__comparison_I2_J, help_If_2_1_T, fact_158_add__gr__0, fact_147_add__less__same__cancel1, tcon_Int_Oint___Num_Oneg__numeral, fact_82_option_Odistinct_I1_J, fact_110_find_Osimps_I2_J, fact_118_field__lbound__gt__zero, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_8, fact_72_Suc__lessE, fact_222_int__int__eq, fact_176_add__less__imp__less__left, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_3, fact_230_verit__comp__simplify1_I1_J, fact_1_nth__Cons__0, fact_173_plus__nat_Oadd__0, fact_234_int__ops_I5_J, tcon_Int_Oint___Groups_Olinordered__ab__group__add, fact_164_add__less__mono1, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_49_nat_Odistinct_I1_J, tcon_Set_Oset___Orderings_Oorder_21, fact_70_less__SucE, fact_21_infinite__descent__measure, fact_97_length__Cons, fact_100_option_Osize_I4_J, fact_51_bot__nat__0_Oextremum__strict, fact_20_Suc__inject, fact_58_not__less__less__Suc__eq, fact_190_group__cancel_Oadd2, conj_1, fact_11_bot__nat__0_Onot__eq__extremum, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_2, fact_95_not__gr__zero, fact_57_gr0I, fact_65_All__less__Suc, fact_185_comm__monoid__add__class_Oadd__0, fact_87_All__less__Suc2, fact_141_Nat_Oadd__0__right, fact_237_add__0__iff, fact_47_old_Onat_Odistinct_I1_J, tcon_Nat_Onat___Groups_Ocomm__monoid__add_14, fact_251_nth__drop, tcon_Nat_Onat___Rings_Osemiring__1_18, fact_233_verit__sum__simplify, tcon_Int_Oint___Nat_Osemiring__char__0, fact_63_less__antisym, fact_247_mformula_Odistinct_I53_J, fact_146_list__ex__simps_I1_J, fact_113_gr__implies__not__zero, tcon_fun___Orderings_Oorder, fact_40_diff__induct, fact_2_less__Suc0, fact_182_add__mono__thms__linordered__field_I5_J, fact_183_add_Ogroup__left__neutral, fact_137_add_Oleft__neutral, fact_50_infinite__descent0__measure, fact_116_list__decode_Ocases, fact_148_add__less__same__cancel2, fact_213_less__iff__Suc__add, fact_154_of__nat__0__eq__iff, fact_125_add__left__cancel, fact_31_neq__if__length__neq, fact_107_mformula_Osize__neq, fact_180_add__mono__thms__linordered__field_I1_J, fact_221_zadd__int__left, fact_153_of__nat__0, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_28_less__not__refl, fact_210_less__natE, fact_67_less__Suc__eq, fact_38_Suc__neq__Zero, fact_250_formula_Osize_I11_J, fact_6_lessI, tcon_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add, fact_160_is__num__normalize_I1_J, fact_199_of__nat__neq__0, fact_42_mem__Collect__eq, fact_236_triangle__Suc, fact_220_zero__less__imp__eq__int, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_12, fact_198_of__nat__less__0__iff, fact_132_add__cancel__left__right, fact_101_option_Osize_I3_J, tcon_Nat_Onat___Orderings_Oorder_19, fact_48_old_Onat_Odistinct_I2_J, conj_0, fact_203_add__pos__pos, fact_205_pos__add__strict, tcon_Nat_Onat___Groups_Omonoid__add_17, fact_103_exists__least__lemma, fact_165_not__add__less2, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, fact_188_add__mono__thms__linordered__semiring_I4_J, tcon_Int_Oint___Groups_Ostrict__ordered__comm__monoid__add, fact_245_mformula_Osize_I14_J, fact_200_less__imp__of__nat__less, fact_115_BNF__Greatest__Fixpoint_Oshift__def, fact_34_old_Onat_Oinducts, fact_161_less__add__eq__less, fact_170_nat__arith_Osuc1
% 78.78/38.08 % No. of inferences in proof: 624
% 78.78/38.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 37577 ms resp. 36710 ms w/o parsing
% 79.01/38.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 79.01/38.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------