TSTP Solution File: DAT160^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT160^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:38 EDT 2024
% Result : Theorem 98.65s 27.97s
% Output : Refutation 99.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 359
% Syntax : Number of formulae : 663 ( 226 unt; 57 typ; 0 def)
% Number of atoms : 1398 ( 498 equ; 2 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 6404 ( 84 ~; 6 |; 26 &;5708 @)
% ( 0 <=>; 580 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 164 ( 164 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 8 con; 0-4 aty)
% Number of variables : 1456 ( 70 ^1332 !; 10 ?;1456 :)
% ( 44 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(numeral_type,type,
numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_1_type,type,
ring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(uminus_type,type,
uminus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_ring_1_type,type,
comm_ring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_numeral_type,type,
semiring_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_mult_type,type,
semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_monoid_mult_type,type,
comm_monoid_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(boolean_algebra_type,type,
boolean_algebra:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semilattice_inf_type,type,
semilattice_inf:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coinductive_lfinite_type,type,
coinductive_lfinite:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_llength_type,type,
coinductive_llength:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > extended_enat ) ).
thf(coinductive_LCons_type,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lmap_type,type,
coinductive_lmap:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( coinductive_llist @ TB ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_ltl_type,type,
coinductive_ltl:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(extended_enat2_type,type,
extended_enat2: nat > extended_enat ).
thf(extended_rec_enat_type,type,
extended_rec_enat:
!>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(hammin2015774020amming_type,type,
hammin2015774020amming: coinductive_llist @ nat ).
thf(hammin1630468845amming_type,type,
hammin1630468845amming: product_unit > ( coinductive_llist @ nat ) ).
thf(hammin1138290136lmerge_type,type,
hammin1138290136lmerge:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(hammin1195055315smooth_type,type,
hammin1195055315smooth: nat > $o ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bitM_type,type,
bitM: num > num ).
thf(neg_numeral_dbl_type,type,
neg_numeral_dbl:
!>[TA: $tType] : ( TA > TA ) ).
thf(neg_numeral_dbl_dec_type,type,
neg_numeral_dbl_dec:
!>[TA: $tType] : ( TA > TA ) ).
thf(neg_numeral_dbl_inc_type,type,
neg_numeral_dbl_inc:
!>[TA: $tType] : ( TA > TA ) ).
thf(neg_numeral_sub_type,type,
neg_numeral_sub:
!>[TA: $tType] : ( num > num > TA ) ).
thf(bit0_type,type,
bit0: num > num ).
thf(bit1_type,type,
bit1: num > num ).
thf(one2_type,type,
one2: num ).
thf(numeral_numeral_type,type,
numeral_numeral:
!>[TA: $tType] : ( num > TA ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Unity_type,type,
product_Unity: product_unit ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(n_type,type,
n: nat ).
thf(134,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_inf__fun__def) ).
thf(645,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(281,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_inf_OorderI) ).
thf(1036,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_le__funE) ).
thf(629,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(30,axiom,
lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_14) ).
thf(365,plain,
lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(181,axiom,
semigroup_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).
thf(760,plain,
semigroup_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(347,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(143,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_one__neq__neg__numeral) ).
thf(666,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(302,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_le__numeral__extra_I4_J) ).
thf(1110,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(25,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_13) ).
thf(352,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(239,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_order__class_Oorder_Oantisym) ).
thf(909,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(126,axiom,
ab_semigroup_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(628,plain,
ab_semigroup_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(259,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA )
= ( times_times @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_ring__normalization__rules_I1_J) ).
thf(962,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA )
= ( times_times @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_nat__1__eq__mult__iff) ).
thf(468,plain,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(188,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_nat__mult__1__right) ).
thf(777,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(103,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_inf_OcoboundedI2) ).
thf(555,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(47,axiom,
! [TA: $tType] :
( ( semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_mult_Oassoc) ).
thf(408,plain,
! [TA: $tType] :
( ( semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(89,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_inf__sup__ord_I1_J) ).
thf(523,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(169,axiom,
monoid_mult @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Omonoid__mult_27) ).
thf(730,plain,
monoid_mult @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(292,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_inf__sup__aci_I4_J) ).
thf(1068,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_uminus__apply) ).
thf(308,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(225,axiom,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_numerals_I1_J) ).
thf(873,plain,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(85,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ one2 @ ( bit0 @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_sub__num__simps_I2_J) ).
thf(511,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ one2 @ ( bit0 @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(94,axiom,
one @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oone_32) ).
thf(533,plain,
one @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(101,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_ord__eq__le__trans) ).
thf(550,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(81,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_eq__refl) ).
thf(500,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(163,axiom,
! [A: num] :
( ( ord_less_eq @ num @ A @ one2 )
= ( A = one2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_le__num__One__iff) ).
thf(715,plain,
! [A: num] :
( ( ord_less_eq @ num @ A @ one2 )
= ( A = one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_lfinite__lmap) ).
thf(814,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(290,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_neg__numeral__le__numeral) ).
thf(1063,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(247,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_semiring__normalization__rules_I11_J) ).
thf(930,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(296,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_numeral__One) ).
thf(1095,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(51,axiom,
comm_monoid_mult @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocomm__monoid__mult_20) ).
thf(417,plain,
comm_monoid_mult @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(230,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( numeral_numeral @ TA @ one2 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mult__numeral__1__right) ).
thf(885,plain,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( numeral_numeral @ TA @ one2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(167,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_mult__le__mono2) ).
thf(724,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(107,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ one2 )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_sub__num__simps_I4_J) ).
thf(570,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ one2 )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(82,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_inf_Ocobounded2) ).
thf(504,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_llist_Oinject) ).
thf(344,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(254,axiom,
preorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).
thf(949,plain,
preorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(114,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_le__minus__iff) ).
thf(587,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(123,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_numeral__times__numeral) ).
thf(619,plain,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(158,axiom,
! [A: num] :
( one2
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_num_Odistinct_I3_J) ).
thf(702,plain,
! [A: num] :
( one2
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(177,axiom,
! [A: num,B: num] :
( ( times_times @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( bit0 @ ( times_times @ num @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_semiring__norm_I13_J) ).
thf(751,plain,
! [A: num,B: num] :
( ( times_times @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( bit0 @ ( times_times @ num @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(98,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_linfinite__lmerge) ).
thf(542,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(68,axiom,
! [A: num] :
( one2
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_semiring__norm_I84_J) ).
thf(460,plain,
! [A: num] :
( one2
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(204,axiom,
ab_semigroup_mult @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_19) ).
thf(817,plain,
ab_semigroup_mult @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(224,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_eq__iff) ).
thf(870,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(64,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_mult__minus1__right) ).
thf(448,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(10,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_minus__equation__iff) ).
thf(316,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(273,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_dec @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_dbl__dec__simps_I5_J) ).
thf(1013,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_dec @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(185,axiom,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_semiring__norm_I71_J) ).
thf(770,plain,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(245,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_inf_OboundedE) ).
thf(924,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(86,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( times_times @ TA @ B @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_numeral__times__minus__swap) ).
thf(514,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( times_times @ TA @ B @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(74,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_semiring__normalization__rules_I7_J) ).
thf(480,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(275,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( times_times @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( times_times @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_semiring__norm_I169_J) ).
thf(1020,plain,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( times_times @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( times_times @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(109,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_numeral__eq__neg__one__iff) ).
thf(574,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_enat_Oinject) ).
thf(353,plain,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(261,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_inf__sup__ord_I2_J) ).
thf(966,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(286,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_neg__numeral__eq__iff) ).
thf(1051,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(206,axiom,
semiring_char_0 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0) ).
thf(821,plain,
semiring_char_0 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(227,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_neg__le__iff__le) ).
thf(877,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(171,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit1 @ one2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_dbl__dec__simps_I4_J) ).
thf(734,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit1 @ one2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(223,axiom,
! [A: num,B: num] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_semiring__norm_I89_J) ).
thf(866,plain,
! [A: num,B: num] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(44,axiom,
lattice @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_3) ).
thf(396,plain,
lattice @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(56,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_numeral__neq__neg__one) ).
thf(428,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(8,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_dbl__dec__simps_I3_J) ).
thf(312,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(117,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ ( bit1 @ A ) @ one2 )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_sub__num__simps_I5_J) ).
thf(602,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ ( bit1 @ A ) @ one2 )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(184,axiom,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_semiring__norm_I85_J) ).
thf(766,plain,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(45,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ~ ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) )
= ( A != one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__neg__one__le__neg__numeral__iff) ).
thf(397,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ~ ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) )
= ( A != one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(152,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_inf_Oabsorb1) ).
thf(687,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(48,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_dec @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl_inc @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_dbl__dec__simps_I1_J) ).
thf(411,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_dec @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl_inc @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(265,axiom,
( hammin2015774020amming
= ( hammin1630468845amming @ product_Unity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_hamming__def) ).
thf(988,plain,
( hammin2015774020amming
= ( hammin1630468845amming @ product_Unity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(300,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_inf__sup__aci_I1_J) ).
thf(1104,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(217,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_not__numeral__le__neg__numeral) ).
thf(849,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(5,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).
thf(307,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(380,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(251,axiom,
order @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_29) ).
thf(942,plain,
order @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(193,axiom,
semiring_numeral @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Osemiring__numeral) ).
thf(793,plain,
semiring_numeral @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_le__funI) ).
thf(761,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(366,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(95,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( A
= ( inf_inf @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_inf_Oorder__iff) ).
thf(534,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( A
= ( inf_inf @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(197,axiom,
! [A: num,B: num] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_enat__ord__number_I1_J) ).
thf(798,plain,
! [A: num,B: num] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(288,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_inf_Oabsorb2) ).
thf(1057,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(233,axiom,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( one_one @ extended_enat ) )
= ( A
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_enat__1__iff_I1_J) ).
thf(894,plain,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( one_one @ extended_enat ) )
= ( A
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(283,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ? [B: nat] :
( ( coinductive_llength @ TA @ A )
= ( extended_enat2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_lfinite__llength__enat) ).
thf(1042,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ? [B: nat] :
( ( coinductive_llength @ TA @ A )
= ( extended_enat2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(24,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_dbl__inc__simps_I4_J) ).
thf(349,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(279,axiom,
linordered_semidom @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom) ).
thf(1032,plain,
linordered_semidom @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(125,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_semiring__normalization__rules_I14_J) ).
thf(625,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) ) @ A )
= ( uminus_uminus @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_mult__1s_I3_J) ).
thf(435,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) ) @ A )
= ( uminus_uminus @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_lfinite__code_I2_J) ).
thf(329,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(179,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_4) ).
thf(757,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(150,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_antisym__conv) ).
thf(682,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(161,axiom,
comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_21) ).
thf(710,plain,
comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(215,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( times_times @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_semiring__norm_I170_J) ).
thf(842,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( times_times @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(324,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_le__cases3) ).
thf(974,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(174,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_minus__le__iff) ).
thf(742,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(294,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_numeral__eq__iff) ).
thf(1089,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(136,axiom,
( ( coinductive_ltl @ nat @ hammin2015774020amming )
= ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ltl__hamming) ).
thf(650,plain,
( ( coinductive_ltl @ nat @ hammin2015774020amming )
= ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(271,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_le__inf__iff) ).
thf(1006,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(388,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_ltl @ TA @ A ) )
= ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_lfinite__ltl) ).
thf(356,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_ltl @ TA @ A ) )
= ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(120,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_dbl__simps_I1_J) ).
thf(610,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(220,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_inf__absorb1) ).
thf(857,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(190,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_inf_Obounded__iff) ).
thf(783,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(53,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_inf__le2) ).
thf(420,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) ) )
= ( uminus_uminus @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_mult__1s_I4_J) ).
thf(471,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) ) )
= ( uminus_uminus @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(248,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_inf_Oright__idem) ).
thf(933,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(102,axiom,
hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_smooth3) ).
thf(554,plain,
hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(96,axiom,
( hammin2015774020amming
= ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_hamming__unfold) ).
thf(537,plain,
( hammin2015774020amming
= ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(144,axiom,
! [A: nat] :
( ( ( one_one @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_enat__1__iff_I2_J) ).
thf(669,plain,
! [A: nat] :
( ( ( one_one @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(236,axiom,
! [A: nat,B: nat] :
( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( times_times @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_times__enat__simps_I1_J) ).
thf(901,plain,
! [A: nat,B: nat] :
( ( times_times @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( extended_enat2 @ ( times_times @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(133,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_inf__left__idem) ).
thf(642,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(100,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( ( coinductive_llength @ TA @ A )
= ( extended_enat2 @ B ) )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_llength__eq__enat__lfiniteD) ).
thf(547,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: nat] :
( ( ( coinductive_llength @ TA @ A )
= ( extended_enat2 @ B ) )
=> ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(159,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_compl__le__swap2) ).
thf(706,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(274,axiom,
! [A: num] :
( ( A != one2 )
=> ( ! [B: num] :
( A
!= ( bit0 @ B ) )
=> ~ ! [B: num] :
( A
!= ( bit1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_num_Oexhaust) ).
thf(1016,plain,
! [A: num] :
( ( A != one2 )
=> ( ! [B: num] :
( A
!= ( bit0 @ B ) )
=> ~ ! [B: num] :
( A
!= ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(115,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_linorder__wlog) ).
thf(590,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(149,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_semiring__normalization__rules_I16_J) ).
thf(679,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(282,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_inf_Oleft__commute) ).
thf(1039,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_inf__apply) ).
thf(393,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(269,axiom,
~ ! [A: nat] :
( ( coinductive_llength @ nat @ hammin2015774020amming )
!= ( extended_enat2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_Ahamming_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(997,plain,
~ ! [A: nat] :
( ( coinductive_llength @ nat @ hammin2015774020amming )
!= ( extended_enat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(138,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_inf__absorb2) ).
thf(654,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(270,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_semiring__norm_I83_J) ).
thf(1002,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(371,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_le__antisym) ).
thf(605,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(124,axiom,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_nat__mult__1) ).
thf(622,plain,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(213,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_le__minus__one__simps_I4_J) ).
thf(837,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(289,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit1 @ one2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_dbl__inc__simps_I3_J) ).
thf(1060,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_inc @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit1 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: TB,D: coinductive_llist @ TB] :
( ( ( coinductive_lmap @ TA @ TB @ A @ B )
= ( coinductive_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ E @ F ) )
& ( C
= ( A @ E ) )
& ( D
= ( coinductive_lmap @ TA @ TB @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_lmap__eq__LCons__conv) ).
thf(457,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA,C: TB,D: coinductive_llist @ TB] :
( ( ( coinductive_lmap @ TA @ TB @ A @ B )
= ( coinductive_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ E @ F ) )
& ( C
= ( A @ E ) )
& ( D
= ( coinductive_lmap @ TA @ TB @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(200,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_neg__numeral__neq__numeral) ).
thf(805,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_llength @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_llength @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_llength__lmap) ).
thf(508,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_llength @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_llength @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(7,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_15) ).
thf(311,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(243,axiom,
monoid_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult) ).
thf(921,plain,
monoid_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_le__funD) ).
thf(657,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(287,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_num_Oinject_I1_J) ).
thf(1054,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(293,axiom,
! [A: num > $o,B: num] :
( ( A @ one2 )
=> ( ! [C: num] :
( ( A @ C )
=> ( A @ ( bit0 @ C ) ) )
=> ( ! [C: num] :
( ( A @ C )
=> ( A @ ( bit1 @ C ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_num_Oinduct) ).
thf(1071,plain,
! [A: num > $o,B: num] :
( ( A @ one2 )
=> ( ! [C: num] :
( ( A @ C )
=> ( A @ ( bit0 @ C ) ) )
=> ( ! [C: num] :
( ( A @ C )
=> ( A @ ( bit1 @ C ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(277,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( neg_numeral_dbl @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_sub__num__simps_I6_J) ).
thf(1026,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( neg_numeral_dbl @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(92,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_le__infI2) ).
thf(530,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(256,axiom,
( ( numeral_numeral @ extended_enat )
= ( ^ [A: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_numeral__eq__enat) ).
thf(953,plain,
( ( numeral_numeral @ extended_enat )
= ( ^ [A: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(186,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_inf_Oleft__idem) ).
thf(773,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(194,axiom,
lattice @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Olattice_28) ).
thf(794,plain,
lattice @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(141,axiom,
( ( coinductive_llength @ nat @ hammin2015774020amming )
= ( extended_enat2 @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_n) ).
thf(662,plain,
( ( coinductive_llength @ nat @ hammin2015774020amming )
= ( extended_enat2 @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(164,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_linear) ).
thf(718,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(231,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( neg_numeral_dbl @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_sub__num__simps_I9_J) ).
thf(888,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( neg_numeral_dbl @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(238,axiom,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit0 @ A ) @ one2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_semiring__norm_I69_J) ).
thf(906,plain,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit0 @ A ) @ one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(260,axiom,
hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_smooth2) ).
thf(965,plain,
hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(55,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_numeral__eq__one__iff) ).
thf(425,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(208,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_inf__assoc) ).
thf(824,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(175,axiom,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_semiring__norm_I72_J) ).
thf(745,plain,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(108,axiom,
numeral @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral) ).
thf(573,plain,
numeral @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(113,axiom,
! [A: num] :
( ( times_times @ num @ A @ one2 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_semiring__norm_I11_J) ).
thf(584,plain,
! [A: num] :
( ( times_times @ num @ A @ one2 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(237,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le__minus__one__simps_I2_J) ).
thf(904,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(155,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_order__refl) ).
thf(694,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(258,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_eq__imp__le) ).
thf(958,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(226,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_inf_OcoboundedI1) ).
thf(875,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(110,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_mult_Ocommute) ).
thf(577,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(162,axiom,
! [A: num] :
( ( bit1 @ A )
!= one2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_semiring__norm_I86_J) ).
thf(711,plain,
! [A: num] :
( ( bit1 @ A )
!= one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(38,axiom,
linorder @ num @ ( type2 @ num ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Olinorder_7) ).
thf(382,plain,
linorder @ num @ ( type2 @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(301,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_ltl @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ltl__lmap) ).
thf(1107,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coinductive_llist @ TA] :
( ( coinductive_ltl @ TB @ ( coinductive_lmap @ TA @ TB @ A @ B ) )
= ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(295,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_semiring__normalization__rules_I17_J) ).
thf(1092,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(18,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_16) ).
thf(335,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(199,axiom,
coinductive_lfinite @ nat @ hammin2015774020amming,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062lfinite_Ahamming_092_060close_062) ).
thf(804,plain,
coinductive_lfinite @ nat @ hammin2015774020amming,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(145,axiom,
semilattice_inf @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_1) ).
thf(672,plain,
semilattice_inf @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(63,axiom,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_semiring__norm_I73_J) ).
thf(445,plain,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(249,axiom,
! [A: num,B: nat] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_numeral__le__enat__iff) ).
thf(936,plain,
! [A: num,B: nat] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(285,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ num @ A @ one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_numeral__le__one__iff) ).
thf(1048,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ num @ A @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(172,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_lfinite__lmergeI) ).
thf(737,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(228,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_dual__order_Oantisym) ).
thf(880,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(122,axiom,
! [A: num,B: num] :
( ( times_times @ num @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( times_times @ num @ ( bit1 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_semiring__norm_I15_J) ).
thf(616,plain,
! [A: num,B: num] :
( ( times_times @ num @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( times_times @ num @ ( bit1 @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_order__subst2) ).
thf(863,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(36,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_equation__minus__iff) ).
thf(377,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(266,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__infI) ).
thf(990,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_fun__Compl__def) ).
thf(362,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(65,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_semiring__normalization__rules_I12_J) ).
thf(451,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(106,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_inf__right__idem) ).
thf(567,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(73,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ A )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_inf_Oabsorb__iff2) ).
thf(477,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(202,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_inf__idem) ).
thf(811,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(79,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_mult__neg__numeral__simps_I2_J) ).
thf(494,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(128,axiom,
semigroup_mult @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_22) ).
thf(631,plain,
semigroup_mult @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(180,axiom,
! [A: num] : ( ord_less_eq @ num @ one2 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_semiring__norm_I68_J) ).
thf(758,plain,
! [A: num] : ( ord_less_eq @ num @ one2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(13,axiom,
preorder @ num @ ( type2 @ num ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Opreorder_6) ).
thf(323,plain,
preorder @ num @ ( type2 @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_dbl__simps_I4_J) ).
thf(483,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(88,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_mult__neg__numeral__simps_I1_J) ).
thf(520,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(278,axiom,
! [TA: $tType] :
( ( coinductive_lfinite @ TA )
= ( ^ [A: coinductive_llist @ TA] :
? [B: nat] :
( ( coinductive_llength @ TA @ A )
= ( extended_enat2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lfinite__conv__llength__enat) ).
thf(1029,plain,
! [TA: $tType] :
( ( coinductive_lfinite @ TA )
= ( ^ [A: coinductive_llist @ TA] :
? [B: nat] :
( ( coinductive_llength @ TA @ A )
= ( extended_enat2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(241,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_inf_OorderE) ).
thf(915,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(252,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_comm__monoid__mult__class_Omult__1) ).
thf(943,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(303,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_order__trans) ).
thf(1112,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(209,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_wlog__linorder__le) ).
thf(827,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(131,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_semiring__normalization__rules_I19_J) ).
thf(636,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_le__fun__def) ).
thf(780,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(229,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_inf_Ocobounded1) ).
thf(883,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_inf__greatest) ).
thf(608,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(4,axiom,
semilattice_inf @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_10) ).
thf(306,plain,
semilattice_inf @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TB @ ( A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_llist_Osimps_I13_J) ).
thf(438,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: coinductive_llist @ TA] :
( ( coinductive_lmap @ TA @ TB @ A @ ( coinductive_LCons @ TA @ B @ C ) )
= ( coinductive_LCons @ TB @ ( A @ B ) @ ( coinductive_lmap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(57,axiom,
semiring_numeral @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_23) ).
thf(431,plain,
semiring_numeral @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(244,axiom,
( ( one_one @ extended_enat )
= ( extended_enat2 @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_one__enat__def) ).
thf(922,plain,
( ( one_one @ extended_enat )
= ( extended_enat2 @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_mult__le__mono) ).
thf(912,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(151,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_le__infI1) ).
thf(685,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(218,axiom,
! [A: num] :
( ( bitM @ ( bit0 @ A ) )
= ( bit1 @ ( bitM @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_semiring__norm_I27_J) ).
thf(851,plain,
! [A: num] :
( ( bitM @ ( bit0 @ A ) )
= ( bit1 @ ( bitM @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(299,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_le__refl) ).
thf(1102,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(166,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_le__cases) ).
thf(722,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(147,axiom,
preorder @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Opreorder_25) ).
thf(675,plain,
preorder @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(195,axiom,
semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_24) ).
thf(795,plain,
semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(250,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_dbl__simps_I5_J) ).
thf(939,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(178,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( times_times @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_semiring__norm_I172_J) ).
thf(754,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( times_times @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(262,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( neg_numeral_dbl_dec @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_sub__num__simps_I7_J) ).
thf(968,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( neg_numeral_dbl_dec @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(246,axiom,
! [A: num] :
( ( times_times @ num @ one2 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_semiring__norm_I12_J) ).
thf(927,plain,
! [A: num] :
( ( times_times @ num @ one2 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(35,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_neg__equal__iff__equal) ).
thf(374,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(135,axiom,
( ( bitM @ one2 )
= one2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_semiring__norm_I26_J) ).
thf(648,plain,
( ( bitM @ one2 )
= one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(77,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_num_Odistinct_I1_J) ).
thf(487,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(187,axiom,
semilattice_inf @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Lattices_Osemilattice__inf_18) ).
thf(776,plain,
semilattice_inf @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(90,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_compl__le__compl__iff) ).
thf(525,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(104,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_inf_Oidem) ).
thf(557,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(111,axiom,
comm_semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(580,plain,
comm_semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(153,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(690,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(173,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( neg_numeral_dbl_inc @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_sub__num__simps_I8_J) ).
thf(739,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( neg_numeral_dbl_inc @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(297,axiom,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit1 @ A ) @ one2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_semiring__norm_I70_J) ).
thf(1098,plain,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit1 @ A ) @ one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(49,axiom,
one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(414,plain,
one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(263,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_mult_Oright__neutral) ).
thf(971,plain,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(146,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_compl__mono) ).
thf(673,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(61,axiom,
hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_smooth5) ).
thf(441,plain,
hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(20,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_add_Oinverse__inverse) ).
thf(338,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(201,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_enat__ord__simps_I1_J) ).
thf(808,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(28,axiom,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_enat_Osimps_I6_J) ).
thf(359,plain,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_mult_Oleft__commute) ).
thf(544,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(19,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_lfinite__LConsI) ).
thf(336,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(276,axiom,
! [A: num,B: num] :
( ( times_times @ num @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( times_times @ num @ A @ ( bit1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_semiring__norm_I14_J) ).
thf(1023,plain,
! [A: num,B: num] :
( ( times_times @ num @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit0 @ ( times_times @ num @ A @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(121,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_inf_Ocommute) ).
thf(613,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(168,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_semiring__normalization__rules_I15_J) ).
thf(727,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(386,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(116,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_inf__unique) ).
thf(595,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(80,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_one__eq__numeral__iff) ).
thf(497,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(216,axiom,
! [A: num,B: num] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_semiring__norm_I88_J) ).
thf(845,plain,
! [A: num,B: num] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(539,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(112,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( ord_less_eq @ num @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_neg__numeral__le__iff) ).
thf(581,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( ord_less_eq @ num @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(232,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_inf__sup__aci_I3_J) ).
thf(891,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(32,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_one__neq__neg__one) ).
thf(368,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(157,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_inf_Oabsorb__iff1) ).
thf(699,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(87,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_antisym) ).
thf(517,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(11,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_double__compl) ).
thf(319,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(176,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_semiring__normalization__rules_I18_J) ).
thf(748,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1,conjecture,
ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) ) @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) @ ( coinductive_llength @ nat @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) ) @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) @ ( coinductive_llength @ nat @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(304,plain,
~ ( ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) ) @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) @ ( coinductive_llength @ nat @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(137,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_le__imp__neg__le) ).
thf(652,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(42,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_numeral__neq__neg__numeral) ).
thf(390,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(129,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_semiring__norm_I171_J) ).
thf(632,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( times_times @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_ord__le__eq__subst) ).
thf(401,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(268,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_compl__le__swap1) ).
thf(995,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(253,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__infE) ).
thf(946,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(298,axiom,
ord @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oord_30) ).
thf(1101,plain,
ord @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(170,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_inf__sup__aci_I2_J) ).
thf(731,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(52,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ ( times_times @ nat @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_le__cube) ).
thf(418,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ ( times_times @ nat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(191,axiom,
! [A: num,B: num] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_num_Odistinct_I5_J) ).
thf(786,plain,
! [A: num,B: num] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(183,axiom,
! [A: nat,B: nat] :
( ( hammin1195055315smooth @ ( times_times @ nat @ A @ B ) )
= ( ( hammin1195055315smooth @ A )
& ( hammin1195055315smooth @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_smooth__times) ).
thf(763,plain,
! [A: nat,B: nat] :
( ( hammin1195055315smooth @ ( times_times @ nat @ A @ B ) )
= ( ( hammin1195055315smooth @ A )
& ( hammin1195055315smooth @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(39,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_compl__eq__compl__iff) ).
thf(383,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_nat__le__linear) ).
thf(899,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(210,axiom,
linorder @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_26) ).
thf(832,plain,
linorder @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(284,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_mult_Ocomm__neutral) ).
thf(1045,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(9,axiom,
order @ num @ ( type2 @ num ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oorder_8) ).
thf(315,plain,
order @ num @ ( type2 @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(58,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_inf__commute) ).
thf(432,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(211,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] : ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_one__le__numeral) ).
thf(833,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] : ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(205,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_inf_Oassoc) ).
thf(818,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(219,axiom,
! [A: num] :
( ( bitM @ ( bit1 @ A ) )
= ( bit1 @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_semiring__norm_I28_J) ).
thf(854,plain,
! [A: num] :
( ( bitM @ ( bit1 @ A ) )
= ( bit1 @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(34,axiom,
ord @ num @ ( type2 @ num ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oord_9) ).
thf(373,plain,
ord @ num @ ( type2 @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(255,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_inc @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_dbl__inc__simps_I5_J) ).
thf(950,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_inc @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(212,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_inf__le1) ).
thf(835,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(54,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_mult__neg__numeral__simps_I3_J) ).
thf(422,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( times_times @ num @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(192,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_inc @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl_dec @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_dbl__inc__simps_I1_J) ).
thf(790,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_inc @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl_dec @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(3,axiom,
uminus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_17) ).
thf(305,plain,
uminus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_lfinite__LCons) ).
thf(326,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_one__reorient) ).
thf(341,plain,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(83,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_order_Otrans) ).
thf(506,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(142,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_le__square) ).
thf(664,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(280,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ one2 @ ( bit1 @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_sub__num__simps_I3_J) ).
thf(1033,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ one2 @ ( bit1 @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(130,axiom,
comm_monoid_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(635,plain,
comm_monoid_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(156,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_semiring__norm_I87_J) ).
thf(696,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(165,axiom,
( hammin1630468845amming
= ( ^ [A: product_unit] : ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_hamming_H_Osimps) ).
thf(720,plain,
( hammin1630468845amming
= ( ^ [A: product_unit] : ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(257,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( one_one @ TA ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_neg__one__eq__numeral__iff) ).
thf(955,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( one_one @ TA ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(196,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_inf__mono) ).
thf(796,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(50,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_dual__order_Otrans) ).
thf(415,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(242,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_dbl__simps_I3_J) ).
thf(918,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(198,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_le__iff__inf) ).
thf(801,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(234,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ TA @ A ) @ ( coinductive_llength @ TA @ B ) ) @ ( coinductive_llength @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_llength__lmerge__above) ).
thf(897,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] : ( ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ TA @ A ) @ ( coinductive_llength @ TA @ B ) ) @ ( coinductive_llength @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(72,axiom,
! [A: num,B: num] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_num_Oinject_I2_J) ).
thf(474,plain,
! [A: num,B: num] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(93,axiom,
numeral @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Onumeral_31) ).
thf(532,plain,
numeral @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(291,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_semiring__normalization__rules_I13_J) ).
thf(1065,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(214,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_nat__mult__eq__1__iff) ).
thf(839,plain,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(69,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ord__le__eq__trans) ).
thf(464,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_ltl @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_ltl__simps_I2_J) ).
thf(332,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_ltl @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(221,axiom,
! [A: num,B: num] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_semiring__norm_I90_J) ).
thf(860,plain,
! [A: num,B: num] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(91,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_dual__order_Orefl) ).
thf(528,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(267,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ one2 ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult__numeral__1) ).
thf(992,plain,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ one2 ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(207,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
=> ( ( coinductive_lfinite @ TA @ A )
| ( coinductive_lfinite @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_lfinite__lmergeD) ).
thf(822,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
=> ( ( coinductive_lfinite @ TA @ A )
| ( coinductive_lfinite @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(154,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_mult__le__mono1) ).
thf(691,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(62,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_le__trans) ).
thf(442,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(12,axiom,
boolean_algebra @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_11) ).
thf(322,plain,
boolean_algebra @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_5) ).
thf(486,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(272,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less_eq @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_enat__ile) ).
thf(1009,plain,
! [A: extended_enat,B: nat] :
( ( ord_less_eq @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(140,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ A )
= ( uminus_uminus @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_mult__minus1) ).
thf(659,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ A )
= ( uminus_uminus @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_ord__eq__le__subst) ).
thf(560,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(132,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_numeral__le__iff) ).
thf(639,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(148,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_inf__left__commute) ).
thf(676,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(78,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mult_Oleft__neutral) ).
thf(491,plain,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_order__subst1) ).
thf(454,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(160,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_inf_OboundedI) ).
thf(708,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(7972,plain,
$false,
inference(cvc4,[status(thm)],[645,1036,629,365,760,347,666,1110,352,909,628,962,468,777,555,408,523,730,1068,308,873,511,533,550,500,715,814,1063,930,1095,417,885,724,570,504,344,949,587,619,702,751,542,460,817,870,448,316,1013,770,924,514,480,1020,574,353,966,1051,821,877,734,866,396,428,312,602,766,397,687,411,988,1104,849,307,380,942,793,761,366,534,798,1057,894,1042,349,1032,625,435,329,757,682,710,842,324,974,742,1089,650,1006,388,356,610,857,783,420,471,933,554,537,669,901,642,547,706,1016,590,679,1039,393,997,654,1002,371,605,622,837,1060,457,805,508,311,921,657,1054,1071,1026,530,953,773,794,662,718,888,906,965,425,824,745,573,584,904,694,958,875,577,711,382,1107,1092,335,804,672,445,936,1048,737,880,616,863,377,990,362,451,567,477,811,494,631,758,323,483,520,1029,915,943,1112,827,636,780,883,608,306,438,431,922,912,685,851,1102,722,675,795,939,754,968,927,374,648,487,776,525,557,580,690,739,1098,414,971,673,441,338,808,359,544,336,1023,613,727,386,595,497,845,539,581,891,368,699,517,319,748,304,652,390,632,401,995,946,1101,731,418,786,763,383,899,832,1045,315,432,833,818,854,373,950,835,422,790,305,326,341,506,664,1033,635,696,720,955,796,415,918,801,897,474,532,1065,839,464,332,860,528,992,822,691,442,322,486,1009,659,560,639,676,491,454,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : DAT160^1 : TPTP v8.1.2. Released v7.0.0.
% 0.10/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n017.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 11:29:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.70/1.13 % [INFO] Parsing done (251ms).
% 1.70/1.14 % [INFO] Running in sequential loop mode.
% 2.62/1.34 % [INFO] eprover registered as external prover.
% 2.62/1.35 % [INFO] cvc4 registered as external prover.
% 2.62/1.35 % [INFO] Scanning for conjecture ...
% 2.79/1.44 % [INFO] Found a conjecture and 302 axioms. Running axiom selection ...
% 3.24/1.53 % [INFO] Axiom selection finished. Selected 301 axioms (removed 1 axioms).
% 3.57/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 3.57/1.68 % [INFO] Type checking passed.
% 3.57/1.68 % [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 ...
% 98.65/27.96 % External prover 'cvc4' found a proof!
% 98.65/27.96 % [INFO] Killing All external provers ...
% 98.65/27.97 % Time passed: 27430ms (effective reasoning time: 26822ms)
% 98.65/27.97 % 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)>
% 98.65/27.97 % Axioms used in derivation (301): tcon_HOL_Obool___Lattices_Olattice_14, fact_193_semiring__normalization__rules_I17_J, fact_5_inf_Obounded__iff, fact_9_semiring__norm_I85_J, fact_25_inf_Oidem, fact_121_order_Otrans, tcon_Extended__Nat_Oenat___Orderings_Oorder_29, fact_51_inf__commute, fact_99_enat_Oinject, tcon_HOL_Obool___Orderings_Oord_16, fact_131_dual__order_Oantisym, fact_101_enat__ile, fact_191_semiring__normalization__rules_I19_J, fact_112_order__subst1, fact_88_inf__sup__ord_I1_J, fact_181_lfinite__code_I2_J, tcon_Extended__Nat_Oenat___Groups_Oone_32, fact_245_minus__le__iff, fact_167_mult_Oleft__neutral, fact_6_semiring__norm_I169_J, fact_214_dbl__inc__simps_I4_J, tcon_Nat_Onat___Orderings_Olinorder, fact_202_dbl__dec__simps_I4_J, tcon_HOL_Obool___Groups_Ouminus_17, fact_94_numeral__le__enat__iff, fact_14_semiring__norm_I90_J, tcon_HOL_Obool___Lattices_Oboolean__algebra_11, fact_228_dbl__simps_I4_J, fact_54_inf_Oassoc, fact_72_inf_OboundedE, fact_237_compl__le__swap2, tcon_Nat_Onat___Orderings_Oord_5, fact_106_ltl__lmap, fact_30_semiring__norm_I11_J, fact_139_nat__le__linear, fact_67_inf_Ocobounded2, tcon_HOL_Obool___Orderings_Opreorder_12, fact_158_nat__mult__1__right, fact_184_ltl__simps_I2_J, fact_128_dual__order_Orefl, fact_162_enat__1__iff_I2_J, fact_229_ring__normalization__rules_I1_J, fact_116_eq__iff, fact_43_le__num__One__iff, fact_77_le__iff__inf, fact_201_sub__num__simps_I2_J, tcon_Extended__Nat_Oenat___Num_Onumeral_31, fact_7_numeral__times__numeral, fact_113_order__subst2, fact_196_semiring__normalization__rules_I14_J, fact_243_not__numeral__le__neg__numeral, tcon_fun___Orderings_Oord, fact_21_inf_Oright__idem, fact_186_llist_Osimps_I13_J, tcon_Num_Onum___Orderings_Oord_9, fact_251_mult__1s_I4_J, fact_34_semiring__norm_I68_J, fact_173_ab__semigroup__mult__class_Omult__ac_I1_J, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_21, fact_74_inf__absorb1, tcon_Nat_Onat___Groups_Ocomm__monoid__mult, fact_197_semiring__normalization__rules_I13_J, fact_247_minus__equation__iff, fact_239_compl__mono, fact_95_enat__ord__simps_I1_J, fact_29_lfinite__lmap, fact_70_inf__greatest, fact_53_inf__assoc, fact_232_one__neq__neg__numeral, fact_122_le__cases3, tcon_Nat_Onat___Num_Osemiring__numeral, fact_136_mult__le__mono, fact_171_mult_Ocommute, fact_36_semiring__norm_I15_J, fact_75_inf_Oabsorb2, fact_215_neg__one__eq__numeral__iff, fact_27_semiring__norm_I88_J, fact_104_dbl__inc__simps_I5_J, fact_73_inf__absorb2, fact_134_le__cube, fact_69_inf_Oorder__iff, tcon_Nat_Onat___Groups_Oone, fact_38_semiring__norm_I70_J, fact_108_le__funD, tcon_Nat_Onat___Rings_Olinordered__semidom, fact_56_inf__sup__aci_I1_J, fact_248_equation__minus__iff, fact_199_semiring__normalization__rules_I11_J, fact_102_numeral__eq__enat, fact_144_enat_Osimps_I6_J, fact_195_semiring__normalization__rules_I15_J, tcon_Extended__Nat_Oenat___Groups_Omonoid__mult_27, tcon_Nat_Onat___Groups_Oab__semigroup__mult, fact_93_mult__numeral__1, fact_200_hamming_H_Osimps, fact_221_semiring__norm_I171_J, fact_61_num_Odistinct_I3_J, fact_110_le__funI, fact_1_llength__lmerge__above, tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_22, fact_166_mult_Oright__neutral, fact_185_lmap__eq__LCons__conv, fact_217_mult__neg__numeral__simps_I1_J, fact_242_neg__numeral__le__numeral, fact_218_mult__neg__numeral__simps_I2_J, fact_58_inf__sup__aci_I3_J, fact_160_one__enat__def, fact_37_semiring__norm_I72_J, fact_132_smooth3, fact_238_compl__le__swap1, fact_92_mult__numeral__1__right, fact_59_inf__sup__aci_I4_J, fact_127_order__trans, fact_169_dbl__dec__simps_I3_J, fact_15_num_Oinject_I2_J, fact_246_le__imp__neg__le, fact_96_times__enat__simps_I1_J, fact_211_mult__minus1__right, fact_97_enat__ord__number_I1_J, tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_23, fact_117_antisym, fact_153_sub__num__simps_I6_J, tcon_Nat_Onat___Lattices_Osemilattice__inf_1, fact_236_fun__Compl__def, fact_107_smooth__times, fact_81_le__infI2, tcon_Num_Onum___Orderings_Olinorder_7, fact_76_inf_Oabsorb1, tcon_Nat_Onat___Orderings_Oorder_4, fact_105_lfinite__ltl, fact_165_numerals_I1_J, fact_178_sub__num__simps_I4_J, fact_11_semiring__norm_I86_J, fact_0__092_060open_062lfinite_Ahamming_092_060close_062, fact_207_add_Oinverse__inverse, fact_68_inf_Ocobounded1, fact_66_inf_Oabsorb__iff1, fact_100_order__refl, fact_159_le__numeral__extra_I4_J, tcon_Num_Onum___Orderings_Oorder_8, tcon_fun___Lattices_Osemilattice__inf, fact_249_one__neq__neg__one, tcon_Extended__Nat_Oenat___Orderings_Opreorder_25, fact_26_inf__apply, fact_2_n, fact_161_enat__1__iff_I1_J, fact_149_nat__mult__eq__1__iff, fact_28_semiring__norm_I13_J, fact_86_inf__le2, tcon_Nat_Onat___Groups_Omonoid__mult, fact_172_mult_Oassoc, fact_219_mult__neg__numeral__simps_I3_J, fact_179_semiring__normalization__rules_I12_J, fact_79_inf_OorderI, fact_190_semiring__norm_I27_J, tcon_Extended__Nat_Oenat___Lattices_Osemilattice__inf_18, fact_203_compl__eq__compl__iff, tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_24, fact_118_linear, fact_40_lfinite__llength__enat, fact_103_smooth5, fact_24_inf__idem, fact_124_ord__eq__le__trans, fact_130_dual__order_Otrans, fact_55_inf__fun__def, fact_17_num_Oinject_I1_J, fact_222_semiring__norm_I172_J, fact_233_hamming__def, fact_48_wlog__linorder__le, fact_22_inf__left__idem, fact_91_num_Oinduct, fact_115_ord__le__eq__subst, fact_87_inf__le1, fact_16_semiring__norm_I87_J, tcon_Nat_Onat___Lattices_Olattice_3, fact_23_inf_Oleft__idem, fact_45_linfinite__lmerge, tcon_Nat_Onat___Orderings_Opreorder_2, fact_209_neg__le__iff__le, fact_57_inf__sup__aci_I2_J, fact_140_le__antisym, fact_141_eq__imp__le, fact_212_mult__minus1, fact_84_le__infI, fact_143_le__refl, fact_78_inf__unique, fact_188_semiring__norm_I26_J, fact_60_num_Odistinct_I5_J, fact_194_semiring__normalization__rules_I16_J, fact_89_inf__sup__ord_I2_J, fact_164_numeral__One, tcon_HOL_Obool___Orderings_Olinorder_13, tcon_fun___Lattices_Oboolean__algebra, fact_231_numeral__neq__neg__one, fact_146_dbl__inc__simps_I3_J, tcon_Extended__Nat_Oenat___Orderings_Olinorder_26, fact_148_nat__1__eq__mult__iff, fact_62_num_Odistinct_I1_J, fact_206_neg__equal__iff__equal, fact_83_inf__mono, fact_42_lfinite__conv__llength__enat, fact_227_sub__num__simps_I3_J, fact_170_mult_Oleft__commute, fact_223_neg__numeral__le__iff, fact_142_le__trans, fact_177_hamming__unfold, tcon_Nat_Onat___Num_Onumeral, fact_119_eq__refl, fact_241_le__minus__one__simps_I4_J, fact_182_lfinite__LCons, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_168_sub__num__simps_I7_J, fact_210_neg__numeral__eq__iff, fact_175_comm__monoid__mult__class_Omult__1, fact_114_ord__eq__le__subst, fact_189_semiring__norm_I28_J, fact_208_compl__le__compl__iff, fact_109_le__funE, fact_135_le__square, fact_213_dbl__simps_I1_J, fact_39_semiring__norm_I69_J, tcon_fun___Orderings_Opreorder, fact_250_mult__1s_I3_J, fact_198_semiring__normalization__rules_I7_J, fact_240_le__minus__one__simps_I2_J, fact_123_antisym__conv, fact_204_double__compl, fact_63_inf_OcoboundedI2, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_19, fact_155_numeral__le__one__iff, fact_13_semiring__norm_I89_J, fact_129_linorder__wlog, fact_126_order__class_Oorder_Oantisym, fact_234_neg__numeral__neq__numeral, fact_150_numeral__eq__one__iff, tcon_HOL_Obool___Lattices_Osemilattice__inf_10, fact_35_semiring__norm_I14_J, fact_33_semiring__norm_I71_J, fact_47_lfinite__lmergeD, fact_244_le__minus__iff, tcon_fun___Orderings_Oorder, fact_49_inf__left__commute, fact_111_le__fun__def, fact_50_inf_Oleft__commute, fact_138_mult__le__mono2, fact_133_smooth2, fact_125_ord__le__eq__trans, fact_41_llength__eq__enat__lfiniteD, tcon_Extended__Nat_Oenat___Orderings_Oord_30, fact_64_inf_OcoboundedI1, fact_85_le__infE, fact_163_one__le__numeral, fact_230_numeral__times__minus__swap, fact_176_mult_Ocomm__neutral, fact_19_numeral__eq__iff, tcon_Nat_Onat___Groups_Osemigroup__mult, fact_18__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_Ahamming_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, tcon_fun___Groups_Ouminus, fact_46_lfinite__lmergeI, fact_205_uminus__apply, fact_80_inf_OorderE, fact_4_le__inf__iff, fact_187_lfinite__LConsI, fact_31_semiring__norm_I12_J, fact_226_dbl__inc__simps_I1_J, fact_65_inf_Oabsorb__iff2, fact_145_sub__num__simps_I5_J, fact_8_numeral__le__iff, fact_216_numeral__eq__neg__one__iff, fact_98_ltl__hamming, tcon_Num_Onum___Orderings_Opreorder_6, tcon_Extended__Nat_Oenat___Lattices_Olattice_28, fact_157_nat__mult__1, fact_52_inf_Ocommute, fact_12_semiring__norm_I84_J, tcon_HOL_Obool___Orderings_Oorder_15, fact_82_le__infI1, fact_192_semiring__normalization__rules_I18_J, fact_151_one__eq__numeral__iff, fact_137_mult__le__mono1, tcon_Extended__Nat_Oenat___Groups_Ocomm__monoid__mult_20, fact_156_dbl__simps_I3_J, fact_71_inf_OboundedI, fact_152_sub__num__simps_I9_J, fact_180_llist_Oinject, tcon_Nat_Onat___Nat_Osemiring__char__0, fact_174_one__reorient, fact_32_semiring__norm_I73_J, fact_225_dbl__dec__simps_I1_J, fact_224_not__neg__one__le__neg__numeral__iff, fact_90_num_Oexhaust, fact_220_semiring__norm_I170_J, fact_147_dbl__simps_I5_J, tcon_fun___Lattices_Olattice, fact_183_dbl__dec__simps_I5_J, fact_154_sub__num__simps_I8_J, fact_235_numeral__neq__neg__numeral, fact_20_inf__right__idem, fact_10_semiring__norm_I83_J, fact_3_llength__lmap, fact_120_le__cases
% 98.65/27.97 % No. of inferences in proof: 606
% 98.65/27.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27430 ms resp. 26822 ms w/o parsing
% 99.01/28.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 99.01/28.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------