%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT253^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:10 AM UTC 2026
% Result : Theorem 26.89s 8.05s
% Output : Refutation 27.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 290
% Syntax : Number of formulae : 582 ( 193 unt; 0 typ; 0 def)
% Number of atoms : 1283 ( 622 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 6436 ( 46 ~; 10 |; 30 &;5964 @)
% ( 0 <=>; 386 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 106 ( 106 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 61 usr; 9 con; 0-4 aty)
% Number of variables : 1512 ( 76 ^;1418 !; 18 ?;1512 :)
% Comments :
%------------------------------------------------------------------------------
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(one_decl,type,
one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(idom_decl,type,
idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(numeral_decl,type,
numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(uminus_decl,type,
uminus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(top_decl,type,
top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(neg_numeral_decl,type,
neg_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_ring_1_decl,type,
comm_ring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_semiring_decl,type,
comm_semiring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_numeral_decl,type,
semiring_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_mult_decl,type,
semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_field_decl,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semilattice_sup_decl,type,
semilattice_sup:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bounded_lattice_top_decl,type,
bounded_lattice_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(inc_decl,type,
inc: num > num ).
thf(neg_numeral_dbl_decl,type,
neg_numeral_dbl:
!>[TA: $tType] : ( TA > TA ) ).
thf(bit0_decl,type,
bit0: num > num ).
thf(one2_decl,type,
one2: num ).
thf(numeral_numeral_decl,type,
numeral_numeral:
!>[TA: $tType] : ( num > TA ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(type2_decl,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(stream865922174rleave_decl,type,
stream865922174rleave:
!>[TA: $tType] : ( ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) ) ).
thf(stream1586597341member_decl,type,
stream1586597341member:
!>[TA: $tType] : ( TA > ( stream170649215stream @ TA ) > $o ) ).
thf(stream857257621smerge_decl,type,
stream857257621smerge:
!>[TA: $tType] : ( ( stream170649215stream @ ( stream170649215stream @ TA ) ) > ( stream170649215stream @ TA ) ) ).
thf(stream370371455e_snth_decl,type,
stream370371455e_snth:
!>[TA: $tType] : ( ( stream170649215stream @ TA ) > nat > TA ) ).
thf(stream30925839e_sset_decl,type,
stream30925839e_sset:
!>[TA: $tType] : ( ( stream170649215stream @ TA ) > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(n_decl,type,
n: nat ).
thf(s1_decl,type,
s1: stream170649215stream @ a ).
thf(s2_decl,type,
s2: stream170649215stream @ a ).
thf(x_decl,type,
x: a ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_sup__fun__def) ).
thf(365,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(196,axiom,
! [TA: $tType,A: stream170649215stream @ ( stream170649215stream @ TA ),B: nat,C: nat] : ( member @ TA @ ( stream370371455e_snth @ TA @ ( stream370371455e_snth @ ( stream170649215stream @ TA ) @ A @ B ) @ C ) @ ( stream30925839e_sset @ TA @ ( stream857257621smerge @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_snth__sset__smerge) ).
thf(846,plain,
! [TA: $tType,A: stream170649215stream @ ( stream170649215stream @ TA ),B: nat,C: nat] : ( member @ TA @ ( stream370371455e_snth @ TA @ ( stream370371455e_snth @ ( stream170649215stream @ TA ) @ A @ B ) @ C ) @ ( stream30925839e_sset @ TA @ ( stream857257621smerge @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(215,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ ( sup_sup @ TA @ A @ B ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_sup__compl__top__left1) ).
thf(893,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ ( sup_sup @ TA @ A @ B ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(24,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_add__mono__thms__linordered__semiring_I4_J) ).
thf(352,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(267,axiom,
monoid_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult) ).
thf(1031,plain,
monoid_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(17,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_sup_Ocommute) ).
thf(333,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(118,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_uminus__numeral__One) ).
thf(628,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(286,axiom,
( suc
= ( plus_plus @ nat @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Suc__eq__plus1__left) ).
thf(1083,plain,
( suc
= ( plus_plus @ nat @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(241,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_nat__add__left__cancel) ).
thf(962,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(136,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_semiring__normalization__rules_I24_J) ).
thf(683,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(153,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add_Ocommute) ).
thf(730,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(280,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_surjD) ).
thf(1068,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(209,axiom,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_double__complement) ).
thf(878,plain,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(134,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_num_Oinject_I1_J) ).
thf(677,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_linordered__field__class_Osign__simps_I24_J) ).
thf(597,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(103,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__normalization__rules_I23_J) ).
thf(582,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( semilattice_sup @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(762,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( semilattice_sup @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(157,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_one__plus__numeral) ).
thf(741,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(282,axiom,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_10) ).
thf(1073,plain,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(271,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rev__image__eqI) ).
thf(1041,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(202,axiom,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_nat__1__eq__mult__iff) ).
thf(861,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)],[202]) ).
thf(284,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_add__Suc) ).
thf(1078,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(92,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_sup_Oright__idem) ).
thf(550,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(159,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_add__neg__numeral__special_I9_J) ).
thf(747,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(235,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Un__commute) ).
thf(945,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(194,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ComplI) ).
thf(841,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(212,axiom,
ab_semigroup_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(885,plain,
ab_semigroup_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(52,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_linordered__field__class_Osign__simps_I36_J) ).
thf(436,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',fact_218_numeral__neq__neg__numeral) ).
thf(320,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)],[12]) ).
thf(97,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_semiring__normalization__rules_I12_J) ).
thf(565,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)],[97]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_209_mult__neg__numeral__simps_I1_J) ).
thf(389,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)],[36]) ).
thf(151,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_semiring__normalization__rules_I8_J) ).
thf(724,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(76,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_sup_Oidem) ).
thf(504,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(193,axiom,
! [TA: $tType] :
( ( stream1586597341member @ TA )
= ( ^ [A: TA,B: stream170649215stream @ TA] : ( member @ TA @ A @ ( stream30925839e_sset @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Stream__Mirabelle__hbrgyiwlrc_Osmember__def) ).
thf(838,plain,
! [TA: $tType] :
( ( stream1586597341member @ TA )
= ( ^ [A: TA,B: stream170649215stream @ TA] : ( member @ TA @ A @ ( stream30925839e_sset @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(143,axiom,
! [A: num] :
( ( plus_plus @ num @ one2 @ A )
= ( plus_plus @ num @ A @ one2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__One__commute) ).
thf(702,plain,
! [A: num] :
( ( plus_plus @ num @ one2 @ A )
= ( plus_plus @ num @ A @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(230,axiom,
( x
= ( stream370371455e_snth @ a @ s1 @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062x_A_061_As1_A_B_B_An_092_060close_062) ).
thf(934,plain,
( x
= ( stream370371455e_snth @ a @ s1 @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(278,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_ball__imageD) ).
thf(1059,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(184,axiom,
( ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ n ) )
= x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062) ).
thf(817,plain,
( ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ n ) )
= x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_205_semiring__norm_I171_J) ).
thf(559,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)],[95]) ).
thf(199,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
= ( suc @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_add__2__eq__Suc) ).
thf(853,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
= ( suc @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',fact_219_neg__numeral__neq__numeral) ).
thf(421,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)],[47]) ).
thf(210,axiom,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(881,plain,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(14,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_sup__assoc) ).
thf(325,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__left__cancel) ).
thf(448,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(244,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_UNIV__I) ).
thf(969,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(606,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(260,axiom,
member @ a @ x @ ( sup_sup @ ( set @ a ) @ ( stream30925839e_sset @ a @ s1 ) @ ( stream30925839e_sset @ a @ s2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062x_A_092_060in_062_Asset_As1_A_092_060union_062_Asset_As2_092_060close_062) ).
thf(1013,plain,
member @ a @ x @ ( sup_sup @ ( set @ a ) @ ( stream30925839e_sset @ a @ s1 ) @ ( stream30925839e_sset @ a @ s2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_127_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(770,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)],[167]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_207_mult__neg__numeral__simps_I3_J) ).
thf(756,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)],[162]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_nat_Oinject) ).
thf(591,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_add_Oleft__commute) ).
thf(485,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(275,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) @ ( sup_sup @ TA @ A @ C ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_sup__cancel__left2) ).
thf(1051,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) @ ( sup_sup @ TA @ A @ C ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(22,axiom,
semilattice_sup @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_12) ).
thf(348,plain,
semilattice_sup @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(100,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_crossproduct__eq) ).
thf(574,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(251,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ A @ ( plus_plus @ nat @ B @ C ) )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_add__mult__distrib2) ).
thf(981,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ A @ ( plus_plus @ nat @ B @ C ) )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(39,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_semiring__normalization__rules_I1_J) ).
thf(397,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_216_minus__equation__iff) ).
thf(634,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)],[120]) ).
thf(139,axiom,
! [TA: $tType] :
( ( semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ D ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_combine__common__factor) ).
thf(692,plain,
! [TA: $tType] :
( ( semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ D ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(3,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_dbl__def) ).
thf(293,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(77,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_mult__2) ).
thf(507,plain,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(8,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_num_Odistinct_I1_J) ).
thf(307,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
member @ a @ x @ ( image @ nat @ a @ ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) ) @ ( top_top @ ( set @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ a @ x @ ( image @ nat @ a @ ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) ) @ ( top_top @ ( set @ nat ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(292,plain,
~ ( member @ a @ x @ ( image @ nat @ a @ ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) ) @ ( top_top @ ( set @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_mult__2__right) ).
thf(380,plain,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_192_mult__minus1) ).
thf(439,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)],[53]) ).
thf(227,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Compl__iff) ).
thf(925,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(86,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_numeral__plus__one) ).
thf(534,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_122_semiring__normalization__rules_I15_J) ).
thf(714,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)],[147]) ).
thf(277,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_rangeI) ).
thf(1057,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(90,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_one__add__one) ).
thf(546,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_linordered__field__class_Osign__simps_I35_J) ).
thf(793,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_surjI) ).
thf(825,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(6,axiom,
( ( plus_plus @ num @ one2 @ one2 )
= ( bit0 @ one2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_semiring__norm_I2_J) ).
thf(302,plain,
( ( plus_plus @ num @ one2 @ one2 )
= ( bit0 @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_mult__minus__left) ).
thf(349,plain,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',fact_199_dbl__simps_I1_J) ).
thf(392,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)],[37]) ).
thf(48,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_add_Oinverse__inverse) ).
thf(424,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)],[48]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',fact_80_dbl__simps_I5_J) ).
thf(467,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)],[63]) ).
thf(268,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Un__UNIV__left) ).
thf(1032,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(117,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__right__cancel) ).
thf(625,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(130,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_numeral__neq__neg__one) ).
thf(665,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)],[130]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_57_numeral__eq__iff) ).
thf(461,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)],[61]) ).
thf(246,axiom,
semiring_numeral @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Osemiring__numeral) ).
thf(974,plain,
semiring_numeral @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_240_mult__1s_I3_J) ).
thf(522,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)],[82]) ).
thf(189,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_UnI1) ).
thf(830,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_43_semiring__norm_I169_J) ).
thf(519,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)],[81]) ).
thf(11,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_add_Oinverse__distrib__swap) ).
thf(317,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(262,axiom,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_5) ).
thf(1017,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(114,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_sup__commute) ).
thf(615,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(41,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_mult_Ocomm__neutral) ).
thf(403,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)],[41]) ).
thf(291,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_top__conj_I1_J) ).
thf(1096,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(258,axiom,
~ ! [A: nat] :
( x
!= ( stream370371455e_snth @ a @ s1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Ax_A_061_As1_A_B_B_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1006,plain,
~ ! [A: nat] :
( x
!= ( stream370371455e_snth @ a @ s1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(25,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_semiring__norm_I168_J) ).
thf(356,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(206,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ ( suc @ A ) @ B )
= ( times_times @ nat @ ( suc @ A ) @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Suc__mult__cancel1) ).
thf(869,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ ( suc @ A ) @ B )
= ( times_times @ nat @ ( suc @ A ) @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_116_mult_Oleft__commute) ).
thf(650,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)],[125]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_surjE) ).
thf(948,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(15,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_is__num__normalize_I1_J) ).
thf(328,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_image__Un) ).
thf(1028,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_239_mult__1s_I4_J) ).
thf(488,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)],[70]) ).
thf(19,axiom,
! [A: num,B: num] :
( ( times_times @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( bit0 @ ( times_times @ num @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_semiring__norm_I13_J) ).
thf(339,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)],[19]) ).
thf(161,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_inf__sup__aci_I8_J) ).
thf(753,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(87,axiom,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_ring__class_Oring__distribs_I2_J) ).
thf(537,plain,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(121,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_n__not__Suc__n) ).
thf(637,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(218,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_sup__compl__top__left2) ).
thf(901,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(137,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_double__compl) ).
thf(686,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)],[137]) ).
thf(283,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_top__apply) ).
thf(1075,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(66,axiom,
bounded_lattice_top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__top_11) ).
thf(476,plain,
bounded_lattice_top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linordered_field @ 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/sandbox/benchmark/theBenchmark.p',fact_141_linordered__field__class_Osign__simps_I23_J) ).
thf(622,plain,
! [TA: $tType] :
( ( linordered_field @ 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)],[116]) ).
thf(59,axiom,
bounded_lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(457,plain,
bounded_lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',fact_176_neg__equal__iff__equal) ).
thf(721,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)],[150]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(779,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)],[170]) ).
thf(30,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__numeral__left) ).
thf(371,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(124,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_sup__left__idem) ).
thf(647,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(255,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_compl__sup__top) ).
thf(997,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_image__cong) ).
thf(984,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(221,axiom,
member @ a @ x @ ( stream30925839e_sset @ a @ s1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062x_A_092_060in_062_Asset_As1_092_060close_062) ).
thf(911,plain,
member @ a @ x @ ( stream30925839e_sset @ a @ s1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(179,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Compl__partition) ).
thf(805,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(9,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_sup_Oassoc) ).
thf(311,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(276,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add__mult__distrib) ).
thf(1054,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(269,axiom,
! [A: num,B: nat] :
( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ A ) @ B ) )
= ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Suc__nat__number__of__add) ).
thf(1035,plain,
! [A: num,B: nat] :
( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ A ) @ B ) )
= ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(281,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_nat__1__add__1) ).
thf(1071,plain,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_123_semiring__normalization__rules_I16_J) ).
thf(674,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)],[133]) ).
thf(168,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_semiring__normalization__rules_I22_J) ).
thf(773,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(129,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_linordered__field__class_Osign__simps_I28_J) ).
thf(662,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(149,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_sup_Oleft__commute) ).
thf(718,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(44,axiom,
! [A: num,B: num] :
( ( plus_plus @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ num @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_semiring__norm_I6_J) ).
thf(412,plain,
! [A: num,B: num] :
( ( plus_plus @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(115,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_semiring__norm_I83_J) ).
thf(618,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(200,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: nat] : ( member @ TA @ ( stream370371455e_snth @ TA @ A @ B ) @ ( stream30925839e_sset @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_snth__sset) ).
thf(856,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: nat] : ( member @ TA @ ( stream370371455e_snth @ TA @ A @ B ) @ ( stream30925839e_sset @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(154,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(733,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(242,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ball__Un) ).
thf(965,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_217_equation__minus__iff) ).
thf(750,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)],[160]) ).
thf(79,axiom,
! [TA: $tType] :
( ( semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_distrib__right) ).
thf(513,plain,
! [TA: $tType] :
( ( semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(50,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_mult_Oleft__neutral) ).
thf(430,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)],[50]) ).
thf(138,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_inf__sup__aci_I5_J) ).
thf(689,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(4,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_one__neq__neg__numeral) ).
thf(296,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)],[4]) ).
thf(185,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_nat__mult__1__right) ).
thf(819,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_surj__def) ).
thf(843,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_173_dbl__simps_I4_J) ).
thf(579,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)],[102]) ).
thf(238,axiom,
semiri456707255roduct @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(958,plain,
semiri456707255roduct @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(96,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_mult_Oright__neutral) ).
thf(562,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)],[96]) ).
thf(219,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_UnCI) ).
thf(904,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(247,axiom,
semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).
thf(975,plain,
semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(208,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_sup__top__right) ).
thf(875,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(577,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_126_semiring__normalization__rules_I19_J) ).
thf(711,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)],[146]) ).
thf(122,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_inf__sup__aci_I6_J) ).
thf(641,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(173,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_dbl__simps_I3_J) ).
thf(787,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)],[173]) ).
thf(74,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__right__imp__eq) ).
thf(498,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(289,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(1090,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(225,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ C ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_sup__cancel__left1) ).
thf(919,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ C ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(88,axiom,
! [TA: $tType] :
( ( linordered_field @ 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/sandbox/benchmark/theBenchmark.p',fact_139_linordered__field__class_Osign__simps_I25_J) ).
thf(540,plain,
! [TA: $tType] :
( ( linordered_field @ 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)],[88]) ).
thf(55,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_linordered__field__class_Osign__simps_I26_J) ).
thf(445,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(231,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Un__UNIV__right) ).
thf(936,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_sup__apply) ).
thf(406,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(172,axiom,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_one__reorient) ).
thf(784,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)],[172]) ).
thf(259,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_9) ).
thf(1011,plain,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_120_semiring__normalization__rules_I13_J) ).
thf(377,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)],[32]) ).
thf(165,axiom,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_mult__minus__right) ).
thf(764,plain,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(250,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_UNIV__witness) ).
thf(979,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(273,axiom,
lattice @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_4) ).
thf(1048,plain,
lattice @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(155,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A != B )
& ( C != D ) )
= ( ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) )
!= ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_crossproduct__noteq) ).
thf(736,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A != B )
& ( C != D ) )
= ( ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) )
!= ( plus_plus @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(27,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_semiring__normalization__rules_I20_J) ).
thf(362,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(57,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_mult_Ocommute) ).
thf(451,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)],[57]) ).
thf(214,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( suc @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_add__2__eq__Suc_H) ).
thf(890,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( suc @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Suc__inject) ).
thf(477,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(72,axiom,
uminus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_16) ).
thf(494,plain,
uminus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(119,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_add__minus__cancel) ).
thf(631,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(183,axiom,
ordere779506340up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(816,plain,
ordere779506340up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(112,axiom,
! [TA: $tType] :
( ( semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_distrib__left) ).
thf(609,plain,
! [TA: $tType] :
( ( semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(323,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(107,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ B )
= ( times_times @ TA @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_semiring__normalization__rules_I2_J) ).
thf(594,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ B )
= ( times_times @ TA @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(177,axiom,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_semiring__norm_I85_J) ).
thf(799,plain,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(197,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Un__absorb) ).
thf(848,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(131,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_semiring__norm_I87_J) ).
thf(668,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( times_times @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_minus__mult__minus) ).
thf(345,plain,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( times_times @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(201,axiom,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_nat__mult__1) ).
thf(858,plain,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(234,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_6) ).
thf(943,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(264,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_UNIV__eq__I) ).
thf(1022,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(222,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_top1I) ).
thf(912,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(239,axiom,
semigroup_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).
thf(959,plain,
semigroup_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(140,axiom,
top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_15) ).
thf(695,plain,
top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(205,axiom,
comm_semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(868,plain,
comm_semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(256,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_nat__mult__eq__1__iff) ).
thf(1000,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)],[256]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_204_semiring__norm_I172_J) ).
thf(299,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)],[5]) ).
thf(198,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_8) ).
thf(851,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(126,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_comm__monoid__mult__class_Omult__1) ).
thf(653,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)],[126]) ).
thf(226,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_top__set__def) ).
thf(922,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(65,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_add_Oassoc) ).
thf(473,plain,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(85,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_sup__left__commute) ).
thf(531,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(135,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_is__num__normalize_I8_J) ).
thf(680,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(31,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_semiring__normalization__rules_I21_J) ).
thf(374,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(181,axiom,
one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(812,plain,
one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(285,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_imageI) ).
thf(1081,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_44_numeral__times__numeral) ).
thf(516,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)],[80]) ).
thf(232,axiom,
semilattice_sup @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__sup_3) ).
thf(939,plain,
semilattice_sup @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_old_Onat_Oinject) ).
thf(342,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(93,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_numeral__Bit0) ).
thf(553,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(274,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(1049,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(243,axiom,
comm_semiring @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring) ).
thf(968,plain,
comm_semiring @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(60,axiom,
! [TA: $tType] :
( ( idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ A )
= ( times_times @ TA @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_square__eq__iff) ).
thf(458,plain,
! [TA: $tType] :
( ( idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ A )
= ( times_times @ TA @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(169,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add__left__imp__eq) ).
thf(776,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(83,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_one__eq__numeral__iff) ).
thf(525,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)],[83]) ).
thf(257,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_top__conj_I2_J) ).
thf(1003,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(265,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( plus_plus @ nat @ ( times_times @ nat @ C @ B ) @ D ) )
= ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_left__add__mult__distrib) ).
thf(1025,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( plus_plus @ nat @ ( times_times @ nat @ C @ B ) @ D ) )
= ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(207,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_add__Suc__shift) ).
thf(872,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(144,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_minus__add__distrib) ).
thf(705,plain,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(245,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Un__left__commute) ).
thf(971,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(739,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(43,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_one__neq__neg__one) ).
thf(409,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)],[43]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(331,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(148,axiom,
lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_14) ).
thf(717,plain,
lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_186_neg__numeral__eq__iff) ).
thf(359,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)],[26]) ).
thf(270,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_nat__add__right__cancel) ).
thf(1038,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(104,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( plus_plus @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_minus__add__cancel) ).
thf(585,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( plus_plus @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(287,axiom,
! [A: nat,B: nat] :
( ( times_times @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ B @ ( times_times @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mult__Suc) ).
thf(1085,plain,
! [A: nat,B: nat] :
( ( times_times @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ B @ ( times_times @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(64,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_semiring__normalization__rules_I25_J) ).
thf(470,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_bex__imageD) ).
thf(951,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_image__eqI) ).
thf(808,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(158,axiom,
! [A: num] :
( ( times_times @ num @ A @ one2 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_semiring__norm_I11_J) ).
thf(744,plain,
! [A: num] :
( ( times_times @ num @ A @ one2 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(18,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ one2 ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_mult__numeral__1) ).
thf(336,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)],[18]) ).
thf(127,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( times_times @ TA @ A @ A )
= ( one_one @ TA ) )
= ( ( A
= ( one_one @ TA ) )
| ( A
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_square__eq__1__iff) ).
thf(656,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( times_times @ TA @ A @ A )
= ( one_one @ TA ) )
= ( ( A
= ( one_one @ TA ) )
| ( A
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_125_semiring__normalization__rules_I18_J) ).
thf(600,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)],[109]) ).
thf(203,axiom,
! [TA: $tType] :
( ( stream30925839e_sset @ TA )
= ( ^ [A: stream170649215stream @ TA] : ( image @ nat @ TA @ ( stream370371455e_snth @ TA @ A ) @ ( top_top @ ( set @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_sset__range) ).
thf(864,plain,
! [TA: $tType] :
( ( stream30925839e_sset @ TA )
= ( ^ [A: stream170649215stream @ TA] : ( image @ nat @ TA @ ( stream370371455e_snth @ TA @ A ) @ ( top_top @ ( set @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_221_fun__Compl__def) ).
thf(727,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)],[152]) ).
thf(10,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA )
= ( times_times @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_ring__normalization__rules_I1_J) ).
thf(314,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)],[10]) ).
thf(99,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_inf__sup__aci_I7_J) ).
thf(571,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_193_mult__minus1__right) ).
thf(612,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)],[113]) ).
thf(249,axiom,
semiring_char_0 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0) ).
thf(978,plain,
semiring_char_0 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(35,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( uminus_uminus @ TA @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_add__neg__numeral__simps_I3_J) ).
thf(386,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( uminus_uminus @ TA @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(94,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_semiring__normalization__rules_I34_J) ).
thf(556,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(229,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_sup__compl__top) ).
thf(931,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(68,axiom,
! [TA: $tType] :
( ( semiring_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( numeral_numeral @ TA @ one2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_mult__numeral__1__right) ).
thf(482,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)],[68]) ).
thf(132,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add_Oright__cancel) ).
thf(671,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(248,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_UnI2) ).
thf(976,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(73,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_add_Oleft__cancel) ).
thf(495,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(163,axiom,
! [TA: $tType] :
( ( ( numeral @ TA @ ( type2 @ TA ) )
& ( semiring @ TA @ ( type2 @ TA ) ) )
=> ! [A: num,B: TA,C: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ B ) @ ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_distrib__left__numeral) ).
thf(759,plain,
! [TA: $tType] :
( ( ( numeral @ TA @ ( type2 @ TA ) )
& ( semiring @ TA @ ( type2 @ TA ) ) )
=> ! [A: num,B: TA,C: TA] :
( ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ B ) @ ( times_times @ TA @ ( numeral_numeral @ TA @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',fact_118_mult_Oassoc) ).
thf(368,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)],[29]) ).
thf(182,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Un__left__absorb) ).
thf(813,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(216,axiom,
comm_monoid_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(896,plain,
comm_monoid_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',fact_206_semiring__norm_I170_J) ).
thf(304,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)],[7]) ).
thf(46,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_numeral__plus__numeral) ).
thf(418,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(171,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_semiring__normalization__rules_I7_J) ).
thf(781,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)],[171]) ).
thf(254,axiom,
( suc
= ( ^ [A: nat] : ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_Suc__eq__plus1) ).
thf(995,plain,
( suc
= ( ^ [A: nat] : ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(105,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_numeral__One) ).
thf(588,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(142,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_sup_Oleft__idem) ).
thf(699,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(98,axiom,
! [A: num] :
( ( times_times @ num @ one2 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_semiring__norm_I12_J) ).
thf(568,plain,
! [A: num] :
( ( times_times @ num @ one2 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(223,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_range__eqI) ).
thf(914,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(34,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_sup__idem) ).
thf(383,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(190,axiom,
ab_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(832,plain,
ab_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(91,axiom,
boolean_algebra @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_13) ).
thf(549,plain,
boolean_algebra @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(1045,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(51,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ A )
= ( times_times @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_semiring__normalization__rules_I4_J) ).
thf(433,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ A )
= ( times_times @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_121_semiring__normalization__rules_I14_J) ).
thf(510,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)],[78]) ).
thf(191,axiom,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_numerals_I1_J) ).
thf(833,plain,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(192,axiom,
! [A: num] :
( ( suc @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Suc__numeral) ).
thf(835,plain,
! [A: num] :
( ( suc @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',fact_200_numeral__eq__neg__one__iff) ).
thf(790,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)],[174]) ).
thf(204,axiom,
numeral @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral) ).
thf(867,plain,
numeral @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(110,axiom,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_minus__mult__commute) ).
thf(603,plain,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(224,axiom,
semiring @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring) ).
thf(918,plain,
semiring @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(40,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_linordered__field__class_Osign__simps_I27_J) ).
thf(400,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(188,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_UnE) ).
thf(828,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(240,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_iso__tuple__UNIV__I) ).
thf(960,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(279,axiom,
! [A: nat,B: nat] :
( ( times_times @ nat @ A @ ( suc @ B ) )
= ( plus_plus @ nat @ A @ ( times_times @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_mult__Suc__right) ).
thf(1065,plain,
! [A: nat,B: nat] :
( ( times_times @ nat @ A @ ( suc @ B ) )
= ( plus_plus @ nat @ A @ ( times_times @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(141,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ A @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( plus_plus @ TA @ B @ ( one_one @ TA ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_semiring__normalization__rules_I3_J) ).
thf(696,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ A @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( plus_plus @ TA @ B @ ( one_one @ TA ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(176,axiom,
! [TA: $tType] :
( ( comm_semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_comm__semiring__class_Odistrib) ).
thf(796,plain,
! [TA: $tType] :
( ( comm_semiring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(217,axiom,
! [A: nat,B: nat] :
( ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
!= ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_double__not__eq__Suc__double) ).
thf(897,plain,
! [A: nat,B: nat] :
( ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
!= ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(166,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_numeral__eq__one__iff) ).
thf(767,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)],[166]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A ) )
!= ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Suc__double__not__eq__double) ).
thf(886,plain,
! [A: nat,B: nat] :
( ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A ) )
!= ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(228,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_add__Suc__right) ).
thf(928,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(45,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__neg__numeral__special_I6_J) ).
thf(415,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(62,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_one__plus__numeral__commute) ).
thf(464,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(49,axiom,
! [TA: $tType] :
( ( ( numeral @ TA @ ( type2 @ TA ) )
& ( semiring @ TA @ ( type2 @ TA ) ) )
=> ! [A: TA,B: TA,C: num] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ ( numeral_numeral @ TA @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ ( numeral_numeral @ TA @ C ) ) @ ( times_times @ TA @ B @ ( numeral_numeral @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_distrib__right__numeral) ).
thf(427,plain,
! [TA: $tType] :
( ( ( numeral @ TA @ ( type2 @ TA ) )
& ( semiring @ TA @ ( type2 @ TA ) ) )
=> ! [A: TA,B: TA,C: num] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ ( numeral_numeral @ TA @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ ( numeral_numeral @ TA @ C ) ) @ ( times_times @ TA @ B @ ( numeral_numeral @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(263,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_bex__Un) ).
thf(1019,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_ring__class_Oring__distribs_I1_J) ).
thf(528,plain,
! [TA: $tType] :
( ( ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_201_neg__one__eq__numeral__iff) ).
thf(644,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)],[123]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Compl__eq__Compl__iff) ).
thf(822,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_180_uminus__apply) ).
thf(442,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)],[54]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_178_compl__eq__compl__iff) ).
thf(501,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)],[75]) ).
thf(290,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_sup__top__left) ).
thf(1093,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top) ).
thf(395,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(220,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Un__iff) ).
thf(908,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(253,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_top__empty__eq) ).
thf(992,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(178,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_7) ).
thf(803,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(233,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_Compl__partition2) ).
thf(940,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_229_numeral__times__minus__swap) ).
thf(659,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)],[128]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_124_semiring__normalization__rules_I17_J) ).
thf(543,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)],[89]) ).
thf(58,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_semiring__normalization__rules_I11_J) ).
thf(454,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)],[58]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',fact_208_mult__neg__numeral__simps_I2_J) ).
thf(708,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)],[145]) ).
thf(211,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_image__iff) ).
thf(882,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(261,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Un__assoc) ).
thf(1014,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(71,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_add__neg__numeral__special_I5_J) ).
thf(491,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(288,axiom,
( ( suc @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_Suc__1) ).
thf(1088,plain,
( ( suc @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1105,plain,
$false,
inference(e,[status(thm)],[365,846,893,352,1031,333,628,1083,962,683,730,1068,878,677,597,582,762,741,1073,1041,861,1078,550,747,945,841,885,436,320,565,389,724,504,838,702,934,1059,817,559,853,421,881,325,448,969,606,1013,770,756,591,485,1051,348,574,981,397,634,692,293,507,307,292,380,439,925,534,714,1057,546,793,825,302,349,392,424,467,1032,625,665,461,974,522,830,519,317,1017,615,403,1096,1006,356,869,650,948,328,1028,488,339,753,537,637,901,686,1075,476,622,457,721,779,371,647,997,984,911,805,311,1054,1035,1071,674,773,662,718,412,618,856,733,965,750,513,430,689,296,819,843,579,958,562,904,975,875,577,711,641,787,498,1090,919,540,445,936,406,784,1011,377,764,979,1048,736,362,451,890,477,494,631,816,609,323,594,799,848,668,345,858,943,1022,912,959,695,868,1000,299,851,653,922,473,531,680,374,812,1081,516,939,342,553,1049,968,458,776,525,1003,1025,872,705,971,739,409,331,717,359,1038,585,1085,470,951,808,744,336,656,600,864,727,314,571,612,978,386,556,931,482,671,976,495,759,368,813,896,304,418,781,995,588,699,568,914,383,832,549,1045,433,510,833,835,790,867,603,918,400,828,960,1065,696,796,897,767,886,928,415,464,427,1019,528,644,822,442,501,1093,395,908,992,803,940,659,543,454,708,882,1014,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT253^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.22 % Computer : n005.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 18:15:16 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.38/1.22 % [INFO] Parsing done (421ms).
% 2.38/1.24 % [INFO] Running in sequential loop mode.
% 3.51/1.62 % [INFO] eprover registered as external prover.
% 3.51/1.63 % [INFO] Scanning for conjecture ...
% 3.70/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 290 axioms. Running axiom selection ...
% 4.18/1.96 % [INFO] Axiom selection finished. Selected 289 axioms (removed 1 axioms).
% 5.23/2.25 % [INFO] Problem is higher-order (TPTP THF).
% 5.23/2.28 % [INFO] Type checking passed.
% 5.23/2.28 % [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 ...
% 26.89/8.04 % External prover 'e' found a proof!
% 26.89/8.04 % [INFO] Killing All external provers ...
% 26.89/8.04 % Time passed: 7684ms (effective reasoning time: 6797ms)
% 26.89/8.04 % 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)>
% 26.89/8.05 % Axioms used in derivation (289): tcon_HOL_Obool___Lattices_Olattice_14, fact_65_semiring__norm_I12_J, fact_0__092_060open_062x_A_061_As1_A_B_B_An_092_060close_062, fact_130_semiring__normalization__rules_I1_J, fact_17_Un__iff, fact_225_square__eq__iff, fact_140_linordered__field__class_Osign__simps_I24_J, fact_18_UnE, fact_38_imageI, fact_248_ComplI, fact_87_semiring__norm_I2_J, fact_151_one__plus__numeral, fact_224_Suc__mult__cancel1, fact_42_sup__top__left, fact_3__092_060open_062x_A_092_060in_062_Asset_As1_092_060close_062, fact_25_Un__commute, fact_26_Un__left__absorb, fact_227_add__Suc, fact_215_add_Oinverse__distrib__swap, fact_154_nat__mult__eq__1__iff, fact_211_Suc__1, fact_191_add__neg__numeral__simps_I3_J, fact_11_surjI, fact_136_linordered__field__class_Osign__simps_I28_J, fact_83_Stream__Mirabelle__hbrgyiwlrc_Osmember__def, fact_93_left__add__mult__distrib, fact_163_semiring__normalization__rules_I11_J, fact_137_linordered__field__class_Osign__simps_I27_J, fact_53_sup__apply, fact_122_semiring__normalization__rules_I15_J, fact_204_semiring__norm_I172_J, fact_147_comm__semiring__class_Odistrib, fact_66_sup__left__commute, fact_194_compl__sup__top, fact_31_Un__UNIV__left, fact_243_Suc__double__not__eq__double, fact_118_mult_Oassoc, fact_74_inf__sup__aci_I6_J, fact_148_linordered__field__class_Osign__simps_I35_J, fact_97_add__left__cancel, fact_179_double__compl, fact_29_top__set__def, fact_103_add_Oleft__commute, fact_187_mult__minus__left, fact_102_add__left__imp__eq, fact_233_square__eq__1__iff, fact_34_ball__imageD, fact_141_linordered__field__class_Osign__simps_I23_J, fact_84_mult__2__right, fact_36_bex__imageD, fact_221_fun__Compl__def, fact_123_semiring__normalization__rules_I16_J, fact_246_Compl__eq__Compl__iff, fact_117_mult_Ocommute, fact_216_minus__equation__iff, fact_49_semiring__norm_I85_J, fact_175_add__2__eq__Suc_H, tcon_Set_Oset___Groups_Ouminus_10, tcon_Set_Oset___Lattices_Oboolean__algebra_7, fact_62_top1I, fact_231_one__neq__neg__numeral, fact_196_sup__compl__top__left1, fact_198_mult__Suc__right, fact_71_sup_Oassoc, tcon_Nat_Onat___Groups_Ocomm__monoid__mult, fact_64_semiring__norm_I11_J, fact_245_add__neg__numeral__special_I6_J, fact_203_Suc__numeral, fact_110_semiring__normalization__rules_I22_J, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_197_sup__compl__top__left2, fact_143_nat__add__left__cancel, fact_164_semiring__normalization__rules_I12_J, fact_9_surjD, fact_186_neg__numeral__eq__iff, tcon_Nat_Onat___Num_Osemiring__numeral, tcon_Nat_Onat___Groups_Oone, fact_89_numeral__plus__numeral, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, fact_189_mult__minus__right, tcon_Set_Oset___Orderings_Otop_9, fact_44_numeral__times__numeral, fact_228_add__Suc__shift, fact_230_numeral__neq__neg__one, fact_133_ring__class_Oring__distribs_I2_J, fact_58_sup_Oright__idem, fact_98_add__right__cancel, fact_200_numeral__eq__neg__one__iff, fact_72_sup__fun__def, fact_180_uminus__apply, fact_120_semiring__normalization__rules_I13_J, fact_212_Suc__eq__plus1, tcon_Nat_Onat___Groups_Oab__semigroup__mult, fact_46_Collect__mem__eq, fact_184_minus__add__cancel, fact_116_mult_Oleft__commute, fact_206_semiring__norm_I170_J, fact_111_semiring__normalization__rules_I23_J, fact_8_image__eqI, fact_104_add_Ocommute, fact_166_one__plus__numeral__commute, fact_201_neg__one__eq__numeral__iff, tcon_Nat_Onat___Lattices_Olattice_4, fact_128_semiring__normalization__rules_I34_J, fact_242_Suc__nat__number__of__add, tcon_HOL_Obool___Orderings_Otop_15, fact_159_nat__mult__1__right, fact_127_ab__semigroup__mult__class_Omult__ac_I1_J, fact_61_sup__idem, fact_213_Suc__eq__plus1__left, tcon_HOL_Obool___Lattices_Osemilattice__sup_12, tcon_fun___Lattices_Obounded__lattice_2, fact_209_mult__neg__numeral__simps_I1_J, tcon_Set_Oset___Lattices_Obounded__lattice__top_5, fact_90_dbl__def, fact_161_mult_Ocomm__neutral, tcon_fun___Lattices_Osemilattice__sup, fact_142_nat__add__right__cancel, fact_222_n__not__Suc__n, fact_176_neg__equal__iff__equal, fact_41_sup__top__right, fact_22_ball__Un, tcon_HOL_Obool___Groups_Ouminus_16, fact_168_semiring__normalization__rules_I3_J, fact_145_distrib__right, fact_183_add__minus__cancel, fact_132_add__mult__distrib2, fact_170_numeral__One, fact_156_mult_Oleft__neutral, fact_126_semiring__normalization__rules_I19_J, fact_14_range__eqI, tcon_Set_Oset___Lattices_Olattice_8, fact_249_add__neg__numeral__special_I5_J, fact_68_sup__commute, fact_13_surj__def, fact_205_semiring__norm_I171_J, fact_202_semiring__norm_I168_J, fact_23_Un__assoc, fact_15_sset__range, fact_234_sup__cancel__left1, fact_218_numeral__neq__neg__numeral, fact_165_one__reorient, fact_45_mem__Collect__eq, fact_101_add__right__imp__eq, fact_199_dbl__simps_I1_J, fact_4__092_060open_062x_A_092_060in_062_Asset_As1_A_092_060union_062_Asset_As2_092_060close_062, fact_59_sup__left__idem, tcon_Nat_Onat___Groups_Omonoid__mult, fact_107_add_Oassoc, fact_81_top__conj_I2_J, fact_99_crossproduct__noteq, fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062, fact_7_top__apply, fact_96_distrib__right__numeral, tcon_Nat_Onat___Rings_Ocomm__semiring, tcon_HOL_Obool___Lattices_Oboolean__algebra_13, fact_94_numeral__Bit0, fact_174_add__neg__numeral__special_I9_J, fact_169_semiring__normalization__rules_I4_J, fact_172_nat__1__add__1, fact_149_dbl__simps_I3_J, fact_241_uminus__numeral__One, fact_54_sup_Oidem, fact_250_double__complement, fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Ax_A_061_As1_A_B_B_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_119_semiring__normalization__rules_I7_J, fact_238_mult__Suc, fact_76_inf__sup__aci_I8_J, fact_135_linordered__field__class_Osign__simps_I36_J, tcon_Nat_Onat___Rings_Osemiring, fact_47_Collect__cong, tcon_fun___Lattices_Obounded__lattice__top, fact_181_old_Onat_Oinject, tcon_Set_Oset___Lattices_Obounded__lattice_1, fact_6_iso__tuple__UNIV__I, fact_27_Un__left__commute, fact_70_sup__assoc, fact_35_image__cong, tcon_fun___Orderings_Otop, tcon_fun___Lattices_Oboolean__algebra, fact_85_mult__2, fact_20_UnI2, fact_16_UnCI, fact_220_is__num__normalize_I8_J, fact_240_mult__1s_I3_J, fact_12_rangeI, fact_226_minus__mult__commute, tcon_Nat_Onat___Num_Onumeral, fact_40_UNIV__eq__I, fact_146_distrib__left, fact_51_mult__numeral__1, fact_33_rev__image__eqI, fact_88_add__numeral__left, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_108_semiring__normalization__rules_I20_J, tcon_HOL_Obool___Lattices_Obounded__lattice__top_11, fact_30_Un__UNIV__right, fact_171_numerals_I1_J, fact_138_linordered__field__class_Osign__simps_I26_J, fact_192_mult__minus1, fact_160_nat__mult__1, fact_235_sup__cancel__left2, fact_56_num_Oinject_I1_J, fact_114_add__mono__thms__linordered__semiring_I4_J, fact_80_dbl__simps_I5_J, fact_77_num_Odistinct_I1_J, fact_124_semiring__normalization__rules_I17_J, fact_139_linordered__field__class_Osign__simps_I25_J, fact_207_mult__neg__numeral__simps_I3_J, fact_162_comm__monoid__mult__class_Omult__1, fact_112_semiring__normalization__rules_I24_J, fact_131_add__mult__distrib, fact_236_Compl__partition, fact_150_numeral__plus__one, tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_21_bex__Un, fact_52_mult__numeral__1__right, fact_55_semiring__norm_I87_J, fact_39_UNIV__witness, fact_244_double__not__eq__Suc__double, fact_188_minus__mult__minus, tcon_Set_Oset___Lattices_Osemilattice__sup_6, fact_223_Suc__inject, fact_237_Compl__partition2, fact_78_top__empty__eq, fact_239_mult__1s_I4_J, fact_79_snth__sset__smerge, fact_144_combine__common__factor, fact_217_equation__minus__iff, fact_91_is__num__normalize_I1_J, fact_105_add_Oright__cancel, fact_5_UNIV__I, fact_60_sup_Oleft__idem, fact_134_ring__class_Oring__distribs_I1_J, fact_63_semiring__norm_I13_J, fact_28_image__Un, fact_177_add_Oinverse__inverse, fact_155_mult_Oright__neutral, tcon_Nat_Onat___Groups_Osemigroup__add, fact_75_inf__sup__aci_I7_J, fact_92_add__One__commute, fact_95_distrib__left__numeral, fact_115_ab__semigroup__add__class_Oadd__ac_I1_J, fact_57_numeral__eq__iff, fact_214_one__neq__neg__one, fact_86_semiring__norm_I6_J, tcon_Nat_Onat___Groups_Osemigroup__mult, fact_50_semiring__norm_I83_J, fact_109_semiring__normalization__rules_I21_J, fact_195_sup__compl__top, fact_67_sup_Oleft__commute, fact_208_mult__neg__numeral__simps_I2_J, fact_24_Un__absorb, fact_232_ring__normalization__rules_I1_J, fact_182_nat_Oinject, fact_19_UnI1, fact_121_semiring__normalization__rules_I14_J, tcon_fun___Groups_Ouminus, fact_153_nat__1__eq__mult__iff, tcon_HOL_Obool___Lattices_Obounded__lattice, fact_69_sup_Ocommute, fact_193_mult__minus1__right, fact_173_dbl__simps_I4_J, fact_43_semiring__norm_I169_J, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_113_semiring__normalization__rules_I25_J, fact_157_one__eq__numeral__iff, fact_210_add__2__eq__Suc, fact_106_add_Oleft__cancel, fact_32_snth__sset, fact_178_compl__eq__compl__iff, fact_158_numeral__eq__one__iff, fact_247_Compl__iff, fact_152_one__add__one, fact_229_numeral__times__minus__swap, fact_167_semiring__normalization__rules_I2_J, fact_73_inf__sup__aci_I5_J, tcon_Nat_Onat___Nat_Osemiring__char__0, fact_190_add__Suc__right, tcon_Nat_Onat___Lattices_Osemilattice__sup_3, fact_185_minus__add__distrib, fact_100_crossproduct__eq, fact_125_semiring__normalization__rules_I18_J, tcon_fun___Lattices_Olattice, fact_82_top__conj_I1_J, fact_129_semiring__normalization__rules_I8_J, fact_10_surjE, fact_37_image__iff, fact_219_neg__numeral__neq__numeral
% 26.89/8.05 % No. of inferences in proof: 582
% 26.89/8.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7684 ms resp. 6797 ms w/o parsing
% 27.70/8.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.70/8.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------